diff --git a/Cargo.toml b/Cargo.toml
index 453a7be..df28fc3 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -17,6 +17,7 @@ opt-level = "z"
 
 [workspace.dependencies]
 ark-bls12-381 = "0.4.0"
+ark-bn254 = "0.4.0"
 ark-ec = "0.4.2"
 ark-ff = "0.4.2"
 ark-std = "0.4.0"
diff --git a/[Tho09]poseidon-hash/Cargo.toml b/[Tho09]poseidon-hash/Cargo.toml
index 29080ff..dfe7b2a 100644
--- a/[Tho09]poseidon-hash/Cargo.toml
+++ b/[Tho09]poseidon-hash/Cargo.toml
@@ -5,3 +5,5 @@ version = "0.1.0"
 
 [dependencies]
 ark-ff = { workspace = true }
+ark-bn254 = { workspace = true }
+ark-std = { workspace = true }
diff --git a/[Tho09]poseidon-hash/README.md b/[Tho09]poseidon-hash/README.md
index e69de29..2d4a01e 100644
--- a/[Tho09]poseidon-hash/README.md
+++ b/[Tho09]poseidon-hash/README.md
@@ -0,0 +1,49 @@
+# Poseidon Hasher
+Poseidon Hasher is a mapping over strings of $F_p$ (for prime $p > 2^{31}$) such that it maps $F_p^* \to F_p^o$ where $o$ is the number of output elements (often chosen value is $o = 1$).
+
+Poseidon is said to be a variant of *HadesMiMC* construction however with a fixed and known key.
+
+## A primer on sponge construction
+Sponge construction looks as follows:
+![sponge_construction](sponge_construction.png)
+In this, the $I$ is maintained state that changes over time, $m_x$ are injected values to be hashed and $h_y$ are the output elements.
+
+General construction looks as follows:
+- Depending on the use case, determine the capacity element value and the input padding if needed.
+- Split the obtained input into chunks of size $r$.
+- Apply the permutation to the capacity element and the first chunk.
+- Until no more chunks are left, add them into the state and apply the permutation.
+- Output $o$ output elements out of the rate part of the state.
+If needed, iterate the permutation more times.
+
+## The HADES design strategy
+The HADES design strategy consists of:
+- First, $R_f$ rounds in the beginning, in which S-boxes
+are applied to the full state. 
+- Next, $R_p$ rounds in the middle contain single S-box application. Rest of the state goes through this phase unchanged
+- Finally, $R_f$ rounds in the end, in which S-boxes
+are applied to the full state. 
+
+![hades_construction](hades_construction.png)
+
+Each such round consists of the following three sub-steps:
+1. $ARC$: Add round constants
+2. $SBOX$: Application of S-Boxes
+3. $MIX$: Mix layers
+
+## Reference implementation for magic values
+Directory `reference/hadeshash` includes `generate_params_poseidong.sage` for generating values used inside poseidon hasher. We build values for BLS12-381's $F_q$ a.k.a Scalar Field. For this, use:
+
+```bash
+# For generating for BLS12-381 Fq;
+# Modulus = `52435875175126190479447740508185965837690552500527637822603658699938581184513`
+# In Hex that is `0x73EDA753299D7D483339D80809A1D80553BDA402FFFE5BFEFFFFFFFF00000001`
+# So, the following command should work:
+sage generate_params_poseidon.sage 1 0 255 3 3 128 0x73EDA753299D7D483339D80809A1D80553BDA402FFFE5BFEFFFFFFFF00000001
+```
+This generates `poseidon_params_n255_t3_alpha3_M128.txt` file. Using values in this file, we generate values ingested in the rust code.
+
+
+## References
+- https://eprint.iacr.org/2019/458.pdf
+- https://github.com/arnaucube/poseidon-ark/
diff --git a/[Tho09]poseidon-hash/hades_construction.png b/[Tho09]poseidon-hash/hades_construction.png
new file mode 100644
index 0000000..2ad9b52
Binary files /dev/null and b/[Tho09]poseidon-hash/hades_construction.png differ
diff --git a/[Tho09]poseidon-hash/reference/hadeshash/LICENSE b/[Tho09]poseidon-hash/reference/hadeshash/LICENSE
new file mode 100644
index 0000000..1522178
--- /dev/null
+++ b/[Tho09]poseidon-hash/reference/hadeshash/LICENSE
@@ -0,0 +1,19 @@
+Copyright (c) 2019 Graz University of Technology
+
+Permission is hereby granted, free of charge, to any person obtaining a copy of
+this software and associated documentation files (the ""Software""), to deal in
+the Software without restriction, including without limitation the rights to
+use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies
+of the Software, and to permit persons to whom the Software is furnished to do
+so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED *AS IS*, WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.
\ No newline at end of file
diff --git a/[Tho09]poseidon-hash/reference/hadeshash/README.md b/[Tho09]poseidon-hash/reference/hadeshash/README.md
new file mode 100644
index 0000000..880b457
--- /dev/null
+++ b/[Tho09]poseidon-hash/reference/hadeshash/README.md
@@ -0,0 +1,12 @@
+# Scripts and Reference Implementations of Poseidon and Starkad
+This repository contains the source code of reference implementations for various versions of Poseidon [1]. The source code is available in Sage. Moreover, scripts to calculate the round numbers, the round constants, and the MDS matrices are also included.
+
+### Update from 02/05/2023
+The script `generate_params_poseidon.sage` should be used to compute the round numbers and to generate the round constants and matrices. The scripts `calc_round_numbers.py` and `generate_parameters_grain.sage` are deprecated and should not be used anymore.
+
+### Update from 07/03/2021
+We fixed several bugs in the implementation. First, the linear layer was computed as `state = state * M` instead of `state = M * state`, and secondly the final matrix multiplication was missing. The test vectors were also changed accordingly.
+
+<br>
+
+[1] *Poseidon: A New Hash Function for Zero-Knowledge Proof Systems*. Cryptology ePrint Archive, Report 2019/458. [https://eprint.iacr.org/2019/458](https://eprint.iacr.org/2019/458). Accepted at USENIX'21.
diff --git a/[Tho09]poseidon-hash/reference/hadeshash/code/calc_round_numbers.py b/[Tho09]poseidon-hash/reference/hadeshash/code/calc_round_numbers.py
new file mode 100644
index 0000000..f7b7881
--- /dev/null
+++ b/[Tho09]poseidon-hash/reference/hadeshash/code/calc_round_numbers.py
@@ -0,0 +1,145 @@
+from math import *
+import sys
+import Crypto.Util.number
+
+def sat_inequiv_alpha(p, t, R_F, R_P, alpha, M):
+    n = ceil(log(p, 2))
+    N = int(n * t)
+    if alpha > 0:
+        R_F_1 = 6 if M <= ((floor(log(p, 2) - ((alpha-1)/2.0))) * (t + 1)) else 10 # Statistical
+        R_F_2 = 1 + ceil(log(2, alpha) * min(M, n)) + ceil(log(t, alpha)) - R_P # Interpolation
+        #R_F_3 = ceil(min(n, M) / float(3*log(alpha, 2))) - R_P # Groebner 1
+        #R_F_3 = ((log(2, alpha) / float(2)) * min(n, M)) - R_P # Groebner 1
+        R_F_3 = 1 + (log(2, alpha) * min(M/float(3), log(p, 2)/float(2))) - R_P # Groebner 1
+        R_F_4 = t - 1 + min((log(2, alpha) * M) / float(t+1), ((log(2, alpha)*log(p, 2)) / float(2))) - R_P # Groebner 2
+        #R_F_5 = ((1.0/(2*log((alpha**alpha)/float((alpha-1)**(alpha-1)), 2))) * min(n, M) + t - 2 - R_P) / float(t - 1) # Groebner 3
+        R_F_max = max(ceil(R_F_1), ceil(R_F_2), ceil(R_F_3), ceil(R_F_4))
+        return (R_F >= R_F_max)
+    elif alpha == (-1):
+        R_F_1 = 6 if M <= ((floor(log(p, 2) - 2)) * (t + 1)) else 10 # Statistical
+        R_P_1 = 1 + ceil(0.5 * min(M, n)) + ceil(log(t, 2)) - floor(R_F * log(t, 2)) # Interpolation
+        R_P_2 = 1 + ceil(0.5 * min(M, n)) + ceil(log(t, 2)) - floor(R_F * log(t, 2))
+        R_P_3 = t - 1 + ceil(log(t, 2)) + min(ceil(M / float(t+1)), ceil(0.5*log(p, 2))) - floor(R_F * log(t, 2)) # Groebner 2
+        R_F_max = ceil(R_F_1)
+        R_P_max = max(ceil(R_P_1), ceil(R_P_2), ceil(R_P_3))
+        return (R_F >= R_F_max and R_P >= R_P_max)
+    else:
+        print("Invalid value for alpha!")
+        exit(1)
+
+def get_sbox_cost(R_F, R_P, N, t):
+    return int(t * R_F + R_P)
+
+def get_size_cost(R_F, R_P, N, t):
+    n = ceil(float(N) / t)
+    return int((N * R_F) + (n * R_P))
+
+def get_depth_cost(R_F, R_P, N, t):
+    return int(R_F + R_P)
+
+def find_FD_round_numbers(p, t, alpha, M, cost_function, security_margin):
+    n = ceil(log(p, 2))
+    N = int(n * t)
+
+    sat_inequiv = sat_inequiv_alpha
+    
+    R_P = 0
+    R_F = 0
+    min_cost = float("inf")
+    max_cost_rf = 0
+    # Brute-force approach
+    for R_P_t in range(1, 500):
+        for R_F_t in range(4, 100):
+            if R_F_t % 2 == 0:
+                if (sat_inequiv(p, t, R_F_t, R_P_t, alpha, M) == True):
+                    if security_margin == True:
+                        R_F_t += 2
+                        R_P_t = int(ceil(float(R_P_t) * 1.075))
+                    cost = cost_function(R_F_t, R_P_t, N, t)
+                    if (cost < min_cost) or ((cost == min_cost) and (R_F_t < max_cost_rf)):
+                        R_P = ceil(R_P_t)
+                        R_F = ceil(R_F_t)
+                        min_cost = cost
+                        max_cost_rf = R_F
+    return (int(R_F), int(R_P))
+
+def calc_final_numbers_fixed(p, t, alpha, M, security_margin):
+    # [Min. S-boxes] Find best possible for t and N
+    n = ceil(log(p, 2))
+    N = int(n * t)
+    cost_function = get_sbox_cost
+    ret_list = []
+    (R_F, R_P) = find_FD_round_numbers(p, t, alpha, M, cost_function, security_margin)
+    min_sbox_cost = cost_function(R_F, R_P, N, t)
+    ret_list.append(R_F)
+    ret_list.append(R_P)
+    ret_list.append(min_sbox_cost)
+
+    # [Min. Size] Find best possible for t and N
+    # Minimum number of S-boxes for fixed n results in minimum size also (round numbers are the same)!
+    min_size_cost = get_size_cost(R_F, R_P, N, t)
+    ret_list.append(min_size_cost)
+
+    return ret_list # [R_F, R_P, min_sbox_cost, min_size_cost]
+
+def print_latex_table_combinations(combinations, alpha, security_margin):
+    for comb in combinations:
+        N = comb[0]
+        t = comb[1]
+        M = comb[2]
+        n = int(N / t)
+        prime = Crypto.Util.number.getPrime(n)
+        ret = calc_final_numbers_fixed(prime, t, alpha, M, security_margin)
+        field_string = "\mathbb F_{p}"
+        sbox_string = "x^{" + str(alpha) + "}"
+        print("$" + str(M) + "$ & $" + str(N) + "$ & $" + str(n) + "$ & $" + str(t) + "$ & $" + str(ret[0]) + "$ & $" + str(ret[1]) + "$ & $" + field_string + "$ & $" + str(ret[2]) + "$ & $" + str(ret[3]) + "$ \\\\")
+
+# Single tests
+# print calc_final_numbers_fixed(Crypto.Util.number.getPrime(64), 24, 3, 128, True)
+# print calc_final_numbers_fixed(Crypto.Util.number.getPrime(253), 6, -1, 128, True)
+print(calc_final_numbers_fixed(Crypto.Util.number.getPrime(255), 3, 5, 128, True))
+print(calc_final_numbers_fixed(Crypto.Util.number.getPrime(255), 6, 5, 128, True))
+print(calc_final_numbers_fixed(Crypto.Util.number.getPrime(254), 3, 5, 128, True))
+print(calc_final_numbers_fixed(Crypto.Util.number.getPrime(254), 6, 5, 128, True))
+print(calc_final_numbers_fixed(Crypto.Util.number.getPrime(64), 24, 3, 128, True))
+
+# x^5 (254-bit prime number)
+#prime = 0x30644e72e131a029b85045b68181585d2833e84879b9709143e1f593f0000001
+x_5_combinations = [
+    [1536, 2, 128], [1536, 4, 128], [1536, 6, 128], [1536, 8, 128], [1536, 16, 128],
+    [1536, 2, 256], [1536, 4, 256], [1536, 6, 256], [1536, 8, 256], [1536, 16, 256]
+]
+
+# With security margin
+print("--- Table x^5 WITH security margin ---")
+print_latex_table_combinations(x_5_combinations, 5, True)
+
+# Without security margin
+print("--- Table x^5 WITHOUT security margin ---")
+print_latex_table_combinations(x_5_combinations, 5, False)
+
+x_3_combinations = [
+    [1536, 2, 128], [1536, 4, 128], [1536, 6, 128], [1536, 8, 128], [1536, 16, 128],
+    [1536, 2, 256], [1536, 4, 256], [1536, 6, 256], [1536, 8, 256], [1536, 16, 256]
+]
+
+# With security margin
+print("--- Table x^3 WITH security margin ---")
+print_latex_table_combinations(x_3_combinations, 3, True)
+
+# Without security margin
+print("--- Table x^3 WITHOUT security margin ---")
+print_latex_table_combinations(x_3_combinations, 3, False)
+
+x_inv_combinations = [
+    [1536, 2, 128], [1536, 4, 128], [1536, 6, 128], [1536, 8, 128], [1536, 16, 128],
+    [1536, 2, 256], [1536, 4, 256], [1536, 6, 256], [1536, 8, 256], [1536, 16, 256]
+]
+
+# With security margin
+print("--- Table x^(-1) WITH security margin ---")
+print_latex_table_combinations(x_inv_combinations, -1, True)
+
+# Without security margin
+print("--- Table x^(-1) WITHOUT security margin ---")
+print_latex_table_combinations(x_inv_combinations, -1, False)
diff --git a/[Tho09]poseidon-hash/reference/hadeshash/code/generate_parameters_grain.sage b/[Tho09]poseidon-hash/reference/hadeshash/code/generate_parameters_grain.sage
new file mode 100644
index 0000000..27d72f6
--- /dev/null
+++ b/[Tho09]poseidon-hash/reference/hadeshash/code/generate_parameters_grain.sage
@@ -0,0 +1,373 @@
+# Remark: This script contains functionality for GF(2^n), but currently works only over GF(p)! A few small adaptations are needed for GF(2^n).
+from sage.rings.polynomial.polynomial_gf2x import GF2X_BuildIrred_list
+
+# Note that R_P is increased to the closest multiple of t
+# GF(p), alpha=3, N = 1536, n = 64, t = 24, R_F = 8, R_P = 42: sage generate_parameters_grain.sage 1 0 64 24 8 42 0xfffffffffffffeff
+# GF(p), alpha=5, N = 1524, n = 254, t = 6, R_F = 8, R_P = 60: sage generate_parameters_grain.sage 1 0 254 6 8 60 0x30644e72e131a029b85045b68181585d2833e84879b9709143e1f593f0000001
+# GF(p), x^(-1), N = 1518, n = 253, t = 6, R_F = 8, R_P = 60: sage generate_parameters_grain.sage 1 1 253 6 8 60 0x1000000000000000000000000000000014def9dea2f79cd65812631a5cf5d3ed
+
+# GF(p), alpha=5, N = 765, n = 255, t = 3, R_F = 8, R_P = 57: sage generate_parameters_grain.sage 1 0 255 3 8 57 0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001
+# GF(p), alpha=5, N = 1275, n = 255, t = 5, R_F = 8, R_P = 60: sage generate_parameters_grain.sage 1 0 255 5 8 60 0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001
+# GF(p), alpha=5, N = 762, n = 254, t = 3, R_F = 8, R_P = 57: sage generate_parameters_grain.sage 1 0 254 3 8 57 0x30644e72e131a029b85045b68181585d2833e84879b9709143e1f593f0000001
+# GF(p), alpha=5, N = 1270, n = 254, t = 5, R_F = 8, R_P = 60: sage generate_parameters_grain.sage 1 0 254 5 8 60 0x30644e72e131a029b85045b68181585d2833e84879b9709143e1f593f0000001
+
+# GF(2^n), alpha=5, N = 768, n = 256, t = 3, R_F = 8, R_P = 57: sage generate_parameters_grain.sage 0 0 256 3 8 57 0x0
+
+if len(sys.argv) < 7:
+    print("Usage: <script> <field> <s_box> <field_size> <num_cells> <R_F> <R_P> (<prime_number_hex>)")
+    print("field = 1 for GF(p)")
+    print("s_box = 0 for x^alpha, s_box = 1 for x^(-1)")
+    exit()
+
+# Parameters
+FIELD = int(sys.argv[1]) # 0 .. GF(2^n), 1 .. GF(p)
+SBOX = int(sys.argv[2]) # 0 .. x^alpha, 1 .. x^(-1)
+FIELD_SIZE = int(sys.argv[3]) # n
+NUM_CELLS = int(sys.argv[4]) # t
+R_F_FIXED = int(sys.argv[5])
+R_P_FIXED = int(sys.argv[6])
+
+INIT_SEQUENCE = []
+
+PRIME_NUMBER = 0
+if FIELD == 1 and len(sys.argv) != 8:
+    print("Please specify a prime number (in hex format)!")
+    exit()
+elif FIELD == 1 and len(sys.argv) == 8:
+    PRIME_NUMBER = int(sys.argv[7], 16) # e.g. 0xa7, 0xFFFFFFFFFFFFFEFF, 0xa1a42c3efd6dbfe08daa6041b36322ef
+elif FIELD == 0:
+    PRIME_NUMBER = GF(2)['x'](GF2X_BuildIrred_list(FIELD_SIZE))
+
+F = None
+if FIELD == 1:
+    F = GF(PRIME_NUMBER)
+elif FIELD == 0:
+    F.<x> = GF(2**FIELD_SIZE, name='x', modulus = PRIME_NUMBER)
+
+def grain_sr_generator():
+    bit_sequence = INIT_SEQUENCE
+    for _ in range(0, 160):
+        new_bit = bit_sequence[62] ^^ bit_sequence[51] ^^ bit_sequence[38] ^^ bit_sequence[23] ^^ bit_sequence[13] ^^ bit_sequence[0]
+        bit_sequence.pop(0)
+        bit_sequence.append(new_bit)
+        
+    while True:
+        new_bit = bit_sequence[62] ^^ bit_sequence[51] ^^ bit_sequence[38] ^^ bit_sequence[23] ^^ bit_sequence[13] ^^ bit_sequence[0]
+        bit_sequence.pop(0)
+        bit_sequence.append(new_bit)
+        while new_bit == 0:
+            new_bit = bit_sequence[62] ^^ bit_sequence[51] ^^ bit_sequence[38] ^^ bit_sequence[23] ^^ bit_sequence[13] ^^ bit_sequence[0]
+            bit_sequence.pop(0)
+            bit_sequence.append(new_bit)
+            new_bit = bit_sequence[62] ^^ bit_sequence[51] ^^ bit_sequence[38] ^^ bit_sequence[23] ^^ bit_sequence[13] ^^ bit_sequence[0]
+            bit_sequence.pop(0)
+            bit_sequence.append(new_bit)
+        new_bit = bit_sequence[62] ^^ bit_sequence[51] ^^ bit_sequence[38] ^^ bit_sequence[23] ^^ bit_sequence[13] ^^ bit_sequence[0]
+        bit_sequence.pop(0)
+        bit_sequence.append(new_bit)
+        yield new_bit
+grain_gen = grain_sr_generator()
+        
+def grain_random_bits(num_bits):
+    random_bits = [next(grain_gen) for i in range(0, num_bits)]
+    # random_bits.reverse() ## Remove comment to start from least significant bit
+    random_int = int("".join(str(i) for i in random_bits), 2)
+    return random_int
+
+def init_generator(field, sbox, n, t, R_F, R_P):
+    # Generate initial sequence based on parameters
+    bit_list_field = [_ for _ in (bin(FIELD)[2:].zfill(2))]
+    bit_list_sbox = [_ for _ in (bin(SBOX)[2:].zfill(4))]
+    bit_list_n = [_ for _ in (bin(FIELD_SIZE)[2:].zfill(12))]
+    bit_list_t = [_ for _ in (bin(NUM_CELLS)[2:].zfill(12))]
+    bit_list_R_F = [_ for _ in (bin(R_F)[2:].zfill(10))]
+    bit_list_R_P = [_ for _ in (bin(R_P)[2:].zfill(10))]
+    bit_list_1 = [1] * 30
+    global INIT_SEQUENCE
+    INIT_SEQUENCE = bit_list_field + bit_list_sbox + bit_list_n + bit_list_t + bit_list_R_F + bit_list_R_P + bit_list_1
+    INIT_SEQUENCE = [int(_) for _ in INIT_SEQUENCE]
+
+def generate_constants(field, n, t, R_F, R_P, prime_number):
+    round_constants = []
+    num_constants = (R_F + R_P) * t
+
+    if field == 0:
+        for i in range(0, num_constants):
+            random_int = grain_random_bits(n)
+            round_constants.append(random_int)
+    elif field == 1:
+        for i in range(0, num_constants):
+            random_int = grain_random_bits(n)
+            while random_int >= prime_number:
+                # print("[Info] Round constant is not in prime field! Taking next one.")
+                random_int = grain_random_bits(n)
+            round_constants.append(random_int)
+    return round_constants
+
+def print_round_constants(round_constants, n, field):
+    print("Number of round constants:", len(round_constants))
+
+    if field == 0:
+        print("Round constants for GF(2^n):")
+    elif field == 1:
+        print("Round constants for GF(p):")
+    hex_length = int(ceil(float(n) / 4)) + 2 # +2 for "0x"
+    print(["{0:#0{1}x}".format(entry, hex_length) for entry in round_constants])
+
+def create_mds_p(n, t):
+    M = matrix(F, t, t)
+
+    # Sample random distinct indices and assign to xs and ys
+    while True:
+        flag = True
+        rand_list = [F(grain_random_bits(n)) for _ in range(0, 2*t)]
+        while len(rand_list) != len(set(rand_list)): # Check for duplicates
+            rand_list = [F(grain_random_bits(n)) for _ in range(0, 2*t)]
+        xs = rand_list[:t]
+        ys = rand_list[t:]
+        # xs = [F(ele) for ele in range(0, t)]
+        # ys = [F(ele) for ele in range(t, 2*t)]
+        for i in range(0, t):
+            for j in range(0, t):
+                if (flag == False) or ((xs[i] + ys[j]) == 0):
+                    flag = False
+                else:
+                    entry = (xs[i] + ys[j])^(-1)
+                    M[i, j] = entry
+        if flag == False:
+            continue
+        return M
+
+def create_mds_gf2n(n, t):
+    M = matrix(F, t, t)
+
+    # Sample random distinct indices and assign to xs and ys
+    while True:
+        flag = True
+        rand_list = [F.fetch_int(grain_random_bits(n)) for _ in range(0, 2*t)]
+        while len(rand_list) != len(set(rand_list)): # Check for duplicates
+            rand_list = [F.fetch_int(grain_random_bits(n)) for _ in range(0, 2*t)]
+        xs = rand_list[:t]
+        ys = rand_list[t:]
+        for i in range(0, t):
+            for j in range(0, t):
+                if (flag == False) or ((xs[i] + ys[j]) == 0):
+                    flag = False
+                else:
+                    entry = (xs[i] + ys[j])^(-1)
+                    M[i, j] = entry
+        if flag == False:
+            continue
+        return M
+
+def generate_vectorspace(round_num, M, M_round, NUM_CELLS):
+    t = NUM_CELLS
+    s = 1
+    V = VectorSpace(F, t)
+    if round_num == 0:
+        return V
+    elif round_num == 1:
+        return V.subspace(V.basis()[s:])
+    else:
+        mat_temp = matrix(F)
+        for i in range(0, round_num-1):
+            add_rows = []
+            for j in range(0, s):
+                add_rows.append(M_round[i].rows()[j][s:])
+            mat_temp = matrix(mat_temp.rows() + add_rows)
+        r_k = mat_temp.right_kernel()
+        extended_basis_vectors = []
+        for vec in r_k.basis():
+            extended_basis_vectors.append(vector([0]*s + list(vec)))
+        S = V.subspace(extended_basis_vectors)
+
+        return S
+
+def subspace_times_matrix(subspace, M, NUM_CELLS):
+    t = NUM_CELLS
+    V = VectorSpace(F, t)
+    subspace_basis = subspace.basis()
+    new_basis = []
+    for vec in subspace_basis:
+        new_basis.append(M * vec)
+    new_subspace = V.subspace(new_basis)
+    return new_subspace
+
+# Returns True if the matrix is considered secure, False otherwise
+def algorithm_1(M, NUM_CELLS):
+    t = NUM_CELLS
+    s = 1
+    r = floor((t - s) / float(s))
+
+    # Generate round matrices
+    M_round = []
+    for j in range(0, t+1):
+        M_round.append(M^(j+1))
+
+    for i in range(1, r+1):
+        mat_test = M^i
+        entry = mat_test[0, 0]
+        mat_target = matrix.circulant(vector([entry] + ([F(0)] * (t-1))))
+
+        if (mat_test - mat_target) == matrix.circulant(vector([F(0)] * (t))):
+            return [False, 1]
+
+        S = generate_vectorspace(i, M, M_round, t)
+        V = VectorSpace(F, t)
+
+        basis_vectors= []
+        for eigenspace in mat_test.eigenspaces_right(format='galois'):
+            if (eigenspace[0] not in F):
+                continue
+            vector_subspace = eigenspace[1]
+            intersection = S.intersection(vector_subspace)
+            basis_vectors += intersection.basis()
+        IS = V.subspace(basis_vectors)
+
+        if IS.dimension() >= 1 and IS != V:
+            return [False, 2]
+        for j in range(1, i+1):
+            S_mat_mul = subspace_times_matrix(S, M^j, t)
+            if S == S_mat_mul:
+                print("S.basis():\n", S.basis())
+                return [False, 3]
+
+    return [True, 0]
+
+# Returns True if the matrix is considered secure, False otherwise
+def algorithm_2(M, NUM_CELLS):
+    t = NUM_CELLS
+    s = 1
+
+    V = VectorSpace(F, t)
+    trail = [None, None]
+    test_next = False
+    I = range(0, s)
+    I_powerset = list(sage.misc.misc.powerset(I))[1:]
+    for I_s in I_powerset:
+        test_next = False
+        new_basis = []
+        for l in I_s:
+            new_basis.append(V.basis()[l])
+        IS = V.subspace(new_basis)
+        for i in range(s, t):
+            new_basis.append(V.basis()[i])
+        full_iota_space = V.subspace(new_basis)
+        for l in I_s:
+            v = V.basis()[l]
+            while True:
+                delta = IS.dimension()
+                v = M * v
+                IS = V.subspace(IS.basis() + [v])
+                if IS.dimension() == t or IS.intersection(full_iota_space) != IS:
+                    test_next = True
+                    break
+                if IS.dimension() <= delta:
+                    break
+            if test_next == True:
+                break
+        if test_next == True:
+            continue
+        return [False, [IS, I_s]]
+
+    return [True, None]
+
+# Returns True if the matrix is considered secure, False otherwise
+def algorithm_3(M, NUM_CELLS):
+    t = NUM_CELLS
+    s = 1
+
+    V = VectorSpace(F, t)
+
+    l = 4*t
+    for r in range(2, l+1):
+        next_r = False
+        res_alg_2 = algorithm_2(M^r, t)
+        if res_alg_2[0] == False:
+            return [False, None]
+
+        # if res_alg_2[1] == None:
+        #     continue
+        # IS = res_alg_2[1][0]
+        # I_s = res_alg_2[1][1]
+        # for j in range(1, r):
+        #     IS = subspace_times_matrix(IS, M, t)
+        #     I_j = []
+        #     for i in range(0, s):
+        #         new_basis = []
+        #         for k in range(0, t):
+        #             if k != i:
+        #                 new_basis.append(V.basis()[k])
+        #         iota_space = V.subspace(new_basis)
+        #         if IS.intersection(iota_space) != iota_space:
+        #             single_iota_space = V.subspace([V.basis()[i]])
+        #             if IS.intersection(single_iota_space) == single_iota_space:
+        #                 I_j.append(i)
+        #             else:
+        #                 next_r = True
+        #                 break
+        #     if next_r == True:
+        #         break
+        # if next_r == True:
+        #     continue
+        # return [False, [IS, I_j, r]]
+    
+    return [True, None]
+
+def generate_matrix(FIELD, FIELD_SIZE, NUM_CELLS):
+    if FIELD == 0:
+        mds_matrix = create_mds_gf2n(FIELD_SIZE, NUM_CELLS)
+        result_1 = algorithm_1(mds_matrix, NUM_CELLS)
+        result_2 = algorithm_2(mds_matrix, NUM_CELLS)
+        result_3 = algorithm_3(mds_matrix, NUM_CELLS)
+        while result_1[0] == False or result_2[0] == False or result_3[0] == False:
+            mds_matrix = create_mds_p(FIELD_SIZE, NUM_CELLS)
+            result_1 = algorithm_1(mds_matrix, NUM_CELLS)
+            result_2 = algorithm_2(mds_matrix, NUM_CELLS)
+            result_3 = algorithm_3(mds_matrix, NUM_CELLS)
+        return mds_matrix
+    elif FIELD == 1:
+        mds_matrix = create_mds_p(FIELD_SIZE, NUM_CELLS)
+        result_1 = algorithm_1(mds_matrix, NUM_CELLS)
+        result_2 = algorithm_2(mds_matrix, NUM_CELLS)
+        result_3 = algorithm_3(mds_matrix, NUM_CELLS)
+        while result_1[0] == False or result_2[0] == False or result_3[0] == False:
+            mds_matrix = create_mds_p(FIELD_SIZE, NUM_CELLS)
+            result_1 = algorithm_1(mds_matrix, NUM_CELLS)
+            result_2 = algorithm_2(mds_matrix, NUM_CELLS)
+            result_3 = algorithm_3(mds_matrix, NUM_CELLS)
+        return mds_matrix
+
+def print_linear_layer(M, n, t):
+    print("n:", n)
+    print("t:", t)
+    print("N:", (n * t))
+    print("Result Algorithm 1:\n", algorithm_1(M, NUM_CELLS))
+    print("Result Algorithm 2:\n", algorithm_2(M, NUM_CELLS))
+    print("Result Algorithm 3:\n", algorithm_3(M, NUM_CELLS))
+    hex_length = int(ceil(float(n) / 4)) + 2 # +2 for "0x"
+    if FIELD == 0:
+        print("Irred:", PRIME_NUMBER)
+    elif FIELD == 1:
+        print("Prime number:", "0x" + hex(PRIME_NUMBER))
+    matrix_string = "["
+    for i in range(0, t):
+        if FIELD == 0:
+            matrix_string += str(["{0:#0{1}x}".format(entry.integer_representation(), hex_length) for entry in M[i]])
+        elif FIELD == 1:
+            matrix_string += str(["{0:#0{1}x}".format(int(entry), hex_length) for entry in M[i]])
+        if i < (t-1):
+            matrix_string += ","
+    matrix_string += "]"
+    print("MDS matrix:\n", matrix_string)
+
+# Init
+init_generator(FIELD, SBOX, FIELD_SIZE, NUM_CELLS, R_F_FIXED, R_P_FIXED)
+
+# Round constants
+round_constants = generate_constants(FIELD, FIELD_SIZE, NUM_CELLS, R_F_FIXED, R_P_FIXED, PRIME_NUMBER)
+print_round_constants(round_constants, FIELD_SIZE, FIELD)
+
+# Matrix
+linear_layer = generate_matrix(FIELD, FIELD_SIZE, NUM_CELLS)
+print_linear_layer(linear_layer, FIELD_SIZE, NUM_CELLS)
diff --git a/[Tho09]poseidon-hash/reference/hadeshash/code/generate_params_poseidon.sage b/[Tho09]poseidon-hash/reference/hadeshash/code/generate_params_poseidon.sage
new file mode 100644
index 0000000..ec4f1a1
--- /dev/null
+++ b/[Tho09]poseidon-hash/reference/hadeshash/code/generate_params_poseidon.sage
@@ -0,0 +1,521 @@
+from math import *
+import sys
+from sage.rings.polynomial.polynomial_gf2x import GF2X_BuildIrred_list
+
+if len(sys.argv) < 8:
+    print("Usage: <script> <field> <s_box> <field_size> <num_cells> <alpha> <security_level> <modulus_hex>")
+    print("field = 1 for GF(p)")
+    print("s_box = 0 for x^alpha, s_box = 1 for x^(-1)")
+    exit()
+
+# GF(p), n = 255, t = 3, alpha=5: sage generate_params_poseidon.sage 1 0 255 3 5 128 0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001
+# GF(p), n = 255, t = 5, alpha=5: sage generate_params_poseidon.sage 1 0 255 5 5 128 0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001
+# GF(p), n = 254, t = 3, alpha=5: sage generate_params_poseidon.sage 1 0 254 3 5 128 0x30644e72e131a029b85045b68181585d2833e84879b9709143e1f593f0000001
+# GF(p), n = 254, t = 5, alpha=5: sage generate_params_poseidon.sage 1 0 254 5 5 128 0x30644e72e131a029b85045b68181585d2833e84879b9709143e1f593f0000001
+# GF(p), n = 64, t = 24, alpha=3: sage generate_params_poseidon.sage 1 0 64 24 3 128 0xffffffffffffffc5
+
+# p = 2^251 + 17 * 2^192 + 1 = 0x800000000000011000000000000000000000000000000000000000000000001
+# sage generate_params_poseidon.sage 1 0 252 3 3 128 0x800000000000011000000000000000000000000000000000000000000000001
+# sage generate_params_poseidon.sage 1 0 252 4 3 128 0x800000000000011000000000000000000000000000000000000000000000001
+# sage generate_params_poseidon.sage 1 0 252 8 3 128 0x800000000000011000000000000000000000000000000000000000000000001
+# sage generate_params_poseidon.sage 1 0 252 16 3 128 0x800000000000011000000000000000000000000000000000000000000000001
+
+# For generating for BLS12-381 Fq;
+# Modulus = `52435875175126190479447740508185965837690552500527637822603658699938581184513`
+# In Hex that is `0x73EDA753299D7D483339D80809A1D80553BDA402FFFE5BFEFFFFFFFF00000001`
+# So, the following command should work:
+# sage generate_params_poseidon.sage 1 0 255 3 3 128 0x73EDA753299D7D483339D80809A1D80553BDA402FFFE5BFEFFFFFFFF00000001
+write_file = True
+
+# Parameters
+FIELD = int(sys.argv[1]) # 0 .. GF(2^n), 1 .. GF(p)
+SBOX = int(sys.argv[2]) # 0 .. x^alpha, 1 .. x^(-1)
+FIELD_SIZE = int(sys.argv[3]) # n
+NUM_CELLS = int(sys.argv[4]) # t
+ALPHA = int(sys.argv[5])
+SECURITY_LEVEL = int(sys.argv[6])
+R_F_FIXED = 0
+R_P_FIXED = 0
+
+INIT_SEQUENCE = []
+
+PRIME_NUMBER = 0
+F = None
+if FIELD == 0:
+    #PRIME_NUMBER = GF(2)['x'](GF2X_BuildIrred_list(FIELD_SIZE))
+    PRIME_NUMBER = int(sys.argv[7], 16)
+    F.<x> = GF(2**FIELD_SIZE, name='x', modulus = PRIME_NUMBER)
+elif FIELD == 1:
+    PRIME_NUMBER = int(sys.argv[7], 16)
+    F = GF(PRIME_NUMBER)
+else:
+    print("Unknown field type, only 0 and 1 supported!")
+    exit()
+
+def sat_inequiv_alpha(p, t, R_F, R_P, alpha, M):
+    N = int(FIELD_SIZE * NUM_CELLS)
+
+    if alpha > 0:
+        R_F_1 = 6 if M <= ((floor(log(p, 2) - ((alpha-1)/2.0))) * (t + 1)) else 10 # Statistical
+        R_F_2 = 1 + ceil(log(2, alpha) * min(M, FIELD_SIZE)) + ceil(log(t, alpha)) - R_P # Interpolation
+        R_F_3 = (log(2, alpha) * min(M, log(p, 2))) - R_P # Groebner 1
+        R_F_4 = t - 1 + log(2, alpha) * min(M / float(t + 1), log(p, 2) / float(2)) - R_P # Groebner 2
+        R_F_5 = (t - 2 + (M / float(2 * log(alpha, 2))) - R_P) / float(t - 1) # Groebner 3
+        R_F_max = max(ceil(R_F_1), ceil(R_F_2), ceil(R_F_3), ceil(R_F_4), ceil(R_F_5))
+        
+        # Addition due to https://eprint.iacr.org/2023/537.pdf
+        r_temp = floor(t / 3.0)
+        over = (R_F - 1) * t + R_P + r_temp + r_temp * (R_F / 2.0) + R_P + alpha
+        under = r_temp * (R_F / 2.0) + R_P + alpha
+        binom_log = log(binomial(over, under), 2)
+        if binom_log == inf:
+            binom_log = M + 1
+        cost_gb4 = ceil(2 * binom_log) # Paper uses 2.3727, we are more conservative here
+
+        return ((R_F >= R_F_max) and (cost_gb4 >= M))
+    else:
+        print("Invalid value for alpha!")
+        exit(1)
+
+def get_sbox_cost(R_F, R_P, N, t):
+    return int(t * R_F + R_P)
+
+def get_size_cost(R_F, R_P, N, t):
+    n = ceil(float(N) / t)
+    return int((N * R_F) + (n * R_P))
+
+def get_depth_cost(R_F, R_P, N, t):
+    return int(R_F + R_P)
+
+def find_FD_round_numbers(p, t, alpha, M, cost_function, security_margin):
+    N = int(FIELD_SIZE * NUM_CELLS)
+
+    sat_inequiv = sat_inequiv_alpha
+    
+    R_P = 0
+    R_F = 0
+    min_cost = float("inf")
+    max_cost_rf = 0
+    # Brute-force approach
+    for R_P_t in range(1, 500):
+        for R_F_t in range(4, 100):
+            if R_F_t % 2 == 0:
+                if (sat_inequiv(p, t, R_F_t, R_P_t, alpha, M) == True):
+                    if security_margin == True:
+                        R_F_t += 2
+                        R_P_t = int(ceil(float(R_P_t) * 1.075))
+                    cost = cost_function(R_F_t, R_P_t, N, t)
+                    if (cost < min_cost) or ((cost == min_cost) and (R_F_t < max_cost_rf)):
+                        R_P = ceil(R_P_t)
+                        R_F = ceil(R_F_t)
+                        min_cost = cost
+                        max_cost_rf = R_F
+    return (int(R_F), int(R_P))
+
+def calc_final_numbers_fixed(p, t, alpha, M, security_margin):
+    # [Min. S-boxes] Find best possible for t and N
+    N = int(FIELD_SIZE * NUM_CELLS)
+    cost_function = get_sbox_cost
+    ret_list = []
+    (R_F, R_P) = find_FD_round_numbers(p, t, alpha, M, cost_function, security_margin)
+    min_sbox_cost = cost_function(R_F, R_P, N, t)
+    ret_list.append(R_F)
+    ret_list.append(R_P)
+    ret_list.append(min_sbox_cost)
+
+    # [Min. Size] Find best possible for t and N
+    # Minimum number of S-boxes for fixed n results in minimum size also (round numbers are the same)!
+    min_size_cost = get_size_cost(R_F, R_P, N, t)
+    ret_list.append(min_size_cost)
+
+    return ret_list # [R_F, R_P, min_sbox_cost, min_size_cost]
+
+def print_latex_table_combinations(combinations, alpha, security_margin):
+    for comb in combinations:
+        N = comb[0]
+        t = comb[1]
+        M = comb[2]
+        n = int(N / t)
+        prime = PRIME_NUMBER
+        ret = calc_final_numbers_fixed(prime, t, alpha, M, security_margin)
+        field_string = "\mathbb F_{p}"
+        sbox_string = "x^{" + str(alpha) + "}"
+        print("$" + str(M) + "$ & $" + str(N) + "$ & $" + str(n) + "$ & $" + str(t) + "$ & $" + str(ret[0]) + "$ & $" + str(ret[1]) + "$ & $" + field_string + "$ & $" + str(ret[2]) + "$ & $" + str(ret[3]) + "$ \\\\")
+
+###
+### Get round number first
+###
+ROUND_NUMBERS = calc_final_numbers_fixed(PRIME_NUMBER, NUM_CELLS, ALPHA, SECURITY_LEVEL, True)
+R_F_FIXED = ROUND_NUMBERS[0]
+R_P_FIXED = ROUND_NUMBERS[1]
+# R_F_FIXED = 8
+# R_P_FIXED = 60
+
+print("Params: n=%d, t=%d, alpha=%d, M=%d, R_F=%d, R_P=%d"%(FIELD_SIZE, NUM_CELLS, ALPHA, SECURITY_LEVEL, R_F_FIXED, R_P_FIXED))
+print("Modulus = %d"%(PRIME_NUMBER))
+print("Number of S-boxes:", ROUND_NUMBERS[2])
+# print("Number of S-boxes per state element:", ceil(ROUND_NUMBERS[2] / float(NUM_CELLS)))
+
+FILE = None
+if write_file == True:
+    FILE = open("poseidon_params_n%d_t%d_alpha%d_M%d.txt"%(FIELD_SIZE, NUM_CELLS, ALPHA, SECURITY_LEVEL),'w')
+    FILE.write("Params: n=%d, t=%d, alpha=%d, M=%d, R_F=%d, R_P=%d\n"%(FIELD_SIZE, NUM_CELLS, ALPHA, SECURITY_LEVEL, R_F_FIXED, R_P_FIXED))
+    FILE.write("Modulus = %d\n"%(PRIME_NUMBER))
+    FILE.write("Number of S-boxes: %d\n"%(ROUND_NUMBERS[2]))
+    # FILE.write("Number of S-boxes per state element: %d\n"%(ceil(ROUND_NUMBERS[2] / float(NUM_CELLS))))
+
+###
+### Matrices and round constants
+###
+def grain_sr_generator():
+    bit_sequence = INIT_SEQUENCE
+    for _ in range(0, 160):
+        new_bit = bit_sequence[62] ^^ bit_sequence[51] ^^ bit_sequence[38] ^^ bit_sequence[23] ^^ bit_sequence[13] ^^ bit_sequence[0]
+        bit_sequence.pop(0)
+        bit_sequence.append(new_bit)
+        
+    while True:
+        new_bit = bit_sequence[62] ^^ bit_sequence[51] ^^ bit_sequence[38] ^^ bit_sequence[23] ^^ bit_sequence[13] ^^ bit_sequence[0]
+        bit_sequence.pop(0)
+        bit_sequence.append(new_bit)
+        while new_bit == 0:
+            new_bit = bit_sequence[62] ^^ bit_sequence[51] ^^ bit_sequence[38] ^^ bit_sequence[23] ^^ bit_sequence[13] ^^ bit_sequence[0]
+            bit_sequence.pop(0)
+            bit_sequence.append(new_bit)
+            new_bit = bit_sequence[62] ^^ bit_sequence[51] ^^ bit_sequence[38] ^^ bit_sequence[23] ^^ bit_sequence[13] ^^ bit_sequence[0]
+            bit_sequence.pop(0)
+            bit_sequence.append(new_bit)
+        new_bit = bit_sequence[62] ^^ bit_sequence[51] ^^ bit_sequence[38] ^^ bit_sequence[23] ^^ bit_sequence[13] ^^ bit_sequence[0]
+        bit_sequence.pop(0)
+        bit_sequence.append(new_bit)
+        yield new_bit
+grain_gen = grain_sr_generator()
+        
+def grain_random_bits(num_bits):
+    random_bits = [next(grain_gen) for i in range(0, num_bits)]
+    # random_bits.reverse() ## Remove comment to start from least significant bit
+    random_int = int("".join(str(i) for i in random_bits), 2)
+    return random_int
+
+def init_generator(field, sbox, n, t, R_F, R_P):
+    # Generate initial sequence based on parameters
+    bit_list_field = [_ for _ in (bin(FIELD)[2:].zfill(2))]
+    bit_list_sbox = [_ for _ in (bin(SBOX)[2:].zfill(4))]
+    bit_list_n = [_ for _ in (bin(FIELD_SIZE)[2:].zfill(12))]
+    bit_list_t = [_ for _ in (bin(NUM_CELLS)[2:].zfill(12))]
+    bit_list_R_F = [_ for _ in (bin(R_F)[2:].zfill(10))]
+    bit_list_R_P = [_ for _ in (bin(R_P)[2:].zfill(10))]
+    bit_list_1 = [1] * 30
+    global INIT_SEQUENCE
+    INIT_SEQUENCE = bit_list_field + bit_list_sbox + bit_list_n + bit_list_t + bit_list_R_F + bit_list_R_P + bit_list_1
+    INIT_SEQUENCE = [int(_) for _ in INIT_SEQUENCE]
+
+def generate_constants(field, n, t, R_F, R_P, prime_number):
+    round_constants = []
+    num_constants = (R_F + R_P) * t
+
+    if field == 0:
+        for i in range(0, num_constants):
+            random_int = grain_random_bits(n)
+            round_constants.append(random_int)
+    elif field == 1:
+        for i in range(0, num_constants):
+            random_int = grain_random_bits(n)
+            while random_int >= prime_number:
+                # print("[Info] Round constant is not in prime field! Taking next one.")
+                random_int = grain_random_bits(n)
+            round_constants.append(random_int)
+    return round_constants
+
+def print_round_constants(round_constants, n, field):
+    print("Number of round constants:", len(round_constants))
+    if write_file == True:
+        FILE.write("Number of round constants: " + str(len(round_constants)) + "\n")
+
+    if field == 0:
+        print("Round constants for GF(2^n):")
+        if write_file == True:
+            FILE.write("Round constants for GF(2^n):\n")
+    elif field == 1:
+        print("Round constants for GF(p):")
+        if write_file == True:
+            FILE.write("Round constants for GF(p):\n")
+    hex_length = int(ceil(float(n) / 4)) + 2 # +2 for "0x"
+    print(["{0:#0{1}x}".format(entry, hex_length) for entry in round_constants])
+    if write_file == True:
+        FILE.write(str(["{0:#0{1}x}".format(entry, hex_length) for entry in round_constants]) + "\n")
+
+def create_mds_p(n, t):
+    M = matrix(F, t, t)
+
+    # Sample random distinct indices and assign to xs and ys
+    while True:
+        flag = True
+        rand_list = [F(grain_random_bits(n)) for _ in range(0, 2*t)]
+        while len(rand_list) != len(set(rand_list)): # Check for duplicates
+            rand_list = [F(grain_random_bits(n)) for _ in range(0, 2*t)]
+        xs = rand_list[:t]
+        ys = rand_list[t:]
+        # xs = [F(ele) for ele in range(0, t)]
+        # ys = [F(ele) for ele in range(t, 2*t)]
+        for i in range(0, t):
+            for j in range(0, t):
+                if (flag == False) or ((xs[i] + ys[j]) == 0):
+                    flag = False
+                else:
+                    entry = (xs[i] + ys[j])^(-1)
+                    M[i, j] = entry
+        if flag == False:
+            continue
+        return M
+
+def create_mds_gf2n(n, t):
+    M = matrix(F, t, t)
+
+    # Sample random distinct indices and assign to xs and ys
+    while True:
+        flag = True
+        rand_list = [F.fetch_int(grain_random_bits(n)) for _ in range(0, 2*t)]
+        while len(rand_list) != len(set(rand_list)): # Check for duplicates
+            rand_list = [F.fetch_int(grain_random_bits(n)) for _ in range(0, 2*t)]
+        xs = rand_list[:t]
+        ys = rand_list[t:]
+        for i in range(0, t):
+            for j in range(0, t):
+                if (flag == False) or ((xs[i] + ys[j]) == 0):
+                    flag = False
+                else:
+                    entry = (xs[i] + ys[j])^(-1)
+                    M[i, j] = entry
+        if flag == False:
+            continue
+        return M
+
+def generate_vectorspace(round_num, M, M_round, NUM_CELLS):
+    t = NUM_CELLS
+    s = 1
+    V = VectorSpace(F, t)
+    if round_num == 0:
+        return V
+    elif round_num == 1:
+        return V.subspace(V.basis()[s:])
+    else:
+        mat_temp = matrix(F)
+        for i in range(0, round_num-1):
+            add_rows = []
+            for j in range(0, s):
+                add_rows.append(M_round[i].rows()[j][s:])
+            mat_temp = matrix(mat_temp.rows() + add_rows)
+        r_k = mat_temp.right_kernel()
+        extended_basis_vectors = []
+        for vec in r_k.basis():
+            extended_basis_vectors.append(vector([0]*s + list(vec)))
+        S = V.subspace(extended_basis_vectors)
+
+        return S
+
+def subspace_times_matrix(subspace, M, NUM_CELLS):
+    t = NUM_CELLS
+    V = VectorSpace(F, t)
+    subspace_basis = subspace.basis()
+    new_basis = []
+    for vec in subspace_basis:
+        new_basis.append(M * vec)
+    new_subspace = V.subspace(new_basis)
+    return new_subspace
+
+# Returns True if the matrix is considered secure, False otherwise
+def algorithm_1(M, NUM_CELLS):
+    t = NUM_CELLS
+    s = 1
+    r = floor((t - s) / float(s))
+
+    # Generate round matrices
+    M_round = []
+    for j in range(0, t+1):
+        M_round.append(M^(j+1))
+
+    for i in range(1, r+1):
+        mat_test = M^i
+        entry = mat_test[0, 0]
+        mat_target = matrix.circulant(vector([entry] + ([F(0)] * (t-1))))
+
+        if (mat_test - mat_target) == matrix.circulant(vector([F(0)] * (t))):
+            return [False, 1]
+
+        S = generate_vectorspace(i, M, M_round, t)
+        V = VectorSpace(F, t)
+
+        basis_vectors= []
+        for eigenspace in mat_test.eigenspaces_right(format='galois'):
+            if (eigenspace[0] not in F):
+                continue
+            vector_subspace = eigenspace[1]
+            intersection = S.intersection(vector_subspace)
+            basis_vectors += intersection.basis()
+        IS = V.subspace(basis_vectors)
+
+        if IS.dimension() >= 1 and IS != V:
+            return [False, 2]
+        for j in range(1, i+1):
+            S_mat_mul = subspace_times_matrix(S, M^j, t)
+            if S == S_mat_mul:
+                print("S.basis():\n", S.basis())
+                return [False, 3]
+
+    return [True, 0]
+
+# Returns True if the matrix is considered secure, False otherwise
+def algorithm_2(M, NUM_CELLS):
+    t = NUM_CELLS
+    s = 1
+
+    V = VectorSpace(F, t)
+    trail = [None, None]
+    test_next = False
+    I = range(0, s)
+    I_powerset = list(sage.misc.misc.powerset(I))[1:]
+    for I_s in I_powerset:
+        test_next = False
+        new_basis = []
+        for l in I_s:
+            new_basis.append(V.basis()[l])
+        IS = V.subspace(new_basis)
+        for i in range(s, t):
+            new_basis.append(V.basis()[i])
+        full_iota_space = V.subspace(new_basis)
+        for l in I_s:
+            v = V.basis()[l]
+            while True:
+                delta = IS.dimension()
+                v = M * v
+                IS = V.subspace(IS.basis() + [v])
+                if IS.dimension() == t or IS.intersection(full_iota_space) != IS:
+                    test_next = True
+                    break
+                if IS.dimension() <= delta:
+                    break
+            if test_next == True:
+                break
+        if test_next == True:
+            continue
+        return [False, [IS, I_s]]
+
+    return [True, None]
+
+# Returns True if the matrix is considered secure, False otherwise
+def algorithm_3(M, NUM_CELLS):
+    t = NUM_CELLS
+    s = 1
+
+    V = VectorSpace(F, t)
+
+    l = 4*t
+    for r in range(2, l+1):
+        next_r = False
+        res_alg_2 = algorithm_2(M^r, t)
+        if res_alg_2[0] == False:
+            return [False, None]
+
+        # if res_alg_2[1] == None:
+        #     continue
+        # IS = res_alg_2[1][0]
+        # I_s = res_alg_2[1][1]
+        # for j in range(1, r):
+        #     IS = subspace_times_matrix(IS, M, t)
+        #     I_j = []
+        #     for i in range(0, s):
+        #         new_basis = []
+        #         for k in range(0, t):
+        #             if k != i:
+        #                 new_basis.append(V.basis()[k])
+        #         iota_space = V.subspace(new_basis)
+        #         if IS.intersection(iota_space) != iota_space:
+        #             single_iota_space = V.subspace([V.basis()[i]])
+        #             if IS.intersection(single_iota_space) == single_iota_space:
+        #                 I_j.append(i)
+        #             else:
+        #                 next_r = True
+        #                 break
+        #     if next_r == True:
+        #         break
+        # if next_r == True:
+        #     continue
+        # return [False, [IS, I_j, r]]
+    
+    return [True, None]
+
+def generate_matrix(FIELD, FIELD_SIZE, NUM_CELLS):
+    if FIELD == 0:
+        mds_matrix = create_mds_gf2n(FIELD_SIZE, NUM_CELLS)
+        result_1 = algorithm_1(mds_matrix, NUM_CELLS)
+        result_2 = algorithm_2(mds_matrix, NUM_CELLS)
+        result_3 = algorithm_3(mds_matrix, NUM_CELLS)
+        while result_1[0] == False or result_2[0] == False or result_3[0] == False:
+            mds_matrix = create_mds_p(FIELD_SIZE, NUM_CELLS)
+            result_1 = algorithm_1(mds_matrix, NUM_CELLS)
+            result_2 = algorithm_2(mds_matrix, NUM_CELLS)
+            result_3 = algorithm_3(mds_matrix, NUM_CELLS)
+        return mds_matrix
+    elif FIELD == 1:
+        mds_matrix = create_mds_p(FIELD_SIZE, NUM_CELLS)
+        result_1 = algorithm_1(mds_matrix, NUM_CELLS)
+        result_2 = algorithm_2(mds_matrix, NUM_CELLS)
+        result_3 = algorithm_3(mds_matrix, NUM_CELLS)
+        while result_1[0] == False or result_2[0] == False or result_3[0] == False:
+            mds_matrix = create_mds_p(FIELD_SIZE, NUM_CELLS)
+            result_1 = algorithm_1(mds_matrix, NUM_CELLS)
+            result_2 = algorithm_2(mds_matrix, NUM_CELLS)
+            result_3 = algorithm_3(mds_matrix, NUM_CELLS)
+        return mds_matrix
+
+def print_linear_layer(M, n, t):
+    print("n:", n)
+    print("t:", t)
+    print("N:", (n * t))
+    print("Result Algorithm 1:\n", algorithm_1(M, NUM_CELLS))
+    print("Result Algorithm 2:\n", algorithm_2(M, NUM_CELLS))
+    print("Result Algorithm 3:\n", algorithm_3(M, NUM_CELLS))
+    if write_file == True:
+        FILE.write("n: " + str(n) + "\n")
+        FILE.write("t: " + str(t) + "\n")
+        FILE.write("N: " + str(n * t) + "\n")
+        FILE.write("Result Algorithm 1:\n" + str(algorithm_1(M, NUM_CELLS)) + "\n")
+        FILE.write("Result Algorithm 2:\n" + str(algorithm_2(M, NUM_CELLS)) + "\n")
+        FILE.write("Result Algorithm 3:\n" + str(algorithm_3(M, NUM_CELLS)) + "\n")
+        
+    hex_length = int(ceil(float(n) / 4)) + 2 # +2 for "0x"
+    if FIELD == 0:
+        print("Modulus:", PRIME_NUMBER)
+        if write_file == True:
+            FILE.write("Modulus: " + str(PRIME_NUMBER) + "\n")
+    elif FIELD == 1:
+        print("Prime number:", hex(PRIME_NUMBER))
+        if write_file == True:
+            FILE.write("Prime number: " + hex(PRIME_NUMBER) + "\n")
+    matrix_string = "["
+    for i in range(0, t):
+        if FIELD == 0:
+            matrix_string += str(["{0:#0{1}x}".format(entry.integer_representation(), hex_length) for entry in M[i]])
+        elif FIELD == 1:
+            matrix_string += str(["{0:#0{1}x}".format(int(entry), hex_length) for entry in M[i]])
+        if i < (t-1):
+            matrix_string += ","
+    matrix_string += "]"
+    print("MDS matrix:\n", matrix_string)
+    if write_file == True:
+        FILE.write("MDS matrix:\n" + str(matrix_string))
+
+# Init
+init_generator(FIELD, SBOX, FIELD_SIZE, NUM_CELLS, R_F_FIXED, R_P_FIXED)
+
+# Round constants
+round_constants = generate_constants(FIELD, FIELD_SIZE, NUM_CELLS, R_F_FIXED, R_P_FIXED, PRIME_NUMBER)
+print_round_constants(round_constants, FIELD_SIZE, FIELD)
+
+# Matrix
+linear_layer = generate_matrix(FIELD, FIELD_SIZE, NUM_CELLS)
+print_linear_layer(linear_layer, FIELD_SIZE, NUM_CELLS)
+
+if write_file == True:
+    FILE.close()
diff --git a/[Tho09]poseidon-hash/reference/hadeshash/code/generate_params_poseidon.sage.py b/[Tho09]poseidon-hash/reference/hadeshash/code/generate_params_poseidon.sage.py
new file mode 100644
index 0000000..81e795a
--- /dev/null
+++ b/[Tho09]poseidon-hash/reference/hadeshash/code/generate_params_poseidon.sage.py
@@ -0,0 +1,528 @@
+
+
+# This file was *autogenerated* from the file generate_params_poseidon.sage
+from sage.all_cmdline import *   # import sage library
+
+_sage_const_8 = Integer(8); _sage_const_1 = Integer(1); _sage_const_2 = Integer(2); _sage_const_3 = Integer(3); _sage_const_4 = Integer(4); _sage_const_5 = Integer(5); _sage_const_6 = Integer(6); _sage_const_0 = Integer(0); _sage_const_7 = Integer(7); _sage_const_16 = Integer(16); _sage_const_2p0 = RealNumber('2.0'); _sage_const_10 = Integer(10); _sage_const_3p0 = RealNumber('3.0'); _sage_const_500 = Integer(500); _sage_const_100 = Integer(100); _sage_const_1p075 = RealNumber('1.075'); _sage_const_160 = Integer(160); _sage_const_62 = Integer(62); _sage_const_51 = Integer(51); _sage_const_38 = Integer(38); _sage_const_23 = Integer(23); _sage_const_13 = Integer(13); _sage_const_12 = Integer(12); _sage_const_30 = Integer(30)
+from math import *
+import sys
+from sage.rings.polynomial.polynomial_gf2x import GF2X_BuildIrred_list
+
+if len(sys.argv) < _sage_const_8 :
+    print("Usage: <script> <field> <s_box> <field_size> <num_cells> <alpha> <security_level> <modulus_hex>")
+    print("field = 1 for GF(p)")
+    print("s_box = 0 for x^alpha, s_box = 1 for x^(-1)")
+    exit()
+
+# GF(p), n = 255, t = 3, alpha=5: sage generate_params_poseidon.sage 1 0 255 3 5 128 0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001
+# GF(p), n = 255, t = 5, alpha=5: sage generate_params_poseidon.sage 1 0 255 5 5 128 0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001
+# GF(p), n = 254, t = 3, alpha=5: sage generate_params_poseidon.sage 1 0 254 3 5 128 0x30644e72e131a029b85045b68181585d2833e84879b9709143e1f593f0000001
+# GF(p), n = 254, t = 5, alpha=5: sage generate_params_poseidon.sage 1 0 254 5 5 128 0x30644e72e131a029b85045b68181585d2833e84879b9709143e1f593f0000001
+# GF(p), n = 64, t = 24, alpha=3: sage generate_params_poseidon.sage 1 0 64 24 3 128 0xffffffffffffffc5
+
+# p = 2^251 + 17 * 2^192 + 1 = 0x800000000000011000000000000000000000000000000000000000000000001
+# sage generate_params_poseidon.sage 1 0 252 3 3 128 0x800000000000011000000000000000000000000000000000000000000000001
+# sage generate_params_poseidon.sage 1 0 252 4 3 128 0x800000000000011000000000000000000000000000000000000000000000001
+# sage generate_params_poseidon.sage 1 0 252 8 3 128 0x800000000000011000000000000000000000000000000000000000000000001
+# sage generate_params_poseidon.sage 1 0 252 16 3 128 0x800000000000011000000000000000000000000000000000000000000000001
+
+# For generating for BLS12-381 Fq;
+# Modulus = `52435875175126190479447740508185965837690552500527637822603658699938581184513`
+# In Hex that is `0x73EDA753299D7D483339D80809A1D80553BDA402FFFE5BFEFFFFFFFF00000001`
+# So, the following command should work:
+# sage generate_params_poseidon.sage 1 0 255 3 3 128 0x73EDA753299D7D483339D80809A1D80553BDA402FFFE5BFEFFFFFFFF00000001
+write_file = True
+
+# Parameters
+FIELD = int(sys.argv[_sage_const_1 ]) # 0 .. GF(2^n), 1 .. GF(p)
+SBOX = int(sys.argv[_sage_const_2 ]) # 0 .. x^alpha, 1 .. x^(-1)
+FIELD_SIZE = int(sys.argv[_sage_const_3 ]) # n
+NUM_CELLS = int(sys.argv[_sage_const_4 ]) # t
+ALPHA = int(sys.argv[_sage_const_5 ])
+SECURITY_LEVEL = int(sys.argv[_sage_const_6 ])
+R_F_FIXED = _sage_const_0 
+R_P_FIXED = _sage_const_0 
+
+INIT_SEQUENCE = []
+
+PRIME_NUMBER = _sage_const_0 
+F = None
+if FIELD == _sage_const_0 :
+    #PRIME_NUMBER = GF(2)['x'](GF2X_BuildIrred_list(FIELD_SIZE))
+    PRIME_NUMBER = int(sys.argv[_sage_const_7 ], _sage_const_16 )
+    F = GF(_sage_const_2 **FIELD_SIZE, name='x', modulus = PRIME_NUMBER, names=('x',)); (x,) = F._first_ngens(1)
+elif FIELD == _sage_const_1 :
+    PRIME_NUMBER = int(sys.argv[_sage_const_7 ], _sage_const_16 )
+    F = GF(PRIME_NUMBER)
+else:
+    print("Unknown field type, only 0 and 1 supported!")
+    exit()
+
+def sat_inequiv_alpha(p, t, R_F, R_P, alpha, M):
+    N = int(FIELD_SIZE * NUM_CELLS)
+
+    if alpha > _sage_const_0 :
+        R_F_1 = _sage_const_6  if M <= ((floor(log(p, _sage_const_2 ) - ((alpha-_sage_const_1 )/_sage_const_2p0 ))) * (t + _sage_const_1 )) else _sage_const_10  # Statistical
+        R_F_2 = _sage_const_1  + ceil(log(_sage_const_2 , alpha) * min(M, FIELD_SIZE)) + ceil(log(t, alpha)) - R_P # Interpolation
+        R_F_3 = (log(_sage_const_2 , alpha) * min(M, log(p, _sage_const_2 ))) - R_P # Groebner 1
+        R_F_4 = t - _sage_const_1  + log(_sage_const_2 , alpha) * min(M / float(t + _sage_const_1 ), log(p, _sage_const_2 ) / float(_sage_const_2 )) - R_P # Groebner 2
+        R_F_5 = (t - _sage_const_2  + (M / float(_sage_const_2  * log(alpha, _sage_const_2 ))) - R_P) / float(t - _sage_const_1 ) # Groebner 3
+        R_F_max = max(ceil(R_F_1), ceil(R_F_2), ceil(R_F_3), ceil(R_F_4), ceil(R_F_5))
+        
+        # Addition due to https://eprint.iacr.org/2023/537.pdf
+        r_temp = floor(t / _sage_const_3p0 )
+        over = (R_F - _sage_const_1 ) * t + R_P + r_temp + r_temp * (R_F / _sage_const_2p0 ) + R_P + alpha
+        under = r_temp * (R_F / _sage_const_2p0 ) + R_P + alpha
+        binom_log = log(binomial(over, under), _sage_const_2 )
+        if binom_log == inf:
+            binom_log = M + _sage_const_1 
+        cost_gb4 = ceil(_sage_const_2  * binom_log) # Paper uses 2.3727, we are more conservative here
+
+        return ((R_F >= R_F_max) and (cost_gb4 >= M))
+    else:
+        print("Invalid value for alpha!")
+        exit(_sage_const_1 )
+
+def get_sbox_cost(R_F, R_P, N, t):
+    return int(t * R_F + R_P)
+
+def get_size_cost(R_F, R_P, N, t):
+    n = ceil(float(N) / t)
+    return int((N * R_F) + (n * R_P))
+
+def get_depth_cost(R_F, R_P, N, t):
+    return int(R_F + R_P)
+
+def find_FD_round_numbers(p, t, alpha, M, cost_function, security_margin):
+    N = int(FIELD_SIZE * NUM_CELLS)
+
+    sat_inequiv = sat_inequiv_alpha
+    
+    R_P = _sage_const_0 
+    R_F = _sage_const_0 
+    min_cost = float("inf")
+    max_cost_rf = _sage_const_0 
+    # Brute-force approach
+    for R_P_t in range(_sage_const_1 , _sage_const_500 ):
+        for R_F_t in range(_sage_const_4 , _sage_const_100 ):
+            if R_F_t % _sage_const_2  == _sage_const_0 :
+                if (sat_inequiv(p, t, R_F_t, R_P_t, alpha, M) == True):
+                    if security_margin == True:
+                        R_F_t += _sage_const_2 
+                        R_P_t = int(ceil(float(R_P_t) * _sage_const_1p075 ))
+                    cost = cost_function(R_F_t, R_P_t, N, t)
+                    if (cost < min_cost) or ((cost == min_cost) and (R_F_t < max_cost_rf)):
+                        R_P = ceil(R_P_t)
+                        R_F = ceil(R_F_t)
+                        min_cost = cost
+                        max_cost_rf = R_F
+    return (int(R_F), int(R_P))
+
+def calc_final_numbers_fixed(p, t, alpha, M, security_margin):
+    # [Min. S-boxes] Find best possible for t and N
+    N = int(FIELD_SIZE * NUM_CELLS)
+    cost_function = get_sbox_cost
+    ret_list = []
+    (R_F, R_P) = find_FD_round_numbers(p, t, alpha, M, cost_function, security_margin)
+    min_sbox_cost = cost_function(R_F, R_P, N, t)
+    ret_list.append(R_F)
+    ret_list.append(R_P)
+    ret_list.append(min_sbox_cost)
+
+    # [Min. Size] Find best possible for t and N
+    # Minimum number of S-boxes for fixed n results in minimum size also (round numbers are the same)!
+    min_size_cost = get_size_cost(R_F, R_P, N, t)
+    ret_list.append(min_size_cost)
+
+    return ret_list # [R_F, R_P, min_sbox_cost, min_size_cost]
+
+def print_latex_table_combinations(combinations, alpha, security_margin):
+    for comb in combinations:
+        N = comb[_sage_const_0 ]
+        t = comb[_sage_const_1 ]
+        M = comb[_sage_const_2 ]
+        n = int(N / t)
+        prime = PRIME_NUMBER
+        ret = calc_final_numbers_fixed(prime, t, alpha, M, security_margin)
+        field_string = "\mathbb F_{p}"
+        sbox_string = "x^{" + str(alpha) + "}"
+        print("$" + str(M) + "$ & $" + str(N) + "$ & $" + str(n) + "$ & $" + str(t) + "$ & $" + str(ret[_sage_const_0 ]) + "$ & $" + str(ret[_sage_const_1 ]) + "$ & $" + field_string + "$ & $" + str(ret[_sage_const_2 ]) + "$ & $" + str(ret[_sage_const_3 ]) + "$ \\\\")
+
+###
+### Get round number first
+###
+ROUND_NUMBERS = calc_final_numbers_fixed(PRIME_NUMBER, NUM_CELLS, ALPHA, SECURITY_LEVEL, True)
+R_F_FIXED = ROUND_NUMBERS[_sage_const_0 ]
+R_P_FIXED = ROUND_NUMBERS[_sage_const_1 ]
+# R_F_FIXED = 8
+# R_P_FIXED = 60
+
+print("Params: n=%d, t=%d, alpha=%d, M=%d, R_F=%d, R_P=%d"%(FIELD_SIZE, NUM_CELLS, ALPHA, SECURITY_LEVEL, R_F_FIXED, R_P_FIXED))
+print("Modulus = %d"%(PRIME_NUMBER))
+print("Number of S-boxes:", ROUND_NUMBERS[_sage_const_2 ])
+# print("Number of S-boxes per state element:", ceil(ROUND_NUMBERS[2] / float(NUM_CELLS)))
+
+FILE = None
+if write_file == True:
+    FILE = open("poseidon_params_n%d_t%d_alpha%d_M%d.txt"%(FIELD_SIZE, NUM_CELLS, ALPHA, SECURITY_LEVEL),'w')
+    FILE.write("Params: n=%d, t=%d, alpha=%d, M=%d, R_F=%d, R_P=%d\n"%(FIELD_SIZE, NUM_CELLS, ALPHA, SECURITY_LEVEL, R_F_FIXED, R_P_FIXED))
+    FILE.write("Modulus = %d\n"%(PRIME_NUMBER))
+    FILE.write("Number of S-boxes: %d\n"%(ROUND_NUMBERS[_sage_const_2 ]))
+    # FILE.write("Number of S-boxes per state element: %d\n"%(ceil(ROUND_NUMBERS[2] / float(NUM_CELLS))))
+
+###
+### Matrices and round constants
+###
+def grain_sr_generator():
+    bit_sequence = INIT_SEQUENCE
+    for _ in range(_sage_const_0 , _sage_const_160 ):
+        new_bit = bit_sequence[_sage_const_62 ] ^ bit_sequence[_sage_const_51 ] ^ bit_sequence[_sage_const_38 ] ^ bit_sequence[_sage_const_23 ] ^ bit_sequence[_sage_const_13 ] ^ bit_sequence[_sage_const_0 ]
+        bit_sequence.pop(_sage_const_0 )
+        bit_sequence.append(new_bit)
+        
+    while True:
+        new_bit = bit_sequence[_sage_const_62 ] ^ bit_sequence[_sage_const_51 ] ^ bit_sequence[_sage_const_38 ] ^ bit_sequence[_sage_const_23 ] ^ bit_sequence[_sage_const_13 ] ^ bit_sequence[_sage_const_0 ]
+        bit_sequence.pop(_sage_const_0 )
+        bit_sequence.append(new_bit)
+        while new_bit == _sage_const_0 :
+            new_bit = bit_sequence[_sage_const_62 ] ^ bit_sequence[_sage_const_51 ] ^ bit_sequence[_sage_const_38 ] ^ bit_sequence[_sage_const_23 ] ^ bit_sequence[_sage_const_13 ] ^ bit_sequence[_sage_const_0 ]
+            bit_sequence.pop(_sage_const_0 )
+            bit_sequence.append(new_bit)
+            new_bit = bit_sequence[_sage_const_62 ] ^ bit_sequence[_sage_const_51 ] ^ bit_sequence[_sage_const_38 ] ^ bit_sequence[_sage_const_23 ] ^ bit_sequence[_sage_const_13 ] ^ bit_sequence[_sage_const_0 ]
+            bit_sequence.pop(_sage_const_0 )
+            bit_sequence.append(new_bit)
+        new_bit = bit_sequence[_sage_const_62 ] ^ bit_sequence[_sage_const_51 ] ^ bit_sequence[_sage_const_38 ] ^ bit_sequence[_sage_const_23 ] ^ bit_sequence[_sage_const_13 ] ^ bit_sequence[_sage_const_0 ]
+        bit_sequence.pop(_sage_const_0 )
+        bit_sequence.append(new_bit)
+        yield new_bit
+grain_gen = grain_sr_generator()
+        
+def grain_random_bits(num_bits):
+    random_bits = [next(grain_gen) for i in range(_sage_const_0 , num_bits)]
+    # random_bits.reverse() ## Remove comment to start from least significant bit
+    random_int = int("".join(str(i) for i in random_bits), _sage_const_2 )
+    return random_int
+
+def init_generator(field, sbox, n, t, R_F, R_P):
+    # Generate initial sequence based on parameters
+    bit_list_field = [_ for _ in (bin(FIELD)[_sage_const_2 :].zfill(_sage_const_2 ))]
+    bit_list_sbox = [_ for _ in (bin(SBOX)[_sage_const_2 :].zfill(_sage_const_4 ))]
+    bit_list_n = [_ for _ in (bin(FIELD_SIZE)[_sage_const_2 :].zfill(_sage_const_12 ))]
+    bit_list_t = [_ for _ in (bin(NUM_CELLS)[_sage_const_2 :].zfill(_sage_const_12 ))]
+    bit_list_R_F = [_ for _ in (bin(R_F)[_sage_const_2 :].zfill(_sage_const_10 ))]
+    bit_list_R_P = [_ for _ in (bin(R_P)[_sage_const_2 :].zfill(_sage_const_10 ))]
+    bit_list_1 = [_sage_const_1 ] * _sage_const_30 
+    global INIT_SEQUENCE
+    INIT_SEQUENCE = bit_list_field + bit_list_sbox + bit_list_n + bit_list_t + bit_list_R_F + bit_list_R_P + bit_list_1
+    INIT_SEQUENCE = [int(_) for _ in INIT_SEQUENCE]
+
+def generate_constants(field, n, t, R_F, R_P, prime_number):
+    round_constants = []
+    num_constants = (R_F + R_P) * t
+
+    if field == _sage_const_0 :
+        for i in range(_sage_const_0 , num_constants):
+            random_int = grain_random_bits(n)
+            round_constants.append(random_int)
+    elif field == _sage_const_1 :
+        for i in range(_sage_const_0 , num_constants):
+            random_int = grain_random_bits(n)
+            while random_int >= prime_number:
+                # print("[Info] Round constant is not in prime field! Taking next one.")
+                random_int = grain_random_bits(n)
+            round_constants.append(random_int)
+    return round_constants
+
+def print_round_constants(round_constants, n, field):
+    print("Number of round constants:", len(round_constants))
+    if write_file == True:
+        FILE.write("Number of round constants: " + str(len(round_constants)) + "\n")
+
+    if field == _sage_const_0 :
+        print("Round constants for GF(2^n):")
+        if write_file == True:
+            FILE.write("Round constants for GF(2^n):\n")
+    elif field == _sage_const_1 :
+        print("Round constants for GF(p):")
+        if write_file == True:
+            FILE.write("Round constants for GF(p):\n")
+    hex_length = int(ceil(float(n) / _sage_const_4 )) + _sage_const_2  # +2 for "0x"
+    print(["{0:#0{1}x}".format(entry, hex_length) for entry in round_constants])
+    if write_file == True:
+        FILE.write(str(["{0:#0{1}x}".format(entry, hex_length) for entry in round_constants]) + "\n")
+
+def create_mds_p(n, t):
+    M = matrix(F, t, t)
+
+    # Sample random distinct indices and assign to xs and ys
+    while True:
+        flag = True
+        rand_list = [F(grain_random_bits(n)) for _ in range(_sage_const_0 , _sage_const_2 *t)]
+        while len(rand_list) != len(set(rand_list)): # Check for duplicates
+            rand_list = [F(grain_random_bits(n)) for _ in range(_sage_const_0 , _sage_const_2 *t)]
+        xs = rand_list[:t]
+        ys = rand_list[t:]
+        # xs = [F(ele) for ele in range(0, t)]
+        # ys = [F(ele) for ele in range(t, 2*t)]
+        for i in range(_sage_const_0 , t):
+            for j in range(_sage_const_0 , t):
+                if (flag == False) or ((xs[i] + ys[j]) == _sage_const_0 ):
+                    flag = False
+                else:
+                    entry = (xs[i] + ys[j])**(-_sage_const_1 )
+                    M[i, j] = entry
+        if flag == False:
+            continue
+        return M
+
+def create_mds_gf2n(n, t):
+    M = matrix(F, t, t)
+
+    # Sample random distinct indices and assign to xs and ys
+    while True:
+        flag = True
+        rand_list = [F.fetch_int(grain_random_bits(n)) for _ in range(_sage_const_0 , _sage_const_2 *t)]
+        while len(rand_list) != len(set(rand_list)): # Check for duplicates
+            rand_list = [F.fetch_int(grain_random_bits(n)) for _ in range(_sage_const_0 , _sage_const_2 *t)]
+        xs = rand_list[:t]
+        ys = rand_list[t:]
+        for i in range(_sage_const_0 , t):
+            for j in range(_sage_const_0 , t):
+                if (flag == False) or ((xs[i] + ys[j]) == _sage_const_0 ):
+                    flag = False
+                else:
+                    entry = (xs[i] + ys[j])**(-_sage_const_1 )
+                    M[i, j] = entry
+        if flag == False:
+            continue
+        return M
+
+def generate_vectorspace(round_num, M, M_round, NUM_CELLS):
+    t = NUM_CELLS
+    s = _sage_const_1 
+    V = VectorSpace(F, t)
+    if round_num == _sage_const_0 :
+        return V
+    elif round_num == _sage_const_1 :
+        return V.subspace(V.basis()[s:])
+    else:
+        mat_temp = matrix(F)
+        for i in range(_sage_const_0 , round_num-_sage_const_1 ):
+            add_rows = []
+            for j in range(_sage_const_0 , s):
+                add_rows.append(M_round[i].rows()[j][s:])
+            mat_temp = matrix(mat_temp.rows() + add_rows)
+        r_k = mat_temp.right_kernel()
+        extended_basis_vectors = []
+        for vec in r_k.basis():
+            extended_basis_vectors.append(vector([_sage_const_0 ]*s + list(vec)))
+        S = V.subspace(extended_basis_vectors)
+
+        return S
+
+def subspace_times_matrix(subspace, M, NUM_CELLS):
+    t = NUM_CELLS
+    V = VectorSpace(F, t)
+    subspace_basis = subspace.basis()
+    new_basis = []
+    for vec in subspace_basis:
+        new_basis.append(M * vec)
+    new_subspace = V.subspace(new_basis)
+    return new_subspace
+
+# Returns True if the matrix is considered secure, False otherwise
+def algorithm_1(M, NUM_CELLS):
+    t = NUM_CELLS
+    s = _sage_const_1 
+    r = floor((t - s) / float(s))
+
+    # Generate round matrices
+    M_round = []
+    for j in range(_sage_const_0 , t+_sage_const_1 ):
+        M_round.append(M**(j+_sage_const_1 ))
+
+    for i in range(_sage_const_1 , r+_sage_const_1 ):
+        mat_test = M**i
+        entry = mat_test[_sage_const_0 , _sage_const_0 ]
+        mat_target = matrix.circulant(vector([entry] + ([F(_sage_const_0 )] * (t-_sage_const_1 ))))
+
+        if (mat_test - mat_target) == matrix.circulant(vector([F(_sage_const_0 )] * (t))):
+            return [False, _sage_const_1 ]
+
+        S = generate_vectorspace(i, M, M_round, t)
+        V = VectorSpace(F, t)
+
+        basis_vectors= []
+        for eigenspace in mat_test.eigenspaces_right(format='galois'):
+            if (eigenspace[_sage_const_0 ] not in F):
+                continue
+            vector_subspace = eigenspace[_sage_const_1 ]
+            intersection = S.intersection(vector_subspace)
+            basis_vectors += intersection.basis()
+        IS = V.subspace(basis_vectors)
+
+        if IS.dimension() >= _sage_const_1  and IS != V:
+            return [False, _sage_const_2 ]
+        for j in range(_sage_const_1 , i+_sage_const_1 ):
+            S_mat_mul = subspace_times_matrix(S, M**j, t)
+            if S == S_mat_mul:
+                print("S.basis():\n", S.basis())
+                return [False, _sage_const_3 ]
+
+    return [True, _sage_const_0 ]
+
+# Returns True if the matrix is considered secure, False otherwise
+def algorithm_2(M, NUM_CELLS):
+    t = NUM_CELLS
+    s = _sage_const_1 
+
+    V = VectorSpace(F, t)
+    trail = [None, None]
+    test_next = False
+    I = range(_sage_const_0 , s)
+    I_powerset = list(sage.misc.misc.powerset(I))[_sage_const_1 :]
+    for I_s in I_powerset:
+        test_next = False
+        new_basis = []
+        for l in I_s:
+            new_basis.append(V.basis()[l])
+        IS = V.subspace(new_basis)
+        for i in range(s, t):
+            new_basis.append(V.basis()[i])
+        full_iota_space = V.subspace(new_basis)
+        for l in I_s:
+            v = V.basis()[l]
+            while True:
+                delta = IS.dimension()
+                v = M * v
+                IS = V.subspace(IS.basis() + [v])
+                if IS.dimension() == t or IS.intersection(full_iota_space) != IS:
+                    test_next = True
+                    break
+                if IS.dimension() <= delta:
+                    break
+            if test_next == True:
+                break
+        if test_next == True:
+            continue
+        return [False, [IS, I_s]]
+
+    return [True, None]
+
+# Returns True if the matrix is considered secure, False otherwise
+def algorithm_3(M, NUM_CELLS):
+    t = NUM_CELLS
+    s = _sage_const_1 
+
+    V = VectorSpace(F, t)
+
+    l = _sage_const_4 *t
+    for r in range(_sage_const_2 , l+_sage_const_1 ):
+        next_r = False
+        res_alg_2 = algorithm_2(M**r, t)
+        if res_alg_2[_sage_const_0 ] == False:
+            return [False, None]
+
+        # if res_alg_2[1] == None:
+        #     continue
+        # IS = res_alg_2[1][0]
+        # I_s = res_alg_2[1][1]
+        # for j in range(1, r):
+        #     IS = subspace_times_matrix(IS, M, t)
+        #     I_j = []
+        #     for i in range(0, s):
+        #         new_basis = []
+        #         for k in range(0, t):
+        #             if k != i:
+        #                 new_basis.append(V.basis()[k])
+        #         iota_space = V.subspace(new_basis)
+        #         if IS.intersection(iota_space) != iota_space:
+        #             single_iota_space = V.subspace([V.basis()[i]])
+        #             if IS.intersection(single_iota_space) == single_iota_space:
+        #                 I_j.append(i)
+        #             else:
+        #                 next_r = True
+        #                 break
+        #     if next_r == True:
+        #         break
+        # if next_r == True:
+        #     continue
+        # return [False, [IS, I_j, r]]
+    
+    return [True, None]
+
+def generate_matrix(FIELD, FIELD_SIZE, NUM_CELLS):
+    if FIELD == _sage_const_0 :
+        mds_matrix = create_mds_gf2n(FIELD_SIZE, NUM_CELLS)
+        result_1 = algorithm_1(mds_matrix, NUM_CELLS)
+        result_2 = algorithm_2(mds_matrix, NUM_CELLS)
+        result_3 = algorithm_3(mds_matrix, NUM_CELLS)
+        while result_1[_sage_const_0 ] == False or result_2[_sage_const_0 ] == False or result_3[_sage_const_0 ] == False:
+            mds_matrix = create_mds_p(FIELD_SIZE, NUM_CELLS)
+            result_1 = algorithm_1(mds_matrix, NUM_CELLS)
+            result_2 = algorithm_2(mds_matrix, NUM_CELLS)
+            result_3 = algorithm_3(mds_matrix, NUM_CELLS)
+        return mds_matrix
+    elif FIELD == _sage_const_1 :
+        mds_matrix = create_mds_p(FIELD_SIZE, NUM_CELLS)
+        result_1 = algorithm_1(mds_matrix, NUM_CELLS)
+        result_2 = algorithm_2(mds_matrix, NUM_CELLS)
+        result_3 = algorithm_3(mds_matrix, NUM_CELLS)
+        while result_1[_sage_const_0 ] == False or result_2[_sage_const_0 ] == False or result_3[_sage_const_0 ] == False:
+            mds_matrix = create_mds_p(FIELD_SIZE, NUM_CELLS)
+            result_1 = algorithm_1(mds_matrix, NUM_CELLS)
+            result_2 = algorithm_2(mds_matrix, NUM_CELLS)
+            result_3 = algorithm_3(mds_matrix, NUM_CELLS)
+        return mds_matrix
+
+def print_linear_layer(M, n, t):
+    print("n:", n)
+    print("t:", t)
+    print("N:", (n * t))
+    print("Result Algorithm 1:\n", algorithm_1(M, NUM_CELLS))
+    print("Result Algorithm 2:\n", algorithm_2(M, NUM_CELLS))
+    print("Result Algorithm 3:\n", algorithm_3(M, NUM_CELLS))
+    if write_file == True:
+        FILE.write("n: " + str(n) + "\n")
+        FILE.write("t: " + str(t) + "\n")
+        FILE.write("N: " + str(n * t) + "\n")
+        FILE.write("Result Algorithm 1:\n" + str(algorithm_1(M, NUM_CELLS)) + "\n")
+        FILE.write("Result Algorithm 2:\n" + str(algorithm_2(M, NUM_CELLS)) + "\n")
+        FILE.write("Result Algorithm 3:\n" + str(algorithm_3(M, NUM_CELLS)) + "\n")
+        
+    hex_length = int(ceil(float(n) / _sage_const_4 )) + _sage_const_2  # +2 for "0x"
+    if FIELD == _sage_const_0 :
+        print("Modulus:", PRIME_NUMBER)
+        if write_file == True:
+            FILE.write("Modulus: " + str(PRIME_NUMBER) + "\n")
+    elif FIELD == _sage_const_1 :
+        print("Prime number:", hex(PRIME_NUMBER))
+        if write_file == True:
+            FILE.write("Prime number: " + hex(PRIME_NUMBER) + "\n")
+    matrix_string = "["
+    for i in range(_sage_const_0 , t):
+        if FIELD == _sage_const_0 :
+            matrix_string += str(["{0:#0{1}x}".format(entry.integer_representation(), hex_length) for entry in M[i]])
+        elif FIELD == _sage_const_1 :
+            matrix_string += str(["{0:#0{1}x}".format(int(entry), hex_length) for entry in M[i]])
+        if i < (t-_sage_const_1 ):
+            matrix_string += ","
+    matrix_string += "]"
+    print("MDS matrix:\n", matrix_string)
+    if write_file == True:
+        FILE.write("MDS matrix:\n" + str(matrix_string))
+
+# Init
+init_generator(FIELD, SBOX, FIELD_SIZE, NUM_CELLS, R_F_FIXED, R_P_FIXED)
+
+# Round constants
+round_constants = generate_constants(FIELD, FIELD_SIZE, NUM_CELLS, R_F_FIXED, R_P_FIXED, PRIME_NUMBER)
+print_round_constants(round_constants, FIELD_SIZE, FIELD)
+
+# Matrix
+linear_layer = generate_matrix(FIELD, FIELD_SIZE, NUM_CELLS)
+print_linear_layer(linear_layer, FIELD_SIZE, NUM_CELLS)
+
+if write_file == True:
+    FILE.close()
+
diff --git a/[Tho09]poseidon-hash/reference/hadeshash/code/poseidon_params_n255_t3_alpha3_M128.txt b/[Tho09]poseidon-hash/reference/hadeshash/code/poseidon_params_n255_t3_alpha3_M128.txt
new file mode 100644
index 0000000..2408b4d
--- /dev/null
+++ b/[Tho09]poseidon-hash/reference/hadeshash/code/poseidon_params_n255_t3_alpha3_M128.txt
@@ -0,0 +1,18 @@
+Params: n=255, t=3, alpha=3, M=128, R_F=8, R_P=83
+Modulus = 52435875175126190479447740508185965837690552500527637822603658699938581184513
+Number of S-boxes: 107
+Number of round constants: 273
+Round constants for GF(p):
+['0x704560fe3d054ee777b5e26734910377e010dfc857833b8342aee456b3bfdb1a', '0x081d6de4975226b404faf95680e16a43d49fabd9a5ab019140151b53681d75a6', '0x33e47a8ba888311dcc4bdca10752f018f83f97fa5e75227063e70813ec20e54d', '0x12ca392a610c91e4f7bc5ad374390a15aa8933361143471316391445ebbd99f6', '0x1dba915b724119f7dc1656894cae4f3e732c6a5105fdd8256c200d7a97b4e725', '0x1eb91f485737973c3cfb1c1e93d1e102511aae398650b284e5b34c8b9f4088e9', '0x62ef3104edda63cd9b846a1903f4fa5f5884a4bc873a7a39bb3e3723480dba4e', '0x042bbe938294087216ee7bd8f93e1d2503b97c4e4e72b5f7ef11c159b1865636', '0x4f14dccdf3975931c7db252cf3864a83bb5581cfc4068a74b3aa6d8ecac9675f', '0x25a1ada14b893ed43beb44534c7f4ba79012d0c5762b9d85ff1705f2cb3a7dfb', '0x1bd6a16bd180891d16d708bf5120123f90e6bd3bc4e2b5d4eb041cd6312b1d7c', '0x20313682eddc4c4fb986815da33455af348cb790a7fb90fcc62305692a1a9a6b', '0x4d492e53c92209d62edaa6c9aac1b9982ef05e17980145902458ed4a7db99991', '0x30159ad162cd1c187eb31680e8fe8bda34fd9710e4c95a458fbdfad2ca8957a4', '0x18d3bb3815f7872957a57ba20425dff04e7aaccfc557b485bb00fd4d73da557f', '0x68a47f2ca25808b31d4cabb8c48652a399f482dbbdef14493bd4a4ef2b8426a0', '0x54221912dbca8c6b145d92703ad5446af6a10690c5bf074737670c13a4e00244', '0x47b4ea7bfd6e94b9e8539c0746a7ba874bc5fbcf2059639d870f1516fbf6bb35', '0x5ec7b21ce09bb32547de4036fe503f7e22af9da768f39617db18f73f0bdf9991', '0x70b0f825abf6ca5345f345a4297130470e62ccac63dfb34a0061e33b5784ad07', '0x62e6ff5ce5d4cb12bb2d25ec1a02554fde2f3347358841658ee0745f2f5f6fca', '0x58f6a11ca70e03893ab78de736014de900a67f768f0de2545290fed090f60455', '0x5ac59352710c6af70b8558d131084a2db48905d2a0106b8fc6d58c97f398e1a0', '0x6bca90ad22a38d051e7c6cb21d933100d20fdb9f60b67bca7c92e63b6b1d352a', '0x2175469422addef7689c456532e9707fe6f7e67075221a88acdca75388d3f02d', '0x30a3161b015fe357d70087979d9c25577bf897f182b4790a63595411b02d9fde', '0x5c562581f3e850e74e0ed2a1240ac67d178b463e4f91cc8132a2a6fc05e6d266', '0x71682b55b3c3416382bce660db9d7abc6ef1fec91e68347a81ae1ac06df15130', '0x52aed31c053f45b3bfd730f17ff58b109471c5085ef986af7716003489f5773d', '0x5ff2583c2d25ddaa29f8332de76f16e50438fa0bdd7f636499ea9aeb59b53ef5', '0x3d3bc2e476e2cd909c858b1f0660344aa1454ec6345b302a0fe94fca04890c23', '0x55f0dbf3ffa6d0b1b3e6a258b66358584da20efd256022241c80b57371a7364f', '0x0d99d18b8c77b7026a113ae94d5ba94c488a174ac993d4d74c7533f559d246e9', '0x3ed6fe4539b6bcadc92faaadc0417152699affa1f38ea988f9306ea3ea114199', '0x0315b409b7b00b6a449b8bcd11cdec2ebb2e330def18dac1345d743646a79545', '0x4af6766f8975e88403a9f571cf5cbe501cf438ad87ea7581cbd6753919bd622b', '0x663b0152829e77080b7174b66afc2be1b997dc9afd708fbf10dc1dfe7f5a7e1c', '0x4924778d673af00064d01b256ebba33c591bbc69e25a16ca3b5469233d93b2f1', '0x12185da1a008d14a6c8106c4c38a13050ba1ffcea09f4d213ca067cd04ffe7d7', '0x2c46a2f63523f8222ed3a0413577c9a8233ac7a54cf2559e0c3253d9119a90fd', '0x6e296a7260e86588f11d105fee7d8e4a6934afc80cd1f6e4940fc538cefa9792', '0x1076e358a54ce79c2d101aa39783d2ef9e043dc41408bca964bb85da866ec5a7', 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'0x48bed1ee256c4688b951394ab03b25a83f007944b04360a7dc56d970693e9ebf', '0x3d5ebb1da13afeaab8215f58d987b2dcd3725eea1af4722ea08d3c60aee5e897', '0x4666c2190d4a0cdd1f45478a4ae42b5a0a07bdb08cc16c77b24a5100512ed29d', '0x4ee1f9f57ef7ed50c6c98b12aaa5d52a860a683584cc8fe998a1a9f7345bb601', '0x55259b63823b4bb6db0bada5594579e4fefc9b05f3f95ef2214bed5e1824b599', '0x2c275a621bf8d750c86eddd5d199cf7e4800057c66491a5f3beff213de564f65', '0x45a37da1c5ba206e6b4d9d700b13873a9fa196b933a5f3eb73b6ba945d9ae9f2', '0x2f7fd8e66c3ca85d30b159966459357f4b5cab5a6fee74fa0b656340be366880', '0x1d6ff089b4984da2784cd69e1263df5e756109c6abfc0b50f0923ac44bdb2949', '0x1bee8a6155b5bc935d8255c9da364986bc2b52b4b670e8d6c450cffd6671b51f', '0x544bf232869c4185ba99d72c30f606cfd2a48830d4fe736404fb4c67dfb52f0c', '0x314762a0353e84e7f9cefb7e3c1092903135905a2029cb78be5b2bcf4701b414', '0x69dfe1606da016dbb91da1df0f3d9977a4f1f5097d37c12eef59f72a56c1c3ca', '0x0b331d2bf548f140b8eada20f3aa93b4287a9d1cdf680e236230b881708bec15', '0x73ae2501c58d7750150a3f4052e77c33dc06e53375912eea9703125f52a87211', '0x0070e24c6632912757bfb41f387285f070a1b899155ec8f9e2339bdd1f00cdcb', '0x42f37906cdc8ea57d6f17d9ce55573100442f0566b7aefacd6b3ab68cb7858cb', '0x364c13bfa4f0f43e432c32ea596118a187ce8cc7a59e76316cd7928fa73910ee', '0x1160d9d8f2f5a97ce1f9a5c280fe09a3d7d1df8eb61b6b2561aa28276d01af7a', '0x6e1076235464e2c662c4c23f85ddef673de47c38871747edc0451a5ca60c63a2', '0x01ab4b79cdf7a563226ac052d3d0defb34854a058944765cfc1ef3c794b11304', '0x65e2331c665350a026d22eb0579aef034d34d9fb945f074b3a0b66eec5b5c555', '0x5e61b1bd368420354f823b494b03e30602c14d956725a25ac8fd86eb7db4aeed', '0x2ab40ad160c2c7c1ec7d2a3e63d87751d16f23b12cfde6217ce05e17a068a4ca', '0x16018ac66d6a57b84f06ccf3a12b23f0dbc1ee8df48353f80066038fedb96e5f', '0x1425ba145acd94405af0469b36ca09f0e48652985428fec79abf4f1ca3a6e997', '0x36edb296ac05cc324eff8a347189f0d7c6aa02c2952adbf9fc81b85c70e09294', '0x669e26a34ff62ab6519c4497f78be1018ee18275f9f07c4f9feb8c90de17cc05', '0x02efcf660afe15d75397c96b7bacd56cbb681a3720e28565fbcdabd00a0d2bb5', '0x711e17443bb3bd556916b19e429fd8199f6e5e12e3d56da59330365eb44bd11f', '0x4cfe078277868dacfacddc5bfddf170760fb05e5d10f0fd34c73111002f2bb67', '0x0bb26810ea197c1748a0680e5df07e8eefc908443b130412af5a3f2070199522', '0x6eabb71bcd7c2cb582d0cf46537ca5faf933fefb3d44c5105bacf4c99c04c3a2', '0x1108955182aa2371f493848c1b6527c40bc1c64ac148da922c88562bd97354d8', '0x524ac434200bbe346c0815c3eb6f69511c2ec79256362221f35623149cc25cad', '0x0906c30f2dd800108f1c9cf6c9cb05c43126a227b712690d68bcbce18c425fc8', '0x0fe9cb2152a668a0941c386f6961762e443f682eaba38ae625db9a33ed4d697b', '0x127b679b85c1f98a7b34985b793461a83b8e4a1d62d98826ed80c5a6f540a461', '0x69ac8b67ad5d14682f89472af58e67c41f55c4a960c752d22de009a795942fc7', '0x1a49b0eaf12b5955553d6cdb7117413ada23b1c21bcc34d662fca100de247fc4', '0x0fe9030e9ab2752fff4f3746f272c427e34ed51d655d259b1da7f2a3c686471f', '0x40822c7050d38f2bf0fc51d99684b3043b948925ec0d203aeb199f4e67fc325e', '0x599364c6330661c8fd31f80fbb89cab102a555ca751fce1fc5de11e92e9b64fb', '0x39155764544a261a2cd438577537128417cdf92e8e7bfba32314882a48956524', '0x596b88b5cc900dd3916d34ac22a356457c466497b8f2fe610f727f5c4ffacfea', '0x5dbac4982b334076c64fc5d48624e3b49877d939c0450f392ef8a71e6afb5c85', '0x0efdd5e2c510b770b99e5279c2b49160b6c1a6be0edd77df1a0b6fa8499eb20e', '0x1b138226b76f30e28c1b730098c9c00047e45ae5a0a1deca7fcd94d35989aace', '0x46ee916c4fff5f7304856dd634361fb4954c36c95b67fe23651b5de2b718376b', '0x226598e71933f31889c0ebbe5872ae56f4f2721359c8459092f3218976881098', '0x0c9c46c69490c90d61caa74207dfabb6d9fdeaa34486646b7e0ea13ee9f3a3a7', '0x567185c646b718ccf10cd7e55d0f839b89e58c6f4ff1a755d6d0cc7d0e0df663', '0x6d08d0b31d26cc4faed98e3e55616a3432f4410dc887bd9d3e06c50820876a98', '0x56d89420573b91a5661076a4245ddc4642356887749197c55c7152a66bcd8f7b', '0x63da452de7cc758d51e353332196cac00c3677f8b2e807ce5999e905f88a0d63', '0x2bbdb21dbfe4f06f36eb3c037e8513d949618656865023cdbb8dba26a4fd1fa6', '0x179fbae02e92c450ad764c4c2a759f4a0eabb2d5fb17bccf8169d7ddd53667bb', '0x3c02c88ab088ee794a1cd3e98d91f4e19ebdad80328fa4f4ab75e63da3e3aca2', '0x288cd3eee44047e2cc922133cd966aa1654f731a9280ab67777818fabad948fe', '0x092fa949f18ec38d0048e97e59631e7f6076be72df9de03fddbd61fe158e50d0', '0x31b629f4c1b209e8d62f0db93c9265cb8b679b20b359c92b4cc8dea16592143b', '0x3140b7f7bdb9b75f0c2021411277f9ca4c2c7b7322e91ba4da31e33f14912036', '0x46b62bf8d3beaa3a00c9dceaf98d9bec59ce6c92bea5a96e7b5ab02db955c177', '0x70a8e9daf6e7eb7a3d2cc0329583b410c510fd262f624a950035058607c68845', '0x2a30a650d0f5748635f8d6065885454a55d39523d7744a9dca72ebae07e5e7aa', '0x4469df5c50de8e3543a69eba372a0878b05485cf361912eeaf3193ab0a11f581', '0x435122f388307ff979ca6096555929b2036eec9322d1790f96b7a5e458438964', '0x07949b5de281769af6058b950115512040916623f94fb0d1bbf80eeac01b5170', '0x6e8034836f9884974d920ff2ec82736954e57d649d1edb0236d821f06bc0c093', '0x6b23cbc714a2f685d9c3085426d000a1857ecd6a6671c46a43c7c799e5028cc4', '0x14989792a71d55f801d16bec736eb92a9d835e4a5a24d41d73d16ad15b745cd4', '0x1a899c23318971e5f9e40ba1cb8a9afba13e727d3945236e44fb3ed09bd8d35d', '0x3fc05581746d7c0e31e4f11cc4818e77a2b0f40c6bd5f076b144556cf41dbca6', '0x2aaffaf7edcb5bc621b98f3cef5ceef77d45013be594e04d75225d92f64fec3e', '0x61b64d647cd116239a26d2cac2dc23ac2e02577e8a8fe168b6ed40cef42f426b', '0x730f50167517177c0927e71f3874784d33c0907676db18db6604a6dcbe0fdd46', '0x44e79b8e0c3cdd0d028496c9d335f3c54bcde36d80bcef956bcb53c5fba0a5c7']
+n: 255
+t: 3
+N: 765
+Result Algorithm 1:
+[True, 0]
+Result Algorithm 2:
+[True, None]
+Result Algorithm 3:
+[True, None]
+Prime number: 0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001
+MDS matrix:
+[['0x62b2303d4c5006ecfffc478bf072274d23a5973cddbc18fd42efc2e7d8f87962', '0x153fc4189d461b99b8145c1437bd7d3bb537711eb1c5a07ec8957f0eeb99cfe6', '0x5890e33e870bc26b20c8a8c66aff43c7fe3aad55a49ef0f975d081fa8d8866c2'],['0x69f976d5eff5cefcab13df96ab604950213df550272b764283c9a8ea69b7dd9f', '0x00c2e9f1b1321774c93c5f3882a18a5732cfcf35fea1abfff1753eeb7d23f518', '0x3a24fa18dbde09d5eb388ef0d1e20df732760b8053fc8b1476e40982b3bb5b95'],['0x644f9dcbac11b66ac61d7ae7275863990a739ed6d502ea074b48a036cc3ef9ed', '0x6a595cab8d8cfe1dea638286b496b93fb482f212e13429ea1cb666558c995845', '0x1d959bd711714469f88ffe242e05af24acc03904e9821720fb9e168d1cdee6f5']]
\ No newline at end of file
diff --git a/[Tho09]poseidon-hash/reference/hadeshash/code/poseidonperm_x3_64_24_optimized.sage b/[Tho09]poseidon-hash/reference/hadeshash/code/poseidonperm_x3_64_24_optimized.sage
new file mode 100644
index 0000000..e49b1c9
--- /dev/null
+++ b/[Tho09]poseidon-hash/reference/hadeshash/code/poseidonperm_x3_64_24_optimized.sage
@@ -0,0 +1,276 @@
+import time
+
+# M = 128
+N = 1536
+t = 24
+n = int(N / t)
+R_F = 8 # 8
+R_P = 42 # 42
+prime = 2^64 - 2^8 - 1 # 0xfffffffffffffeff
+F = GF(prime)
+
+timer_start = 0
+timer_end = 0
+
+round_constants = ['0x240ec2a793108b4a', '0x753452ad8cbbbecb', '0xa3612a53da19a265', '0x18a083f17b5a94eb', '0x30d1c3ecb4f44b99', '0xaea865a3e5830f71', '0x4a9134c89190acc6', '0xed37c99a612065b1', '0xafd9964e15975e77', '0xa77147766c1ff75e', '0x1f075012654c408f', '0xc5e11b29262d9283', '0x6b6495600eb3ac52', '0x2b3b599ae4fa1d12', '0x90cda513782b872f', '0x78d9b4ea0f82d0e9', '0xbcbe92c86e626013', '0xa24fb10ca2a94fe8', '0xca3d8d1ebcc8b0b8', '0x01f19977b5ae425b', '0xdcb91f4a2ee555e1', '0x522fc03d8de5625b', '0x8093493f225f5fe0', '0xe34925160dd8ac6a', '0x0d849db4c9677f3e', '0xdb3c9dba3951d80a', '0x69ebf310531af9cb', '0x618c6e79c2131c9a', '0xf753bfda5bea2713', '0xc764d2dcfe66b834', '0x1428f86c920dc41f', '0x32eec3f568ba6a6a', '0xd348b99d1be142d1', '0x5a54339e5cf85764', '0xfcfcfcd93a85db2c', '0x5bf91d3330de1254', '0x7497efbc720c4d29', '0xb7f823baf4fb4ad3', '0xecbdc0ce5ce155f7', '0x1e98e24a11060158', '0xd68cc1bc7a734e3b', '0x8b5192beefe56d76', '0xcb37590292ed5d94', '0x3c0f4ac4442e718d', '0x7f28481f271ac458', '0x95a29062b8b7ef10', '0x5e35d63f60ebe7a4', '0x6f0cce8765194a54', '0xb2c5368f33cfdb88', '0x23d4c5242d9031d8', '0xa01e66ab5e6bf11d', '0x37b3c3f35a2c2db7', '0x6b0f16e664da3bc7', '0xa2edd28b4157761c', '0x772f8d3d4b7bbe30', '0x067d7f034ea64273', '0x9c04b9ef0ad21b49', '0xec615fcfe5fb17e3', '0xe5d5a133b594b39d', '0x5575c2ad9cfb2e71', '0x8b8bec6fa05ae8ec', '0xfdfe46961b74f8ca', '0x81826d165c8db1f4', '0xebb8dd7f53d2873a', '0xa74d8725a61f697c', '0xa48bbebeb12e5ba1', '0x1dc2cfba8304fb0d', '0x121ce1466d109dd6', '0x2e4a7c3aba839378', '0x540a4d98e030dcdc', '0x215ac5039c8dacf7', '0x8627aac1074f6776', '0xbd9f007a00342dad', '0x0485d9997c5d2d43', '0xf73dc1f105ba7b82', '0x75dfe4727676a769', '0x9226a74d24479a98', '0x1f9526e943307c60', '0xf8ec7859af0ac374', '0xbf084ca320167a51', '0x19225ef89b83a433', '0x4eea3af3cf87a21d', '0x5f32bfe642a25785', '0xee18341408e7109e', '0x095086a0fd9e22f4', '0x24bbb72c5af99867', '0xf0bdd8ee27e7a897', '0x19c9f25475ec0a13', '0x9fae6ed0f262b68c', '0x8521b8743284e615', '0x11341ea6613ab6ed', '0x66efe6ca18cd3dca', '0xf1ac5951a2934237', '0x22f7e35282498908', '0xb5bcdc16593c6674', '0x865eaa9fa7c40873', '0x9dee60da82ac4465', '0x22735f881786cc39', '0x6de9f9171436b66e', '0xf2aadeaa6a66b7ad', '0x4aacc905f9272cb4', '0x2c2714c649e42a81', '0x76d73405217d9dc7', '0xc883b51c111a8c32', '0x75dc8b2a293b801a', '0xcca8a5875b768909', '0xb9fd56aef43fe7cc', '0xafbfec0102d26c2c', '0x5157f8d356757a65', '0x26e3b538e13b9d5c', '0xca1497b238a3dc52', '0x995c0df77c5b3940', '0x7ff238ddc7075582', '0xa6efe8632d790673', '0x3f402fcafb803b75', '0xd0a9b5989fa80648', '0xd731da881957d177', '0xce282dcdbed66f47', '0x1270fea846832c28', '0x873da44928addef1', '0x3946531d53229dec', '0x5f09a6e3919f98c7', '0x8ea315a8fc0618f9', '0x4fd30e28e515e81c', '0x2cdbf5e36d8c63a5', '0xcce53304047e771a', '0xb710cb8e0564ca50', '0x1631a30bdc219de3', '0xde3e13bfac4ab80c', '0xc37e18414100ead5', '0x99e5043b30387161', '0x3c6bb225d1d78d15', '0x65c5d73b4a5f9807', '0x137c582109bc3643', '0x05f762e5b1d480fd', '0xb389c617c45d5bd0', '0x2a23ba94c54ad1ef', '0xeb4440f0a237d56a', '0x9d503447cce854b3', '0xfc5b688737c2aae9', '0x80f39542543f321c', '0xbaf3e8826b9e7c31', '0x1f7e8de645be342f', '0xd5c2dcab1d053e13', '0x986a4a8db3280f18', '0x4b242191c7dadd25', '0x50882bd23adf7857', '0x09f16b633e545bdc', '0x5e0981215a746ce5', '0x9ece3a04ded2e454', '0x8a7d4f600e85d88b', '0xab49152709ed581d', '0xed825bf8b3d32ab2', '0x1f37d6e31dd92ee7', '0x4a766830058f5e67', '0xd413d3bb4acf6432', '0x93da3397b6581f7a', '0x5fd4de23b579e4f8', '0xcf0bb8b34bfed3e6', '0x1a31a6eccc154f82', '0x4ec5a45b2444daea', '0x5cb0b6b9fe239e7e', '0x35a035640d1457f8', '0x6dbc1e53fa738977', '0x5efa24c87a749e3a', '0x27613437239afc6b', '0xfca89d793bf3a0c1', '0x993a7c1d8b509373', '0xae990f255bf5e977', '0x7b7acad0dea808d9', '0xe4df51bda3d6834a', '0x3e7516a279ce8e04', '0xc50749a33a60fb83', '0x8eb497c64e56d7a9', '0xade425408c5d2fe5', '0xb6f34f730c10daa1', '0xbcef2e56ac305d87', '0x2d2a447c10e46c62', '0x1580f32c34717e21', 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'0x8e9446a2306273a7', '0xe56bc7dd7e269d86', '0xd268629e15540a61', '0xcc1ae494f6cbe85c', '0xf9b67e546f345d61', '0x1f2a1dcc922535ab', '0xcb32f767dd99c7ea', '0x7c5484ced2210dc2', '0xee7e959891973ed7', '0x5a8854c0aa276e78', '0xebbd2c49615891f5', '0xc3e702e07c097227', '0x14062e4969cfd241', '0x119201016761e94c', '0xdeb61fcfef6c8164', '0x4728d6620731f961', '0xd35f176670a0fb71', '0x1c389c333b9b48df', '0x3a2f748490b79666', '0xee1cdc0805cb5f53', '0x8f671e24771a48ea', '0xad05502389b8498c', '0x1e180b87e426c7ff']
+
+MDS_matrix = [['0x70e6dae2c651cead', '0x090e1669a71a5d00', '0x850eb1097fab4a21', '0x0b897348e7e0fab0', '0xdba1e3e5b76ed64c', '0x3334f13fa046b4ad', '0x8a4d7cf4f0429ffb', '0x19ea5fc1afb8c40d', '0xbc9b82c52e2d16d3', '0x6ef233462dfb9102', '0xb78f9a4aa5692674', '0x137434135cab157a', '0xdcfc4fb1fad92667', '0xf2da17d8ccaf5dba', '0xdc562eb3b775a230', '0x3a579ccd17e69b21', '0xcd4371daa1f50ce1', '0xf3fb536f0880da4b', '0xd4c0d70cbe266d00', '0x922f62855fcdcccf', '0xf2587b5670e3f932', '0x83cbc18d3068858d', '0x42418957cdb87f03', '0x8a1c2e26886dcc62'],['0x59ff431e0b5017a3', '0x5f5653f6d4b07aee', '0xf3a7fabec4bfaa90', '0xeaa1c6cf8a5f93b6', '0x640fe1aec663543c', '0x5e8b2eb00c0b8f20', '0xff0e9e271c3cd79a', '0x8f893f3bf126360f', '0x09ace012c2348c75', '0x53fddfe811ff2173', '0x42b52ba39e72e1af', '0x2d4ae7306cd3dee8', '0xcca7a772494dda3f', '0xc3c21065f335c8ed', '0xa38e5f985541602e', '0xcf88ae035fab200b', '0xc3e845fab9e1952b', '0x7e80802dab7470dc', '0x3394d8795d6f79d9', '0x700e544671622092', 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'0x8999fcbd397a5930', '0x625448ae7510ca03', '0x5758f7704c27f739', '0x213b1f365e92efae'],['0x75b99a800f6a4e50', '0x6480016a5692c75c', '0xa1b8e0944dbf341d', '0x9d8a004f8b956f3b', '0x4c06adc09d37c7f5', '0x52bceba90cc316ef', '0xa4c726bf0a05c621', '0xa25fa8b92fbbee55', '0x722b97245d3359c0', '0xb7a455711a461a0c', '0x231cbb34de2a15fe', '0x7cec97f425eb2d45', '0xb84585a25203a89a', '0x77aba4c7e88873f1', '0x37fe478b2c36cf66', '0xcb6484b2339f5f8e', '0x9d7bfa01a9e43ecf', '0x6e0ab9fcc52a6de5', '0x0cd364e0a15796e1', '0x05d93140e2e3f2ca', '0xe204443778179d0b', '0xbef305850f048544', '0xd32256924554a49b', '0xc53511ffa12bb90f'],['0x24963e56058f634e', '0x42ba953bf6a2ebe4', '0xf59b3de68f6e561f', '0x97fde1b7e2e04fa9', '0xd54550d47e251af5', '0x06d59e915cb62071', '0x3fb9da70660121f0', '0x9c6d745cda9317bd', '0x9b2e7bad646b7572', '0xeaecc8fa9e3f8ca6', '0x86da1cdb3cfcc903', '0x7d89bccf99ca4618', '0xc424b3165b1272c6', '0x655f29202ed109b5', '0x6084931c4c587edd', '0xbf254b666533c51f', '0x6986d415ab4569de', '0x84c5542ce3d641e6', '0xbecfc4b066cf816b', '0xb8c67054069cbcf0', '0x0c104c400ca7e269',
+    '0xacd24cf52548e6c0', '0x539da2943a2cea96', '0x4b34154f23ce7f50'],['0x27a8fcc9a30540a5', '0x2a384863fa279560', '0xd30ad1b8bb0b5e63', '0x2e86af6a6f62fa02', '0x34bca2387740fcfa', '0xbfb4397008b15dce', '0x14a5bfb5f0dc9d97', '0xe4649e64d9177252', '0xd7be1ade0ddbc8b6', '0x390a00e89f5cbcf9', '0x4d72acfede73bbb0', '0x187ee525fe64a12c', '0xaeb1ef1688d202d8', '0x5be593c3c65b0667', '0xf3aa608de6ecc65c', '0x9d7126e3db70b9f7', '0x2c64d046e025840c', '0x415d660d4c1159e0', '0xff20ed0db79423b6', '0x6d0d1d2b46e267a6', '0x33bcd8b3cb1ae3c2', '0x3ccf87b1d6f07a52', '0x6aa98e243986b159', '0xacea4c929bc468f1'],['0xda6bb46f0b2af6a8', '0x67d0fd089cc0898c', '0xb7dd68a9042cb514', '0xcdf03ff3c7130f3e', '0xffd80a8c40d6ae3f', '0x4a44e7f5385c546c', '0xb129828ecd7e97a5', '0xbaf520f816202bee', '0x35706f5a82d07680', '0xb29eab3da9398698', '0xb5992f06769f0df6', '0xf83e56af0cc2860a', '0x3378bd8b7bbd925c', '0x78cc26b72180477e', '0x7cfb9d3c73b4e3c6', '0x0307a503873383ed', '0x4f8ddac642662c7b', '0x880a2b8923b753b9', '0x555e02695ba71c4b', '0x602bbaa3ae7f3df3', '0x89c865c1b0286a0f', '0x519c7245c1b05972', '0xb4c9cb14d4f5cb27', '0x9fabb53b3093a0c1'],['0xc3255de2a5e262f6', '0xb784448972fb2770', '0xa4ea00d549571431', '0x45a22c337fd9e7b0', '0x287182295a73e5cb', '0xa24808a6cd756b23', '0xfd80b40176916b20', '0x385c2c05a01e88c7', '0x871a4fce2bf9da58', '0x38be6874cec2dfab', '0xb5b845b9dd7e6c7a', '0x2ac37898d7ab3b6a', '0x0c220f53bdce7b01', '0x5a1245438b2db20e', '0xd334bc485d92f3d8', '0x1db892c2bc97cb0b', '0x5a238c35ee29f12a', '0xbb640f62634add31', '0x9ad6871d056d0e7f', '0x6a6651c733137dcf', '0x34d5c1babf149ef7', '0xfe3edad768e25afa', '0x00cf7b9294eac04e', '0x8427ba6d9dd6193e'],['0xfce915ab6e25b3e6', '0x3688b8fa8c9f5f2c', '0x18b9f2b3bfe960f4', '0x326a77fae4be97b6', '0x96b1cfe94cbbb3fe', '0x14faa9260126b6c6', '0xb1247f567f78c70a', '0x385d2b599cb24e41', '0x177c0ac30bb6dfde', '0x06c45afb8fe169a7', '0x774b3f49d7b331e5', '0x043bc5b74dcddd15', '0xd6686614e69af832', '0x00b13abc2a3e3af5', '0x965b038aa331b415', '0xf61b80d291a40f3e', '0xdf59a4d74a728fd7', '0x25e58ab87a486039', '0xbf553e8dc30f8f85', '0x1d479d64073d2f92', '0xac79c8b3ba7185da', '0xf64bcdb3a4250bf6', '0x31cfe575eaed24f3', '0xd71997c2aeb6ea3f'],['0x4bf704fb6a8f8d11', '0x58db2b3041328f85', '0xebe72c913f9abdd3', '0x46feb18d627d5bff', '0xd03e70bc1e79149d', '0xe5c1990fb10fd8dc', '0xd159b10ee894d37a', '0x245b633f6d5b526d', '0x411fa8aba6831734', '0xc7ae395a1329b0e1', '0x06116b8774d84f8a', '0x293107b5bc6c5637', '0x57d15c428b496288', '0x65145619b98d0cb3', '0x9b4a4f48dde636ba', '0x08740a600dc09d46', '0xbb132862b24cdd70', '0xf4547a7a98c78c49', '0x75d6aade510d3184', '0x78f002115511f2e9', '0x61554fca09413122', '0xc6758a78edfc076a', '0x993dc19cb110e565', '0x6b5259f029a70694']]
+
+MDS_matrix_field = matrix(F, t, t)
+
+for i in range(0, t):
+    for j in range(0, t):
+        MDS_matrix_field[i, j] = F(int(MDS_matrix[i][j], 16))
+round_constants_field = []
+for i in range(0, (R_F + R_P) * t):
+    round_constants_field.append(F(int(round_constants[i], 16)))
+
+#MDS_matrix_field = MDS_matrix_field.transpose() # QUICK FIX TO CHANGE MATRIX MUL ORDER (BOTH M AND M^T ARE SECURE HERE!)
+
+def print_words_to_hex(words):
+    hex_length = int(ceil(float(n) / 4)) + 2 # +2 for "0x"
+    print(["{0:#0{1}x}".format(int(entry), hex_length) for entry in words])
+
+def print_concat_words_to_large(words):
+    hex_length = int(ceil(float(n) / 4))
+    nums = ["{0:0{1}x}".format(int(entry), hex_length) for entry in words]
+    final_string = "0x" + ''.join(nums)
+    print(final_string)
+
+def calc_equivalent_constants(constants):
+    constants_temp = [constants[index:index+t] for index in range(0, len(constants), t)]
+
+    MDS_matrix_field_transpose = MDS_matrix_field.transpose()
+
+    # Start moving round constants up
+    # Calculate c_i' = M^(-1) * c_(i+1)
+    # Split c_i': Add c_i'[0] AFTER the S-box, add the rest to c_i
+    # I.e.: Store c_i'[0] for each of the partial rounds, and make c_i = c_i + c_i' (where now c_i'[0] = 0)
+    num_rounds = R_F + R_P
+    R_f = R_F / 2
+    for i in range(num_rounds - 2 - R_f, R_f - 1, -1):
+        inv_cip1 = list(vector(constants_temp[i+1]) * MDS_matrix_field_transpose.inverse())
+        constants_temp[i] = list(vector(constants_temp[i]) + vector([0] + inv_cip1[1:]))
+        constants_temp[i+1] = [inv_cip1[0]] + [0] * (t-1)
+
+    return constants_temp
+
+def calc_equivalent_matrices():
+    # Following idea: Split M into M' * M'', where M'' is "cheap" and M' can move before the partial nonlinear layer
+    # The "previous" matrix layer is then M * M'. Due to the construction of M', the M[0,0] and v values will be the same for the new M' (and I also, obviously)
+    # Thus: Compute the matrices, store the w_hat and v_hat values
+
+    MDS_matrix_field_transpose = MDS_matrix_field.transpose()
+
+    w_hat_collection = []
+    v_collection = []
+    v = MDS_matrix_field_transpose[[0], list(range(1,t))]
+    # print "M:", MDS_matrix_field_transpose
+    # print "v:", v
+    M_mul = MDS_matrix_field_transpose
+    M_i = matrix(F, t, t)
+    for i in range(R_P - 1, -1, -1):
+        M_hat = M_mul[list(range(1,t)), list(range(1,t))]
+        w = M_mul[list(range(1,t)), [0]]
+        v = M_mul[[0], list(range(1,t))]
+        v_collection.append(v.list())
+        w_hat = M_hat.inverse() * w
+        w_hat_collection.append(w_hat.list())
+
+        # Generate new M_i, and multiplication M * M_i for "previous" round
+        M_i = matrix.identity(t)
+        M_i[list(range(1,t)), list(range(1,t))] = M_hat
+        #M_mul = MDS_matrix_field_transpose * M_i
+
+        test_mat = matrix(F, t, t)
+        test_mat[[0], list(range(0, t))] = MDS_matrix_field_transpose[[0], list(range(0, t))]
+        test_mat[[0], list(range(1, t))] = v
+        test_mat[list(range(1, t)), [0]] = w_hat
+        test_mat[list(range(1,t)), list(range(1,t))] = matrix.identity(t-1)
+
+        # print M_mul == M_i * test_mat
+        M_mul = MDS_matrix_field_transpose * M_i
+        #return[M_i, test_mat]
+
+
+        #M_mul = MDS_matrix_field_transpose * M_i
+        #exit()
+    #exit()
+        
+
+    # print [M_i, w_hat_collection, MDS_matrix_field_transpose[0, 0], v.list()]
+    return [M_i, v_collection, w_hat_collection, MDS_matrix_field_transpose[0, 0]]
+
+def cheap_matrix_mul(state_words, v, w_hat, M_0_0):
+    state_words_new = [0] * t
+    # row_1 = [M_0_0] + v
+    # print "r1:", row_1
+    # state_words_new[0] = sum([row_1[i] * state_words[i] for i in range(0, t)])
+    # mul_column = [(state_words[0] * w_hat[i]) for i in range(0, t-1)]
+    # add_column = [(mul_column[i] + state_words[i+1]) for i in range(0, t-1)]
+    # state_words_new = [state_words_new[0]] + add_column
+    # print "1:", state_words_new
+    column_1 = [M_0_0] + w_hat
+    state_words_new[0] = sum([column_1[i] * state_words[i] for i in range(0, t)])
+    mul_row = [(state_words[0] * v[i]) for i in range(0, t-1)]
+    add_row = [(mul_row[i] + state_words[i+1]) for i in range(0, t-1)]
+    state_words_new = [state_words_new[0]] + add_row
+
+    # test_mat = matrix(F, t, t)
+    # # print "r2:", matrix([M_0_0] + v).list()
+    # # print row_1 == matrix([M_0_0] + v).list()
+    # test_mat[[0], range(0, t)] = matrix([M_0_0] + v)
+    # test_mat[range(1, t), [0]] = matrix(w_hat).transpose()
+    # test_mat[range(1,t), range(1,t)] = matrix.identity(t-1)
+    # state_words_new = list(vector(state_words) * test_mat)
+    # print "2:", state_words_new
+
+    return state_words_new
+
+def perm(input_words):
+    round_constants_field_new = calc_equivalent_constants(round_constants_field)
+    [M_i, v_collection, w_hat_collection, M_0_0] = calc_equivalent_matrices()
+    #[M_i, test_mat] = calc_equivalent_matrices()
+    
+    global timer_start, timer_end
+
+    timer_start = time.time()
+
+    R_f = int(R_F / 2)
+
+    round_constants_round_counter = 0
+
+    state_words = list(input_words)
+
+    # First full rounds
+    for r in range(0, R_f):
+        # Round constants, nonlinear layer, matrix multiplication
+        for i in range(0, t):
+            state_words[i] = state_words[i] + round_constants_field_new[round_constants_round_counter][i]
+        for i in range(0, t):
+            state_words[i] = (state_words[i])^3
+        state_words = list(MDS_matrix_field * vector(state_words))
+        round_constants_round_counter += 1
+
+    # Middle partial rounds
+    # Initial constants addition
+    for i in range(0, t):
+        state_words[i] = state_words[i] + round_constants_field_new[round_constants_round_counter][i]
+    # First full matrix multiplication
+    state_words = list(vector(state_words) * M_i)
+    for r in range(0, R_P):
+        # Round constants, nonlinear layer, matrix multiplication
+        #state_words = list(vector(state_words) * M_i)
+        state_words[0] = (state_words[0])^3
+        # Moved constants addition
+        if r < (R_P - 1):
+            round_constants_round_counter += 1
+            state_words[0] = state_words[0] + round_constants_field_new[round_constants_round_counter][0]
+        # Optimized multiplication with cheap matrices
+        state_words = cheap_matrix_mul(state_words, v_collection[R_P - r - 1], w_hat_collection[R_P - r - 1], M_0_0)
+    round_constants_round_counter += 1
+
+    # Last full rounds
+    for r in range(0, R_f):
+        # Round constants, nonlinear layer, matrix multiplication
+        for i in range(0, t):
+            state_words[i] = state_words[i] + round_constants_field_new[round_constants_round_counter][i]
+        for i in range(0, t):
+            state_words[i] = (state_words[i])^3
+        state_words = list(MDS_matrix_field * vector(state_words))
+        round_constants_round_counter += 1
+
+    timer_end = time.time()
+    
+    return state_words
+
+def perm_original(input_words):
+    round_constants_field_new = [round_constants_field[index:index+t] for index in range(0, len(round_constants_field), t)]
+
+    global timer_start, timer_end
+    
+    timer_start = time.time()
+
+    R_f = int(R_F / 2)
+
+    round_constants_round_counter = 0
+
+    state_words = list(input_words)
+
+    # First full rounds
+    for r in range(0, R_f):
+        # Round constants, nonlinear layer, matrix multiplication
+        for i in range(0, t):
+            state_words[i] = state_words[i] + round_constants_field_new[round_constants_round_counter][i]
+        for i in range(0, t):
+            state_words[i] = (state_words[i])^3
+        state_words = list(MDS_matrix_field * vector(state_words))
+        round_constants_round_counter += 1
+
+    # Middle partial rounds
+    for r in range(0, R_P):
+        # Round constants, nonlinear layer, matrix multiplication
+        for i in range(0, t):
+            state_words[i] = state_words[i] + round_constants_field_new[round_constants_round_counter][i]
+        state_words[0] = (state_words[0])^3
+        state_words = list(MDS_matrix_field * vector(state_words))
+        round_constants_round_counter += 1
+
+    # Last full rounds
+    for r in range(0, R_f):
+        # Round constants, nonlinear layer, matrix multiplication
+        for i in range(0, t):
+            state_words[i] = state_words[i] + round_constants_field_new[round_constants_round_counter][i]
+        for i in range(0, t):
+            state_words[i] = (state_words[i])^3
+        state_words = list(MDS_matrix_field * vector(state_words))
+        round_constants_round_counter += 1
+    
+    timer_end = time.time()
+
+    return state_words
+
+input_words = []
+for i in range(0, t):
+    input_words.append(F(i))
+
+output_words = None
+num_iterations = 10
+total_time_passed = 0
+for i in range(0, num_iterations):
+    output_words = perm_original(input_words)
+    time_passed = timer_end - timer_start
+    total_time_passed += time_passed
+average_time = total_time_passed / float(num_iterations)
+print("Average time for unoptimized:", average_time)
+
+# print "Input:"
+# print_words_to_hex(input_words)
+# print "Output:"
+# print_words_to_hex(output_words)
+
+print("Input (concat):")
+print_concat_words_to_large(input_words)
+print("Output (concat):")
+print_concat_words_to_large(output_words)
+
+total_time_passed = 0
+for i in range(0, num_iterations):
+    output_words = perm(input_words)
+    time_passed = timer_end - timer_start
+    total_time_passed += time_passed
+average_time = total_time_passed / float(num_iterations)
+print("Average time for optimized:", average_time)
+
+# print "Input:"
+# print_words_to_hex(input_words)
+# print "Output:"
+# print_words_to_hex(output_words)
+
+print("Input (concat):")
+print_concat_words_to_large(input_words)
+print("Output (concat):")
+print_concat_words_to_large(output_words)
diff --git a/[Tho09]poseidon-hash/reference/hadeshash/code/poseidonperm_x5_254_3.sage b/[Tho09]poseidon-hash/reference/hadeshash/code/poseidonperm_x5_254_3.sage
new file mode 100644
index 0000000..c1f8089
--- /dev/null
+++ b/[Tho09]poseidon-hash/reference/hadeshash/code/poseidonperm_x5_254_3.sage
@@ -0,0 +1,87 @@
+# M = 128
+N = 762
+t = 3
+n = int(N / t)
+R_F = 8
+R_P = 57
+prime = 0x30644e72e131a029b85045b68181585d2833e84879b9709143e1f593f0000001
+F = GF(prime)
+
+round_constants = ['0x0ee9a592ba9a9518d05986d656f40c2114c4993c11bb29938d21d47304cd8e6e', '0x00f1445235f2148c5986587169fc1bcd887b08d4d00868df5696fff40956e864', '0x08dff3487e8ac99e1f29a058d0fa80b930c728730b7ab36ce879f3890ecf73f5', '0x2f27be690fdaee46c3ce28f7532b13c856c35342c84bda6e20966310fadc01d0', '0x2b2ae1acf68b7b8d2416bebf3d4f6234b763fe04b8043ee48b8327bebca16cf2', '0x0319d062072bef7ecca5eac06f97d4d55952c175ab6b03eae64b44c7dbf11cfa', '0x28813dcaebaeaa828a376df87af4a63bc8b7bf27ad49c6298ef7b387bf28526d', '0x2727673b2ccbc903f181bf38e1c1d40d2033865200c352bc150928adddf9cb78', '0x234ec45ca27727c2e74abd2b2a1494cd6efbd43e340587d6b8fb9e31e65cc632', '0x15b52534031ae18f7f862cb2cf7cf760ab10a8150a337b1ccd99ff6e8797d428', '0x0dc8fad6d9e4b35f5ed9a3d186b79ce38e0e8a8d1b58b132d701d4eecf68d1f6', '0x1bcd95ffc211fbca600f705fad3fb567ea4eb378f62e1fec97805518a47e4d9c', '0x10520b0ab721cadfe9eff81b016fc34dc76da36c2578937817cb978d069de559', '0x1f6d48149b8e7f7d9b257d8ed5fbbaf42932498075fed0ace88a9eb81f5627f6', '0x1d9655f652309014d29e00ef35a2089bfff8dc1c816f0dc9ca34bdb5460c8705', '0x04df5a56ff95bcafb051f7b1cd43a99ba731ff67e47032058fe3d4185697cc7d', '0x0672d995f8fff640151b3d290cedaf148690a10a8c8424a7f6ec282b6e4be828', '0x099952b414884454b21200d7ffafdd5f0c9a9dcc06f2708e9fc1d8209b5c75b9', '0x052cba2255dfd00c7c483143ba8d469448e43586a9b4cd9183fd0e843a6b9fa6', '0x0b8badee690adb8eb0bd74712b7999af82de55707251ad7716077cb93c464ddc', '0x119b1590f13307af5a1ee651020c07c749c15d60683a8050b963d0a8e4b2bdd1', '0x03150b7cd6d5d17b2529d36be0f67b832c4acfc884ef4ee5ce15be0bfb4a8d09', '0x2cc6182c5e14546e3cf1951f173912355374efb83d80898abe69cb317c9ea565', '0x005032551e6378c450cfe129a404b3764218cadedac14e2b92d2cd73111bf0f9', '0x233237e3289baa34bb147e972ebcb9516469c399fcc069fb88f9da2cc28276b5', '0x05c8f4f4ebd4a6e3c980d31674bfbe6323037f21b34ae5a4e80c2d4c24d60280', '0x0a7b1db13042d396ba05d818a319f25252bcf35ef3aeed91ee1f09b2590fc65b', '0x2a73b71f9b210cf5b14296572c9d32dbf156e2b086ff47dc5df542365a404ec0', 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'0x169a177f63ea681270b1c6877a73d21bde143942fb71dc55fd8a49f19f10c77b', '0x04ef51591c6ead97ef42f287adce40d93abeb032b922f66ffb7e9a5a7450544d', '0x256e175a1dc079390ecd7ca703fb2e3b19ec61805d4f03ced5f45ee6dd0f69ec', '0x30102d28636abd5fe5f2af412ff6004f75cc360d3205dd2da002813d3e2ceeb2', '0x10998e42dfcd3bbf1c0714bc73eb1bf40443a3fa99bef4a31fd31be182fcc792', '0x193edd8e9fcf3d7625fa7d24b598a1d89f3362eaf4d582efecad76f879e36860', '0x18168afd34f2d915d0368ce80b7b3347d1c7a561ce611425f2664d7aa51f0b5d', '0x29383c01ebd3b6ab0c017656ebe658b6a328ec77bc33626e29e2e95b33ea6111', '0x10646d2f2603de39a1f4ae5e7771a64a702db6e86fb76ab600bf573f9010c711', '0x0beb5e07d1b27145f575f1395a55bf132f90c25b40da7b3864d0242dcb1117fb', '0x16d685252078c133dc0d3ecad62b5c8830f95bb2e54b59abdffbf018d96fa336', '0x0a6abd1d833938f33c74154e0404b4b40a555bbbec21ddfafd672dd62047f01a', '0x1a679f5d36eb7b5c8ea12a4c2dedc8feb12dffeec450317270a6f19b34cf1860', '0x0980fb233bd456c23974d50e0ebfde4726a423eada4e8f6ffbc7592e3f1b93d6', '0x161b42232e61b84cbf1810af93a38fc0cece3d5628c9282003ebacb5c312c72b', '0x0ada10a90c7f0520950f7d47a60d5e6a493f09787f1564e5d09203db47de1a0b', '0x1a730d372310ba82320345a29ac4238ed3f07a8a2b4e121bb50ddb9af407f451', '0x2c8120f268ef054f817064c369dda7ea908377feaba5c4dffbda10ef58e8c556', '0x1c7c8824f758753fa57c00789c684217b930e95313bcb73e6e7b8649a4968f70', '0x2cd9ed31f5f8691c8e39e4077a74faa0f400ad8b491eb3f7b47b27fa3fd1cf77', '0x23ff4f9d46813457cf60d92f57618399a5e022ac321ca550854ae23918a22eea', '0x09945a5d147a4f66ceece6405dddd9d0af5a2c5103529407dff1ea58f180426d', '0x188d9c528025d4c2b67660c6b771b90f7c7da6eaa29d3f268a6dd223ec6fc630', '0x3050e37996596b7f81f68311431d8734dba7d926d3633595e0c0d8ddf4f0f47f', '0x15af1169396830a91600ca8102c35c426ceae5461e3f95d89d829518d30afd78', '0x1da6d09885432ea9a06d9f37f873d985dae933e351466b2904284da3320d8acc', '0x2796ea90d269af29f5f8acf33921124e4e4fad3dbe658945e546ee411ddaa9cb', '0x202d7dd1da0f6b4b0325c8b3307742f01e15612ec8e9304a7cb0319e01d32d60', '0x096d6790d05bb759156a952ba263d672a2d7f9c788f4c831a29dace4c0f8be5f', '0x054efa1f65b0fce283808965275d877b438da23ce5b13e1963798cb1447d25a4', '0x1b162f83d917e93edb3308c29802deb9d8aa690113b2e14864ccf6e18e4165f1', '0x21e5241e12564dd6fd9f1cdd2a0de39eedfefc1466cc568ec5ceb745a0506edc', '0x1cfb5662e8cf5ac9226a80ee17b36abecb73ab5f87e161927b4349e10e4bdf08', '0x0f21177e302a771bbae6d8d1ecb373b62c99af346220ac0129c53f666eb24100', '0x1671522374606992affb0dd7f71b12bec4236aede6290546bcef7e1f515c2320', '0x0fa3ec5b9488259c2eb4cf24501bfad9be2ec9e42c5cc8ccd419d2a692cad870', '0x193c0e04e0bd298357cb266c1506080ed36edce85c648cc085e8c57b1ab54bba', '0x102adf8ef74735a27e9128306dcbc3c99f6f7291cd406578ce14ea2adaba68f8', '0x0fe0af7858e49859e2a54d6f1ad945b1316aa24bfbdd23ae40a6d0cb70c3eab1', '0x216f6717bbc7dedb08536a2220843f4e2da5f1daa9ebdefde8a5ea7344798d22', '0x1da55cc900f0d21f4a3e694391918a1b3c23b2ac773c6b3ef88e2e4228325161']
+
+MDS_matrix = [['0x109b7f411ba0e4c9b2b70caf5c36a7b194be7c11ad24378bfedb68592ba8118b', '0x16ed41e13bb9c0c66ae119424fddbcbc9314dc9fdbdeea55d6c64543dc4903e0', '0x2b90bba00fca0589f617e7dcbfe82e0df706ab640ceb247b791a93b74e36736d'],['0x2969f27eed31a480b9c36c764379dbca2cc8fdd1415c3dded62940bcde0bd771', '0x2e2419f9ec02ec394c9871c832963dc1b89d743c8c7b964029b2311687b1fe23', '0x101071f0032379b697315876690f053d148d4e109f5fb065c8aacc55a0f89bfa'],['0x143021ec686a3f330d5f9e654638065ce6cd79e28c5b3753326244ee65a1b1a7', '0x176cc029695ad02582a70eff08a6fd99d057e12e58e7d7b6b16cdfabc8ee2911', '0x19a3fc0a56702bf417ba7fee3802593fa644470307043f7773279cd71d25d5e0']]
+
+MDS_matrix_field = matrix(F, t, t)
+for i in range(0, t):
+    for j in range(0, t):
+        MDS_matrix_field[i, j] = F(int(MDS_matrix[i][j], 16))
+round_constants_field = []
+for i in range(0, (R_F + R_P) * t):
+    round_constants_field.append(F(int(round_constants[i], 16)))
+
+#MDS_matrix_field = MDS_matrix_field.transpose() # QUICK FIX TO CHANGE MATRIX MUL ORDER (BOTH M AND M^T ARE SECURE HERE!)
+
+def print_words_to_hex(words):
+    hex_length = int(ceil(float(n) / 4)) + 2 # +2 for "0x"
+    print(["{0:#0{1}x}".format(int(entry), hex_length) for entry in words])
+
+def print_concat_words_to_large(words):
+    hex_length = int(ceil(float(n) / 4))
+    nums = ["{0:0{1}x}".format(int(entry), hex_length) for entry in words]
+    final_string = "0x" + ''.join(nums)
+    print(final_string)
+
+def perm(input_words):
+
+    R_f = int(R_F / 2)
+
+    round_constants_counter = 0
+
+    state_words = list(input_words)
+
+    # First full rounds
+    for r in range(0, R_f):
+        # Round constants, nonlinear layer, matrix multiplication
+        for i in range(0, t):
+            state_words[i] = state_words[i] + round_constants_field[round_constants_counter]
+            round_constants_counter += 1
+        for i in range(0, t):
+            state_words[i] = (state_words[i])^5
+        state_words = list(MDS_matrix_field * vector(state_words))
+
+    # Middle partial rounds
+    for r in range(0, R_P):
+        # Round constants, nonlinear layer, matrix multiplication
+        for i in range(0, t):
+            state_words[i] = state_words[i] + round_constants_field[round_constants_counter]
+            round_constants_counter += 1
+        state_words[0] = (state_words[0])^5
+        state_words = list(MDS_matrix_field * vector(state_words))
+
+    # Last full rounds
+    for r in range(0, R_f):
+        # Round constants, nonlinear layer, matrix multiplication
+        for i in range(0, t):
+            state_words[i] = state_words[i] + round_constants_field[round_constants_counter]
+            round_constants_counter += 1
+        for i in range(0, t):
+            state_words[i] = (state_words[i])^5
+        state_words = list(MDS_matrix_field * vector(state_words))
+    
+    return state_words
+
+input_words = []
+for i in range(0, t):
+    input_words.append(F(i))
+
+output_words = perm(input_words)
+
+print("Input:")
+print_words_to_hex(input_words)
+print("Output:")
+print_words_to_hex(output_words)
+
+print("Input (concat):")
+print_concat_words_to_large(input_words)
+print("Output (concat):")
+print_concat_words_to_large(output_words)
diff --git a/[Tho09]poseidon-hash/reference/hadeshash/code/poseidonperm_x5_254_5.sage b/[Tho09]poseidon-hash/reference/hadeshash/code/poseidonperm_x5_254_5.sage
new file mode 100644
index 0000000..c7723be
--- /dev/null
+++ b/[Tho09]poseidon-hash/reference/hadeshash/code/poseidonperm_x5_254_5.sage
@@ -0,0 +1,87 @@
+# M = 128
+N = 1270
+t = 5
+n = int(N / t)
+R_F = 8
+R_P = 60
+prime = 0x30644e72e131a029b85045b68181585d2833e84879b9709143e1f593f0000001
+F = GF(prime)
+
+round_constants = ['0x0eb544fee2815dda7f53e29ccac98ed7d889bb4ebd47c3864f3c2bd81a6da891', '0x0554d736315b8662f02fdba7dd737fbca197aeb12ea64713ba733f28475128cb', '0x2f83b9df259b2b68bcd748056307c37754907df0c0fb0035f5087c58d5e8c2d4', '0x2ca70e2e8d7f39a12447ac83052451b461f15f8b41a75ef31915208f5aba9683', '0x1cb5f9319be6a45e91b04d7222271c94994196f12ed22c5d4ec719cb83ecfea9', '0x2eb4f99c69f966ebf8a42192de7ff61621c7bb47b93750c2b9ea08d18446c122', '0x224a28e5a35385a7c5198169e405d9ea0fc7da8b93ee13b6d5f7d099e299520e', '0x0f7411b465e600eed8afdd6afca49c3036f33ecbd9a0f97823796b993bbd82f7', '0x0f9d0d5aad2c9555a2be7150392d8d9819b208ae3370f99a0626f9ff5d90e4e3', '0x1e9a96dc8292bb596f52a59538d329229732b25259cf744b6a12d30702d6fba0', '0x08780514ccd90380887d578c45555e593cfe52eab4b945c6c2cd4d528fb3fe3c', '0x272498fced686c7ac8149fa3f73ef8c2ced64717e3556d5a59f119d629ccb5fc', '0x01ef8f9dd7c93aac4b7cb80930bd06eb45bd350aff585f10e3d0ef8a782ef7df', '0x045b9f59b6595e614dc08f222b469b138e886e64bf3c40aa97ea0ae754934d30', '0x0ac1e91c57d9da919fd6f59d2a40ff8ea3e41e24e247a387adf2584295d61c66', '0x028a1621a94054b0c7f9a421353cd89d0fd67061aee99979d12e68f04e62d134', '0x26b41802c071ea4c9632647ed059236e50c19c3fb3c96d09d02aae2a0dcd9dbc', '0x2fb5dda8072bb72cbaac2f63e468215e05c9de06758db6a94af34384aedb462b', '0x2212d3a0f5fccaf244ff3547fd823249ad8ab8ba2a18d383dd05c56ee894d850', '0x1b041ad5b2f0684258e4dfaeea09be56a3276fdb19f44c015cd0c7eed465e2e3', '0x0a01776bb22f4b6b8eccff33e76fded3144fb7e3ac14e846a91e64afb1500eff', '0x2b7b5674aaecc3cbf34d3f275066d549a4f33ae8c15cf827f7936440810ace43', '0x29d299b80cd4489e4cf75779ed54b48c60b042257b78fc004c1b803381a3bdfd', '0x1c46831d9a74529357641c219d721a74a427110032b5e1dd19dde30424be401e', '0x06d7626c953ccb72f37141dc34d578e036296c0657674f80739ae1d883e91269', '0x28ffddc86f18c136c54002748e0c410edc5c440a3022cd960f108c71cda2930c', '0x2e67f7ee5e4aa295f85deed09e400b17be67f1b7ed2ab6adb8ec0619f6fbc5e9', '0x26ce38fa636c90630e97f25114a79a2dca56859ef759e53ce7abf22c24e80f27', '0x2e6e07c3c95bf7c34dd7a01d00a7ffec42cb3d16a1f72721afacb4c4cfd35db1', '0x2aa74f7597f0c9f45f91d7961c3a54fb8890d276612e1246384b1470da24d8cc', '0x287d681a46a2faae2c7c090f668ab45b8a71313c1509183e2ec0ca639b7f73fe', '0x212bd19df812eaaef4a40600528f3d7da5d3106ff565aa3b11e29f3305e73c04', '0x1154f7cf519186bf1aafb14b350eb860f97fd9740926dab93809c28404713504', '0x1dff6385cb31f1c24637810a4bd1b16fbf5152905be36583da747e79661fc207', '0x0e444582d22b4e76c081d34c44c18e424011a34d5476252863ea3c606b551e5c', '0x0323c9e433ba66c4abab6638328f02f1815773e9c2846323ff72d3aab7e4eff8', '0x12746bbd71791059193bba79cdec448f25b8cf002740112db70f2c6876a9c29d', '0x1173b7d112c2a798fd9b9d3751842c75d466c837cf50d73efd049eb4438a2240', '0x13d51c1090a1ad4876d1e555d7fed13da8e5713b25026ebe5fdb4808703243da', '0x00874c1344a4ad51ff8dcb7cbd2d9743cb72743f0394efe7f4a58ebeb956baa1', '0x22df22131aaab85865ce236b07f244fa0eea48d3546e97d6a32a562074fef08f', '0x0bf964d2dbd25b908708b437a445fc3e984524a59101e6c18bf5eb05a919f155', '0x09b18d9b917a55bca302be1f7f181e0e640b9d73a9ab298c69b435b5fc502f32', '0x094f5534444fae36a4bfc1d5bf3dc05bfbbbc70a6365366dd6745a5067289e43', '0x2999bab1a5f25210519fa6622af53a15a3e240c0da5701cb784fddc0dc23f01f', '0x2f6898c07581f6371ca94db73710e88084301bce8a93d13669575a11b03a3d23', '0x07268eaaba08bc19ec16d7e1318a4740565deb1e8e5742f862174b1a6866fccb', '0x186279b003454db01339ff77113bc9eb62603e078e1c6689a6c9582c41a0529f', '0x18a3f736509197d6e4915bdd04d3e5ddb67e2cc5de9a22750768e5524737172c', '0x0a21fa1988cf38d877cc1e2ed24c808c725e2d4bcb2d3a007b5987b87085671d', '0x15b285cbe26c467f1faf5ef6a64625228328c184a2c43bc00b36a135e785fba2', '0x164b7062c4671cf08c08b8c3f9806d560b7775b7c902f5788cd28de3e779f161', '0x0890ba0819ac0a6f86d9865fe7e50ef361c61d3d43b6e65d7a24f651249baa70', '0x2fbea4d65d7ed425a42712e5a721e4eaa627ac5cb0eb878ccc2ee0aed543e922', '0x0492bf383c36fa55540303a3b536f85e7b70a58e854ab9b9103d7f5f379abaaa', '0x05e91fe944e944104e20251c565142d61d6185a9ce85675f6a969d56292dc24e', '0x12fe5c2029e4b33893d463cb041acad0995b9621e6e49c3b7e380a76e36e6c1c', '0x024154adf0255d47958f7723921474131f2629fadc89496906cd01dc6fa0784e', '0x18824a09e6afaf4a36ed2462a86bd0bad798815644f2bbde8813c13457a45550', '0x0c8b482dba0ad51be9f255de0c3dbddddf84a630af68d50bbb06983e3d5d58a5', '0x17325fd0ab635871363e0a1667d3b67c5a4fa67fcd6aaf86441392878fdb05e6', '0x050ae95f6d2f1519122f5af67b690f31e550773fa8d18bf71cc6d0e911fa402e', '0x0f0d139a0e81e943038cb288d62636764bbb6295f07569885771ec84edc50c40', '0x1c0f8697795689cdf70fd2f2c0f93d1a79b39ebc7a1b1c549dbbca7b8e747cd6', '0x2bd0f940ad936b796d2bc2e048bc979e49be23a4b13598f9fe536a16dc1d81e6', '0x27eb1be27c9c4e934778c09a0053337fa06ebb275e096d167ce54d1e96ee62cb', '0x2e4889d830a67e5a8f96bdd3155a7ca3284fbd307d1f71b0f151be62548e2aea', '0x193fe3db0ab47d3c5d2ec5e9c5bd9983c9891f2cadc165db6064bbe6fcc1e305', '0x2bf3086e96c36c7bce415907ad0c40ed6e9661c009679e4e37cb13027c83e525', '0x12f16e2de6d4ad46a98cdb697c6cad5dd5e7e413f741ccf29ff2ea486e59bb28', '0x2a72147d230119f3a0262e3653ddd19f33f3d5d6ec6c4bf0ad919b0343b92d2f', '0x21be0e2c4bfd64e56dc47f957806dc5f0a2d9bcc26412e2977df79acc10ba974', '0x0e2d7e1dc946d70b2749a3b54367b25a71b84fb911aa57ae137fd4b6c21b444a', '0x2667f7fb5a4fa1246170a745d8a4188cc31adb0eae3325dc9f3f07d4b92b3e2e', '0x2ccc6f431fb7400730a783b66064697a1550c12b08dfeb72830e107da78e3405', '0x08888a94fc5a2ca34f0201462420001fae6dbee9e8ca0c242ec50621e38e6e5d', '0x02977b34eeaa3cb6ad40dd42c9b6fdd7a0d2fbe753af88b36acfcd3ccbc53f2a', '0x120ccce13d28b75cfd6fb6c9ea13a648bfcfe0d7e6ff8e9610b5e9f971e16b9a', '0x09fad2269c4a8e93c81e1b9770ea098c92787a4575b2bd73a0bf2af32f86ff3c', '0x026091fd3d4c44d50a4b310e4ac6f0fa0debdb70775eeb8af630cffb60092d6f', '0x29404aa2ba565b77bb7fba9dfb6fc3212543cc56afad6afcb904fd2bca893994', '0x2749475c399aaf39d4e87c2548695b4ef1ffd86590e0827de7201351b7c883f9', '0x098c842322479f7239912b50424685cba2ebe2dc2e4da70ac7557dab65ffa222', '0x18cef581222b647e31238e57fead7d5c758ace14c93c4da40191d0c053b51936', 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'0x2de32ad15497aef4d504d4deeb53b13c66db790ce486130caa9dc2b57ef5be0d', '0x0dc108f2b0a280d2fd5d341310722a2d28c738dddaec9f3d255754448eefd001', '0x1869f3b763fe8164c96858a1bb9efad5bcdc3eebc409be7c7d34ca50365d832f', '0x022ed3a2d9ff31cbf82559fe6a911843b616945e16a568d48c6d33767129682d', '0x2155d6005210169e3944ed1365bd0e7292fca1f27c19c26610c6aec077d026bc', '0x0de1ba7a562a8f7acae93263f5f1b4bbec0c0556c91af3db3ea5928c8caeae85', '0x05dbb4406024beabcfce5bf46ec7da38126f740bce8d637b6351dfa7da902563', '0x05d4149baac413bed4d8dc8ad778d32c00e789e3fcd72dccc97e5427a368fd5e', '0x01cdf8b452d97c2b9be5046e7397e76ff0b6802fa941c7879212e22172c27b2e', '0x1fc6a71867027f56af8085ff81adce33c4d7c5015eced8c71b0a22279d46c07c', '0x1040bef4c642d0345d4d59a5a7a3a42ba9e185b75306d9c3568e0fda96aaafc2', '0x16b79c3a6bf316e0ff2c91b289334a4d2b21e95676431918a8081475ab8fad0d', '0x20dff1bc30f6db6b434b3a1387e3c8c6a34070e52b601fc13cbe1cdcd59f474e', '0x0212ac2ab7a6eaaec254955030a970f8062dd4171a726a8bdfb7fd8512ae060d', '0x2f29377491474442869a109c9215637cb02dc03134f0044213c8119f6996ae09', '0x0984ca6a5f9185d525ec93c33fea603273be9f3866aa284c5837d9f32d814bfa', '0x0d080a6b6b3b60700d299bd6fa81220de491361c8a6bd19ceb0ee9294b24f028', '0x0e65cd99e84b052f6789530638cb0ad821acc85b6400264dce929ed7c85a4544', '0x2e208875bc7ac1224808f72c716cd05ee30e3d20380ff6a655975da12736920b', '0x2989f3ae477c2fd376a0b0ff3d7dfac1ae2e3b894afd29f64a60d1aa8592bad5', '0x11361ce544e941379222d101e6fac0ce918106a463290a3e3a74c3cea7189459', '0x1e8d014b86cb5a7da539e10c173f6a75d122a822b8fb366c34c8bd05a2061438', '0x173f65adec8deee27ba812ad29558e23a0c2324167ef6c91212ee2c28ee98733', '0x01c36daaf9f01f1bafee8bd0c779ac3e5da5df7ad45499d0991bd695310eddd9', '0x1353acb08c05adb4aa9ab1c485bb85fff277d1a3f2fc89944a6f5741f381e562', '0x2e5abd2537207cad1860e71ea1188ee4009d33deb4f93aeb20f1c87a3b064d34', '0x191d5c5edaef42d3d02eedbb7ab8562513deb4eb34913a13421726ba8f69455c', '0x11d7f8d1f269264282a263fea6d7599d82a04c74c127de9dee7939dd2dcd089e', '0x04218fde366829ed90f79ad5e67997973445cb4cd6bc6f951bad085286cac971', '0x0070772f7cf52453048397ca5f47a202027b73b489301c3227b71c730d76d6dd', '0x038a389baef5d9a7c865b065687a1d9b67681a98cd051634c1dc04dbe3d2b861', '0x09a5eefab8b36a80cda446b2b4b59ccd0f39d00966a50beaf19860789015a6e5', '0x01b588848b8b47c8b969c145109b4b583d9ec99edfacb7489d16212c7584cd8c', '0x0b846e4a390e560f6e1af6dfc3341419545e5abfa323d817fed91e30d42954a6', '0x23a6679c7d9adb660d43a02ddb900040eb1513bc394fc4f985cabfe85ce72fe3', '0x2e0374a699197e343e5caa35f1351e9f4c3402fb7c85ecccf72f31d6fe089254', '0x0752cd899e52dc4d7f7a08af4cde3ff64b8cc0b1176bb9ec37d41913a7a27b48', '0x068f8813127299dac349a2b6d57397a50275142b664b802c99e2873dd7ae55a7', '0x2ba70a102355d549677574167434b3f986872d04a295b5b8b374330f2da202b5', '0x2c467af88748abf6a334d1df03b5521309f9099b825dd289b8609e70a0b50828', '0x05c5f20bef1bd82701009a2b448ae881e3a52c2d1a31957296d29e5763e8f497', '0x0dc6385fdc567be5842a381f6006e2c60cd083a2c649d9f23ac8c9fe61b73871', '0x142d3983f3dc7f7e19d49911b8670fa70378d5b84150d25ed255baa8114b369c', '0x29a01efb2f6aa894fd7e6d98c96a0fa0f36f86a7a99aa35c00fa18c1b2df67bf', '0x0525ffee737d605138c4a5066644ec630ab9e8afc64555b7d2a1af04eb613a76', '0x1e807dca81d79581f076677ca0e822767e164f614910264ef177cf4238301dc8', '0x0385fb3f89c74dc993510816472474d34c0223e0f733a52fdba56082dbd8757c', '0x037640dc1afc0143e1a6298e53cae59fcfabd7016fd6ef1af558f337bab0ea01', '0x1341999a1ed86919f12a6c5260829eee5fd56cf031da8050b7e4c0de896074b4', '0x069eb075866b0af356906d4bafb10ad773afd642efdcc5657b244f65bed8ece7', '0x171c0b81e62136e395b38e8e08b3e646d2726101d3afaa02ea1909a619033696', '0x2c81814c9453f51cb6eb55c311753e84cbbdcb39bfe696f95575107502acced8', '0x29d843c0415d35d9e3b33fadcf274b2ab04b39032adca92ce39b8a86a7c3a604', '0x085d6a1070f3513d8436bccdabb78750d8e15ea5947f2cdaa7669cf3fae7728b', '0x11820363ed541daa10a44ba665bf302cdbf1dd4e6706b02c9e2a5cda412fc394', '0x201935a58f5c57fc02b60d61a83785bddfd3150e05f1df5d105840b751a16317', '0x0a8c2820c56971aae27a952abd33a03d46794eedd686cd8ecfed610e87c02e9a', '0x180638ff301a64ca04abd6d0bd7500b6650b65ff33e6be1fd50dbc163a281877', '0x095c716266f1de59044f97114a4158a3f85ca8a937cfbec63e9b321a812dd36b', '0x17c31ea02fbc378320d86ffed6c7ca1583b618c5c1a687818d4087a497d73490', '0x05b86c4bb8ef318b6a7227e4192d149d3c17a9764ccd660de4d50a77f192a91b', '0x265bc95df4a4c4876ff70d7ea2fde2c7ab15f4a6ae0d237cd6ce74ba986c7a7b', '0x24752b47bc6c6bc8d9bbe48f5fef2f6908701739c5f5b4b3d6c886d4715c7929', '0x14814a1e0f492a4ea0d86e527a96482178d624b98da96ee5e583b9324d974efe', '0x10def931073b6479bd60577378f29381997c8e041d3cfb3dc7523bca906f00bd', '0x14f7ae770bf7e95f7f706c0d8ab4ed03fa0b880d28c69d031b4592c98610175f', '0x1aef50a0cee751b59f926af40e8035d19decc9d428ebe4e775c5cc9dce1ce589', '0x041935607172f68eba65ca60068dfe3b086c2a2d57d09602951214b57e73cf5a', '0x26863e9dd24255d1573bd083959b856c0493fbefe83c819837a151d3bf452cb8', '0x2036efb6f9830965eb3d7a068bd087c9f5adf251ba62052c652738e63ff8b3af', '0x0c712a975b74dc9d766b639a029969ca30be4f75a753f854b00fa4f1b4f4ee9b', '0x08014dab3cd1667e27afc99bfac1e6807afdff6456492ca3375731d387539699', '0x198d07192db4fac2a82a4a79839d6a2b97c4dd4d37b4e8f3b53009f79b34e6a4', '0x29eb1de42a3ad381b23b4131426897a32709b29d53bb946dfd15784d1f63e572']
+
+MDS_matrix = [['0x251e7fdf99591080080b0af133b9e4369f22e57ace3cd7f64fc6fdbcf38d7da1', '0x25fb50b65acf4fb047cbd3b1c17d97c7fe26ea9ca238d6e348550486e91c7765', '0x293d617d7da72102355f39ebf62f91b06deb5325f367a4556ea1e31ed5767833', '0x104d0295ab00c85e960111ac25da474366599e575a9b7edf6145f14ba6d3c1c4', '0x0aaa35e2c84baf117dea3e336cd96a39792b3813954fe9bf3ed5b90f2f69c977'],['0x2a70b9f1d4bbccdbc03e17c1d1dcdb02052903dc6609ea6969f661b2eb74c839', '0x281154651c921e746315a9934f1b8a1bba9f92ad8ef4b979115b8e2e991ccd7a', '0x28c2be2f8264f95f0b53c732134efa338ccd8fdb9ee2b45fb86a894f7db36c37', '0x21888041e6febd546d427c890b1883bb9b626d8cb4dc18dcc4ec8fa75e530a13', '0x14ddb5fada0171db80195b9592d8cf2be810930e3ea4574a350d65e2cbff4941'],['0x2f69a7198e1fbcc7dea43265306a37ed55b91bff652ad69aa4fa8478970d401d', '0x001c1edd62645b73ad931ab80e37bbb267ba312b34140e716d6a3747594d3052', '0x15b98ce93e47bc64ce2f2c96c69663c439c40c603049466fa7f9a4b228bfc32b', '0x12c7e2adfa524e5958f65be2fbac809fcba8458b28e44d9265051de33163cf9c', '0x2efc2b90d688134849018222e7b8922eaf67ce79816ef468531ec2de53bbd167'],['0x0c3f050a6bf5af151981e55e3e1a29a13c3ffa4550bd2514f1afd6c5f721f830', '0x0dec54e6dbf75205fa75ba7992bd34f08b2efe2ecd424a73eda7784320a1a36e', '0x1c482a25a729f5df20225815034b196098364a11f4d988fb7cc75cf32d8136fa', '0x2625ce48a7b39a4252732624e4ab94360812ac2fc9a14a5fb8b607ae9fd8514a', '0x07f017a7ebd56dd086f7cd4fd710c509ed7ef8e300b9a8bb9fb9f28af710251f'],['0x2a20e3a4a0e57d92f97c9d6186c6c3ea7c5e55c20146259be2f78c2ccc2e3595', '0x1049f8210566b51faafb1e9a5d63c0ee701673aed820d9c4403b01feb727a549', '0x02ecac687ef5b4b568002bd9d1b96b4bef357a69e3e86b5561b9299b82d69c8e', '0x2d3a1aea2e6d44466808f88c9ba903d3bdcb6b58ba40441ed4ebcf11bbe1e37b', '0x14074bb14c982c81c9ad171e4f35fe49b39c4a7a72dbb6d9c98d803bfed65e64']]
+
+MDS_matrix_field = matrix(F, t, t)
+for i in range(0, t):
+    for j in range(0, t):
+        MDS_matrix_field[i, j] = F(int(MDS_matrix[i][j], 16))
+round_constants_field = []
+for i in range(0, (R_F + R_P) * t):
+    round_constants_field.append(F(int(round_constants[i], 16)))
+
+#MDS_matrix_field = MDS_matrix_field.transpose() # QUICK FIX TO CHANGE MATRIX MUL ORDER (BOTH M AND M^T ARE SECURE HERE!)
+
+def print_words_to_hex(words):
+    hex_length = int(ceil(float(n) / 4)) + 2 # +2 for "0x"
+    print(["{0:#0{1}x}".format(int(entry), hex_length) for entry in words])
+
+def print_concat_words_to_large(words):
+    hex_length = int(ceil(float(n) / 4))
+    nums = ["{0:0{1}x}".format(int(entry), hex_length) for entry in words]
+    final_string = "0x" + ''.join(nums)
+    print(final_string)
+
+def perm(input_words):
+
+    R_f = int(R_F / 2)
+
+    round_constants_counter = 0
+
+    state_words = list(input_words)
+
+    # First full rounds
+    for r in range(0, R_f):
+        # Round constants, nonlinear layer, matrix multiplication
+        for i in range(0, t):
+            state_words[i] = state_words[i] + round_constants_field[round_constants_counter]
+            round_constants_counter += 1
+        for i in range(0, t):
+            state_words[i] = (state_words[i])^5
+        state_words = list(MDS_matrix_field * vector(state_words))
+
+    # Middle partial rounds
+    for r in range(0, R_P):
+        # Round constants, nonlinear layer, matrix multiplication
+        for i in range(0, t):
+            state_words[i] = state_words[i] + round_constants_field[round_constants_counter]
+            round_constants_counter += 1
+        state_words[0] = (state_words[0])^5
+        state_words = list(MDS_matrix_field * vector(state_words))
+
+    # Last full rounds
+    for r in range(0, R_f):
+        # Round constants, nonlinear layer, matrix multiplication
+        for i in range(0, t):
+            state_words[i] = state_words[i] + round_constants_field[round_constants_counter]
+            round_constants_counter += 1
+        for i in range(0, t):
+            state_words[i] = (state_words[i])^5
+        state_words = list(MDS_matrix_field * vector(state_words))
+    
+    return state_words
+
+input_words = []
+for i in range(0, t):
+    input_words.append(F(i))
+
+output_words = perm(input_words)
+
+print("Input:")
+print_words_to_hex(input_words)
+print("Output:")
+print_words_to_hex(output_words)
+
+print("Input (concat):")
+print_concat_words_to_large(input_words)
+print("Output (concat):")
+print_concat_words_to_large(output_words)
diff --git a/[Tho09]poseidon-hash/reference/hadeshash/code/poseidonperm_x5_255_3.sage b/[Tho09]poseidon-hash/reference/hadeshash/code/poseidonperm_x5_255_3.sage
new file mode 100644
index 0000000..4d2a31c
--- /dev/null
+++ b/[Tho09]poseidon-hash/reference/hadeshash/code/poseidonperm_x5_255_3.sage
@@ -0,0 +1,87 @@
+# M = 128
+N = 765
+t = 3
+n = int(N / t)
+R_F = 8
+R_P = 57
+prime = 0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001
+F = GF(prime)
+
+round_constants = ['0x6c4ffa723eaf1a7bf74905cc7dae4ca9ff4a2c3bc81d42e09540d1f250910880', '0x54dd837eccf180c92c2f53a3476e45a156ab69a403b6b9fdfd8dd970fddcdd9a', '0x64f56d735286c35f0e7d0a29680d49d54fb924adccf8962eeee225bf9423a85e', '0x670d5b6efe620f987d967fb13d2045ee3ac8e9cbf7d30e8594e733c7497910dc', '0x2ef5299e2077b2392ca874b015120d7e7530f277e06f78ee0b28f33550c68937', '0x0c0981889405b59c384e7dfa49cd4236e2f45ed024488f67c73f51c7c22d8095', '0x0d88548e6296171b26c61ea458288e5a0d048e2fdf5659de62cfca43f1649c82', '0x3371c00f3715d44abce4140202abaaa44995f6f1df12384222f61123faa6b638', '0x4ce428fec6d178d10348f4857f0006a652911085c8d86baa706f6d7975b0fe1b', '0x1a3c26d755bf65326b03521c94582d91a3ae2c0d8dfb2a345847aece52070ab0', '0x02dbb4709583838c35a118742bf482d257ed4dfb212014c083a6b059adda82b5', '0x41f2dd64b9a0dcea721b0035259f45f2a9066690de8f13b9a48ead411d8ff5a7', '0x5f154892782617b26993eea6431580c0a82c0a4dd0efdb24688726b4108c46a8', '0x0db98520f9b97cbcdb557872f4b7f81567a1be374f60fc4281a6e04079e00c0c', '0x71564ed66b41e872ca76aaf9b2fa0ca0695f2162705ca6a1f7ef043fd957f12d', '0x69191b1fe6acbf888d0c723f754c89e8bd29cb34b1e43ab27be105ea6b38d8b8', '0x04e9919eb06ff327152cfed30028c5edc667809ce1512e5963329c7040d29350', '0x573bc78e3ed162e5edd38595feead65481c991b856178f6182a0c7090ff71288', '0x102800af87fd92eb1dec942469e076602695a1996a4db968bb7f38ddd455db0b', '0x593d1894c17e5b626f8779acc32d8f188d619c02902ef775ebe81ef1c0fb7a8f', '0x66850b1b1d5d4e07b03bac49c9feadd051e374908196a806bd296957fa2fe2b7', '0x46aaa1206232ceb480d6aa16cc03465d8e96a807b28c1e494a81c43e0faffc57', '0x2102aab97ce5bd94ffd5db908bf28b7f8c36671191d4ee9ac1c5f2fae4780579', '0x14387b24d1c0c712bbe720164c4093185fcb546a2a7d481abc94e5b8fb5178b7', '0x5f2179b3a7845836cfced83e64e206f6a6cef2cf737f020b5cfd713c9550fe9f', '0x1787986ab56e1b56b5443334562b0bc3657d27323b87e3a8485e68ab96d57188', '0x39ef4b00deefe7e7451adda44428aa22074c496de2c9ed67dcf4861da65f543a', '0x7271d384cf5c90fd0c48af190c5c765937c7468088b081a99337e6eae53bb20c', 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'0x03b8aba0ee959a4e51cb5cfc458b0f4ad3a9b59797394c3d3c9eb57adeca2308', '0x0f24cc57f3b2fbf25375c71d71bbb97b2d193fc1a203ccc514c074d461001ec4', '0x71e9bfa7f66afbafbf139a70baedfb1b202a2e51e6b6c420e28dd342a5eb0cd6', '0x3ac9c11890e96a2dcda6405a6c52a47e803d6674e65117f1a8adf701d68cd02a', '0x45c00146e1b89ad5ccb8a02202482023751b88997d8fba1af5c0e7a68dadb63c', '0x1f98bdb8dc318e3e2e28cc3d8b85e334f74b57e15b02e1637ae035b04bda3b5c', '0x2ec077dbbc7bf2affe7ddd8b8a7f900f3019cddc8ce55cf9782004f65f51257b', '0x32c377fc988f600a2c2ef5d5376e2e31faf1c2d1a618db011fbfec1ff337568d', '0x0a820d131da844383bdfc1a053d8aceec7f2eb345ab6c21d38e829db8d05861e', '0x5bd95df8a933f7b7e263e013f45a92c0e786dba563e210b77d5a40f961092e60', '0x264cf7b75095fb96b420fb3f31c064299e78e796e8b3735bd0a186cd3817708d', '0x27d3e47b2f11ada6a9a5d329e00a128c9836be92ee92429ab891e71d11dc29f2', '0x64354b412c8cfa1319e4afd891e619a8fbbde04d85bef4ad0548689295d2bce2', '0x0db0f967487ee52e0836fb7135bce37fbd32887e911de52d0b855a5afac1f770', '0x1c9a155911b36c896475995417197faad870737a9ce5d9d3a5000f5396978e9d', '0x65ae557151ae9ec7f870fa2804bfb88e669dc0f8865b140f964f1f93180ac531', '0x52c6f6242517362c066020764fef4a5574749106a6dad534d136e7fe885fcb40', '0x6e44c5bcd5dc6591e2f84290a313b71a04da8da398dd10135d22bb23df41e883', '0x2146d3e371040feba8595049a285944bd45a458dccb059c785c2adf032c8b710', '0x16db9ceb3074a795499a37c20ffc9eaca9b07a5a25824aa6adcdb19fabdff0b9', '0x5903725fd86fec14c9cf2a273017eb01d3a1785039397060650c4e228a6e6571', '0x54c75952f908e3f99e05718bd1f59bb6c414bc2aebacd81c47189885cbbc566a', '0x0dba4abc7f188e33e7f309317b7b9f5c22870ca90bcee7b576dd0b52619a39f6', '0x3950231611808399ad3ba5b78cad4c6bed6f364b9346541dfffa4d16366d257e', '0x1a6d8230bb9e8d1af552b9bab8babfe505931dd87e200fc7b3c57160a5bc4ae2', '0x6b3dd35220ecd616eea4309ac9a8118e9dc65a3f7c1ef52dde7a3d33578c43a0', '0x6da00240c3505b214c8d8ce3f48914247adb9f0ecf239d7baeada5183d31ba54', '0x37c3720b132d3a719424e29c37acb7dfbd709ec9497a3162175424bf063c6e18', '0x500f85a3d06a0b5a05c5e93ae70084802fd499c7e6ed1ee6e26b4bf8fd6838fb', '0x2b37f70d73366d32d575186d0787fc8ce539b73f83c6e7eaab27be85f4faaaf4', '0x1d8efd6e52d4f936415e5c4814f3366804e2386857a4befa2a53aab21ddb68de', '0x33303b8a8f2d811be65a977907d17d133f3a64c59fe2a9c5c2d4517e3eb390e3', '0x2c1ba860f51e0c2eaf4a9a6bf095c65fab3ee15c145f404fbb0272b5ca14a449', '0x0b0849c7a3adea03a89d101081c9c9f4f66ef917d09c7957584db9a75aec2378', '0x41e7e30c77579da7809c3e757821c869b53f103fcb752ac82f8a734d4abdc792', '0x182e66be60686c8c5e6518430845f98924fe8d7d43e628bf75ff52a716371b9c', '0x373b2508c2fca1a288fa4f54a6edf02f2661e664dcf4ff2a74f3d06b1a00ddc4', '0x1735b442b3acaad0bbe630f308e03f1aa6f56bdb029e50c1393533cee1a45c30', '0x22abe8ea470a0372911bcef1367e10aa220491d76caeaa5959feb5d75f4a1f9f', '0x5caab387eb997f774f64151ed21abfa5364a83c6f065d92bd9c92f2719b8e80b', '0x57b33094aeff828377897b56e1c432978d07c668ef25a36bc5e2e835aaeff725']
+
+MDS_matrix = [['0x3d955d6c02fe4d7cb500e12f2b55eff668a7b4386bd27413766713c93f2acfcd', '0x3798866f4e6058035dcf8addb2cf1771fac234bcc8fc05d6676e77e797f224bf', '0x2c51456a7bf2467eac813649f3f25ea896eac27c5da020dae54a6e640278fda2'],['0x20088ca07bbcd7490a0218ebc0ecb31d0ea34840e2dc2d33a1a5adfecff83b43', '0x1d04ba0915e7807c968ea4b1cb2d610c7f9a16b4033f02ebacbb948c86a988c3', '0x5387ccd5729d7acbd09d96714d1d18bbd0eeaefb2ddee3d2ef573c9c7f953307'],['0x1e208f585a72558534281562cad89659b428ec61433293a8d7f0f0e38a6726ac', '0x0455ebf862f0b60f69698e97d36e8aafd4d107cae2b61be1858b23a3363642e0', '0x569e2c206119e89455852059f707370e2c1fc9721f6c50991cedbbf782daef54']]
+
+MDS_matrix_field = matrix(F, t, t)
+for i in range(0, t):
+    for j in range(0, t):
+        MDS_matrix_field[i, j] = F(int(MDS_matrix[i][j], 16))
+round_constants_field = []
+for i in range(0, (R_F + R_P) * t):
+    round_constants_field.append(F(int(round_constants[i], 16)))
+
+#MDS_matrix_field = MDS_matrix_field.transpose() # QUICK FIX TO CHANGE MATRIX MUL ORDER (BOTH M AND M^T ARE SECURE HERE!)
+
+def print_words_to_hex(words):
+    hex_length = int(ceil(float(n) / 4)) + 2 # +2 for "0x"
+    print(["{0:#0{1}x}".format(int(entry), hex_length) for entry in words])
+
+def print_concat_words_to_large(words):
+    hex_length = int(ceil(float(n) / 4))
+    nums = ["{0:0{1}x}".format(int(entry), hex_length) for entry in words]
+    final_string = "0x" + ''.join(nums)
+    print(final_string)
+
+def perm(input_words):
+
+    R_f = int(R_F / 2)
+
+    round_constants_counter = 0
+
+    state_words = list(input_words)
+
+    # First full rounds
+    for r in range(0, R_f):
+        # Round constants, nonlinear layer, matrix multiplication
+        for i in range(0, t):
+            state_words[i] = state_words[i] + round_constants_field[round_constants_counter]
+            round_constants_counter += 1
+        for i in range(0, t):
+            state_words[i] = (state_words[i])^5
+        state_words = list(MDS_matrix_field * vector(state_words))
+
+    # Middle partial rounds
+    for r in range(0, R_P):
+        # Round constants, nonlinear layer, matrix multiplication
+        for i in range(0, t):
+            state_words[i] = state_words[i] + round_constants_field[round_constants_counter]
+            round_constants_counter += 1
+        state_words[0] = (state_words[0])^5
+        state_words = list(MDS_matrix_field * vector(state_words))
+
+    # Last full rounds
+    for r in range(0, R_f):
+        # Round constants, nonlinear layer, matrix multiplication
+        for i in range(0, t):
+            state_words[i] = state_words[i] + round_constants_field[round_constants_counter]
+            round_constants_counter += 1
+        for i in range(0, t):
+            state_words[i] = (state_words[i])^5
+        state_words = list(MDS_matrix_field * vector(state_words))
+    
+    return state_words
+
+input_words = []
+for i in range(0, t):
+    input_words.append(F(i))
+
+output_words = perm(input_words)
+
+print("Input:")
+print_words_to_hex(input_words)
+print("Output:")
+print_words_to_hex(output_words)
+
+print("Input (concat):")
+print_concat_words_to_large(input_words)
+print("Output (concat):")
+print_concat_words_to_large(output_words)
diff --git a/[Tho09]poseidon-hash/reference/hadeshash/code/poseidonperm_x5_255_5.sage b/[Tho09]poseidon-hash/reference/hadeshash/code/poseidonperm_x5_255_5.sage
new file mode 100644
index 0000000..3d16020
--- /dev/null
+++ b/[Tho09]poseidon-hash/reference/hadeshash/code/poseidonperm_x5_255_5.sage
@@ -0,0 +1,87 @@
+# M = 128
+N = 1275
+t = 5
+n = int(N / t)
+R_F = 8
+R_P = 60
+prime = 0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001
+F = GF(prime)
+
+round_constants = ['0x5ee52b2f39e240a4006e97a15a7609dce42fa9aa510d11586a56db98fa925158', '0x3e92829ce321755f769c6fd0d51e98262d7747ad553b028dbbe98b5274b9c8e1', '0x7067b2b9b65af0519cef530217d4563543852399c2af1557fcd9eb325b5365e4', '0x725e66aa00e406f247f00002487d092328c526f2f5a3c456004a71cea83845d5', '0x72bf92303a9d433709d29979a296d98f147e8e7b8ed0cb452bd9f9508f6e4711', '0x3d7e5deccc6eb706c315ff02070232127dbe99bc6a4d1b23e967d35205b87694', '0x13558f81fbc15c2793cc349a059d752c712783727e1443c74098cd66fa12b78b', '0x686f2c6d24dfb9cddbbf717708ca6e04a70f0e077766a39d5bc5de5155e6fcb2', '0x582bc59317a001ed75ffe1c225901d67d8d3764a70eb254f810afc895cbf231b', '0x076df166a42eae40f6df9e5908a54f69a77f4c507ea6dd07d671682cbc1a9534', '0x531f360b9640e565d580688ee5d09e2635997037e87129303bf8297459ab2492', '0x30be41b5a9d8af19a5f922794008a263a121837bcbe113d59621ea30beefd075', '0x39f57e4c8a1178d875210f820977f7fcd33812d444f88e471040676e3e591306', '0x3514084b13bc0be636482204d9cddb072ee674c5cb1238890ee6206a3e7bf035', '0x6372b6bc660daf6b04361caff785b46bbe59eb6a34ab93e23d6364e655dc3a36', '0x422af985e648814bec5af62c142828e002d4b014b702760106b0b90c50d11de5', '0x3296e51f12e0f5c49747c1beb050ff320e2eb7422807eb0c157a372dba2ea013', '0x3b76246abaf33b03dd5b589b80a7fac0ae7f1ad8a9623bb7cf7432c90e27358d', '0x0b40e7e02f5cb836c883c7cef72ec48e87c1808f7d829e2ee0bec0ee709f7409', '0x2ee81b5c29c93b8a6e8871c01d0380a698e547475359b4a4befc22ed2232690f', '0x341ff90fc4a8afee9b74c464955ba9b357252e915b8d39ea7c1318eda718f54d', '0x55eddabde058f3b5e9dae90873ec9bd7b05927da36925e7dfb7bc290c1da125e', '0x6b34ad8cec56aae4595c403377cd2aa990a2f09b931f832781221965bb081b1c', '0x707de76df294fb845309d2160e1bdffebefd57a80c8658899e2c95e77254c752', '0x05e9b152bfd4946b9c109f930eb01892f314597507d28c735a266f4277bb2a32', '0x1589a5cbcee13b696b6f0a1dbbabc08394ab00ed5a6ae6435020e9e3e2fc909a', '0x7116a5d027fe73fbc45bfc60fd875c3116fe3a567e830d1d2d38655223dbd7ec', '0x05382ee6ad97381eb3137f5a90ea13298dac6bc7c2204906044fafc01bfe6ae4', '0x0900bcfe5e7c1b7d0aa80c714b7b2a0c1df7473362138a9dc5c552d11c1d0015', '0x0513deb89d2e48fc729440dc08d0256a79cda84d511a04e0d92cce3c7e55a7c2', '0x6bbb5f1736d499fe3fda42ad40a2b124952ac35fe970ebde38c65cc20ad2afc8', '0x5782ac68a8da0ba09f4d17e7e4b46caa4411a27e60be92168ce75bed95453e05', '0x2d83f3324639c5d83a1ffcf6ac693eef98d8ea4877d547c62b304b0a9f4a0c28', '0x16d3a13700ec503e29ca4d0c6342864595134408b6668bbf1766bb48d7f96cba', '0x318050e971e075931253b00430d35f89f40a88fc73d62150882a8e87149d7244', '0x7180760dd839d8bffbf9b1e26826cb4f6de65fa868a8143e1dc8c2b6ac6d1ac2', '0x5cf2aa95907e59c4725cc17c8cf492f9a7eeef2de337ac227a983c444ae0e80e', '0x2b8345763484d7ec02d6ee267b7c737ca9de41e2186416bf91c65eb0cd11c0a4', '0x055aa90aa60ef9b7f3c29c7500c64e6b85929220a6418dfad37ead3928059117', '0x541d5e4be0967bf49a595c1d8290b750305a334f3347c01b57f8ba313170e1ca', '0x05c0a1f16f97f582caaf4338f018f869e8dd0fa32f007bad1a1a4780053d5817', '0x01519e13858591aa93b9c1d7f849276ac1d2011b7fd19a475371c7968d9f52cd', '0x69c30d5a27f4dffa19c956c348287a704676d999f23044036b9e687a45a1a113', '0x58c93b899aa53e06e82b6346e36338841ba7279d2b7a0ecd3aa20f292852936f', '0x06b8a12870a15479d41018fed6f1a29102ae23e13d0fbccec93ace48bdb9dc93', '0x33eda3c347379e61c2297aa1026682d22f95dc3c7e46e68ab3adb4b0939d76e2', '0x187728045111275b93a1218a148ada85a1f6e2059c443ac7d61fe81e3130b89b', '0x397ec485c5a8b0c8a03ff543e9a9e5a4dc0dd4849fe955bb77b452e2e22c4f17', '0x2f33f8de90f81248455d5a6592667092992be0468372addbaff664caa84cd2d5', '0x061a1a458994ddf9f38c5edfbd737d3ceb05deaee685058b14943e7e9246ebca', '0x4b73ab5b9d35f47307b731e3cf1a1a22e7068e2744f2af0ef6bd78bf8aae4845', '0x5578b7ad5f8d4f3b8e618af7d8d5ec8bf837d2d9486527fe2f9bf7464f8516ad', '0x50b4f055d860f89e12883209f847a4b1a2395fb419eb53c182dbb555c962255c', '0x0b2da770936d6c778be289557ddd2ca024b93fa38c5d4541344e883a69611813', '0x47d8441e1ae7cb8ffc52a18c67afff3cf7543cad51605b2d4e2513f1e1868b68', '0x619da3bf44b42acd949ed572c9f3c195ed20b0b91bcd9e95ee3750d26f3b0ebd', '0x6c9e249e89b2b4cf9cd7772950e0cc9d06688d4f051095eafd116371ede49ab7', '0x210bd3217a141c55877d4528a4e80d5d81d78de7addce85994082281a6250d4b', '0x4e1d8e4079c14c83847af6394d7dc23f33ebf71593379583ec574bf5c86ea9a6', '0x699187330fc1d606e8b31b677651a2c7d1c87d4d001018031792cad0ad3f2826', '0x2946bfc0f45c1f1a0dc4c343a85259f6a6237f064481fe66eda76f01998a01ea', '0x5543e07588375c6d800e5e42d1bfd8b7a92a2a35d65b234ded85f879f82a3d66', '0x660e9d0f2f866e8d12b40dd9d9c03cc8b9ca78600bd649f0fffb2c388dcc8b43', '0x38f06c48d4dc53cb1b69619244cc2a610fdc4229ea316980dffe9131a72b4209', '0x5c9a73a16521ddf463f9de314dd5f7255bc66add48297615b761f34e4636762d', '0x310931f0204c9936fe659e9ebbda832c930172130b3f5476c6c6ee5e7fef3e45', '0x72eb1d833664d8989998af11441ac49654c12210b3465e5ac67a99679634a3af', '0x6981346585a2a466a9255841f710e1d083bdcc21c0aa6721745e158218767a94', '0x0370a259836b3766d563ed3cdcf55ace52655111a1017d8c76eaf8f97e81d858', '0x4f63c45a324b8b974c22a20a6c670eb62d47ef900541b63f1d362b8bbe4ec418', '0x6a4c7347121c2d4745ecffaad22281cc4d58ea74453b7d2b625b890190fdc7ad', '0x36d8869bb69a51ee99622af09d6878c5b715084b25f6e4560a7498557fe87fb5', '0x18faa7f51e1b7a442f9123806872094c0de8a46a6d8402f31f0cde3fcb878394', '0x3610d022aacbe58593e0d6aa7eefdca767f5ddfe7fa1fb9fb4f80225d82b617b', '0x3b5f13d6a8bbff31569bc6860087b2a4b361146a04ad5fc7396a3d0c59f68c1c', '0x40e919335051c6aaaee033745c41b6fa36739a097d94ce6eb075ec03da2a978b', '0x2f54586ab9b7886340f8ed5254f29128a85e2fb1e3725bf3c9cd8bddadc947f1', '0x00606231b689a040363e5afc050f9fc9296d6c620a885eeaffe91be387cbe96c', '0x4b55696db6b0fa327527a76e6ab6b688561c879e53d858e4c90a1122210130e1', '0x569c39bd78356991953aef4b1a01fdf71710bb05eea1f447c3e5efe13bd62894', '0x537f73fcaa256497a2582e45105f1dc10f39c7fce9b88cab5523af3f5f82dcd9', '0x2d58d32120c25995cd0754ab9fdf9ad67d67623cfd1fcbf489f51fa6e6eee4a2', '0x37cb0f655951fca18a4ccdddd4d8466f8839ba8e320a104cb47a59cd387d322f', '0x4e29d154430c9bced788d2eed8f3e01b5da24c1d3710e490bc40ee6d5903213c', 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'0x421826bc690adac2b1f3637bc5e2333cb5e4bce3f9e8eac1a0a76df32a7ebff7', '0x30ac2452c3a07bb924b6f7ed47cd6581499d532c5f90bf7fbc69556ff3bf6b09', '0x40ce93f92b281e538efbe7cec9a22a9c005eef428dde3cdd46191630f563ba04', '0x4fc3dd6720c87f672f7b6ff129e9b2a3236ec760a71f78aee84925d8e7616e97', '0x3f3ba6f9f12ca6f934f92b17f4f3bd8ec261e5870610557f687bc734eadaa2d4', '0x11d9eedda8d94fcbed859f5787fe20b7d4483cd319d8215530e2e316c89ee635', '0x29981cff92be6c882c89feb59849d014fcd163699b5b4fdafca335552c4581d1', '0x4c4fe2838d175c666c0d3f20d8dfefdcbcdacebca86e013d8ad29b6a0cf6bb79', '0x630428a99469c03f9027d3c601864185d360d920771ea950732cf000b869a09a', '0x46a776fbf1f36d7fdfa7a210cbb2ffa533540068c169e12f127cb14d9b587056', '0x41a775960677e6c5fdf73c2a409b6e5c08e271cbb8c825f598a1801c84fde5ae', '0x3086af931c41d791deb57f7f82dc511e4d349f42b52c3e0080097c4e44373dc8', '0x155516da7a229b61392a39cc10a67112f512203cab706428f5fbbb3a9fd89fbd', '0x41bdb1e32081ac55f42969658f78e308bdf50175b619c3ca8e3bfdf1ca984684', '0x01344d21e02b9c20d0d886a02167cf8502c3614ab909ae2fa7929b12d3e88519', '0x733a3e92f74b793915beab78e87bd88a2227aa5406df54dc9a2c5e80a11f71e5', '0x6a6cc17a31ba2fe1411cdebeb0809bf4ff0069b0d6ac681edf816ef4c59b6f64', '0x0a77e0a85b06c1b152098066bd36933264641627192e3acdbf611bd002918820', '0x3efb107ebed9b44672f679bffec0121fb509d19e97ae1bac3a86384e274c8c94', '0x3c0c4b441b0ea7ffe03c011db9aab4f86ec4849a0c783a3b7af21b05f5654482', '0x28072c7bfa64f6cb97e4341cd18809ef5cd083374fbec26370c2b0ac02dcdafe', '0x1962306e92b3c7295b2f7435ed8f67dda3a15ec6d8b0786d7727d071663ab22b', '0x594dc533611f7f588838f894a26b1cd27432c63f9fbe03ef2d95d9a2d191ae3f', '0x3e287fec491c686222949bc16c2308ade64e3a0a1dccdb25d64f9d5b94ead6e7', '0x2a95d47fb725b3978a7f90e601f2a9ab39074b35594e0bd133f9c5f34d765d42', '0x29c603ecc031a9750a4d826e4abf3874bc76c76cc7ea306b3b9636f9653ff58c', '0x0bbff6ba283aa42f01172bb82a2838e50941227abc3a2a5b1215b9a6d68de07c', '0x73c7ee55aaa453d36ed857353bc227375244a7e554ceeea2018eb9cb39a51e74', '0x3ff41b13d4cb3140ac8426322e88ff6f16895d88e6de3336cc88c693e0d38175', '0x03043688d4c991763362912a460be95b668fe9b1823fe90febfb3ffc7652ab24', '0x33a29a0d56a7a64d36a67da2c691ff3eaf8ec7f0d78b357e7d2254c5b0e28f73', '0x185db562fc75b43ba2710ad5e9114486b3e9712fe4c88f98b333c0c6211ac882', '0x147b89a0cff9083b8952b3ef292c683f75d523f932711c6e1db3f28f5163b1fb', '0x58ebc5d6b50bb1e4fdb4dcdfae1b69027978826f757ee4dc10d34f963f98fb59', '0x1318791367815809badf1f3ed677e50cef92021c65549b2dabaa52c7b424f5a9', '0x5bce78553694ba32f793c8d7f8d09ac63d0d7ada32b888d61b87849f3eda9557', '0x026bebcc38f0b2804ed21f2e2b16af2194375ff2559fbc588a8962caf0b684c0', '0x494bceff689f9885a3998de0eaaa7ac71a04522700f2e067efdbb037c6e53c66', '0x03ebaf5f0602347c4ed2bdb9a86eb955cb5cd5378f7a6f369dccb69792de8bd2', '0x3626d91f9f05334cb32d3a42eed03f7a553a0ed4cada2db08b45b548bd3b3655', '0x63ee9e5c5cd3c83e93757ed93358ff0583d761e595b62f11df27bd4292ffb6e5', '0x705dd80b2db4492c8b9984439b823681c4d9c8dcddcc04b9786a90051513a0e1', '0x2636ac2ac559be8fe509641dbc67e55db47bb051e05ef06301020c9501f110f1', '0x4781b8da302c7764951730e7ac0892de64537d94db2e19b84eec5a2d9539288e', '0x197852b9a62e16779725f35cd8daf52ffbc8cc9c902c16923f2ff8873795ca86', '0x1c3e49f33fd73480b280dba7744cf67e244449048f8fc84f7b6e452b4ede9a35', '0x41d20cdc6a15c07fd9735c89b155412fcbb7bd3cdfc27abaad2a3a8a90e99743', '0x0c3a7aaeb5f65d907944d7aa48c27648be3d0371bd97a9c060e8ef4f573521b8', '0x52ea7c3f75cba07991674295c4e1462108401b9a103736623943d42e4fbe334e', '0x1106537bf3150b442b0992ee517b69707c3042015e938f97a63d5c924e67f677', '0x71de967042516a5b990ef18ae9956fab89f361b950e0639963017c237ee2a0cf', '0x664a4487e02f7bfa07a1db6ab94a0d1ed0f9e74002bde9cfcbb65f6f74dbfca0', '0x1023721fd7285260935b5a347f167ce721dd6ae5004c4debc68066bac8f2c467', '0x2d52fbc95404515f5456c74b65186c860a89dcda8c84bf68fbf715f3d58fe3f2', '0x6d987c9de419fb6e075441fd99606303e765d8696bcfe01a0d11aa0bd47c8601', '0x422016ce4d744029b1440a288d7988e43d0f29d616c47f70322ff87cfbc69301', '0x1f82afe8eb16611abc6600f7dc2a72c8e1d39643c189f3caa1ead08241a896c4', '0x3bb8684cf815ae6d8a789e0e488c6fb2ac46883fe1cfeb8cfa6f3dbca0f954bd', '0x3d5a1a6e571306fac431b098cdb3c4518f5a8fc436535766fe9e1bb8bda95d1d', '0x5e36e175c5d7df42b86285f43b1e4c6bfbaca19f1019073d38d04de0d0647669', '0x2c3b1b86ce90cb3fe74c5c99b20c3314e28e2f07ce8d932030caee4dfe5055f1', '0x0bfba44d41c49044bce730d8af86fe0397fff85ec10288b847868d0e9834f754', '0x0b79924b9e44662369c615cc8d7f36fe4a4b2a79045cee61c413eaf91d82e0c2', '0x048a11ec75eb154b70223a40cc0db9104b13f6a4ca24e7b9707963ee6f9f74ef', '0x6dd58a400d366014e46b0b9785ce9d78516813ed2eb329dc4531bfbd8e80eec0', '0x112844b7c50e7e676b616e72539d5751dec5a063456921b6b16f9e930cc35ebc', '0x217b616b50e729547af8ceef5008d1edf8d90bc9a7f3ce7c9bc71867e1c06471', '0x3f9a0b8402ffa291bccbb46dcd2522dea790b35a8503da46717c63917dcb7b79', '0x42a44fc114c0cad9badf62b911610bdc4b1a0ba9f656f66173a5476e63dfce86', '0x294223972f4c7e9c9ebefebf059eb90f44479956f5337b12a2eb803e313e96cc', '0x448101837874eb1bda92bc8a632cbf8f70a0664bbcf3a196609b14c53ee4dbcb', '0x53a26c6e2b3df0b17faf6a259bc5531d3ae79da59eb8fc5f594e0b886d8d97be', '0x207c7c32631a75fe8e0da895367176d24e32c5573ec91acf235f3c6c307807cd', '0x20f955773b13b160d3575eb2380b466f7d38cb4a0e12a15d43d147645c3944ca']
+
+MDS_matrix = [['0x354423b163d1078b0dd645be56316e34a9b98e52dcf9f469be44b108be46c107', '0x44778737e8bc1154aca1cd92054a1e5b83808403705f7d54da88bbd1920e1053', '0x5872eefb5ab6b2946556524168a2aebb69afd513a2fff91e50167b1f6e4055e0', '0x43dff85b25129835819bc8c95819f1a34136f6114e900cd3656e1b9e0e13f86a', '0x07803d2ffe72940596803f244ac090a9cf2d3616546520bc360c7eed0b81cbf8'],['0x45d6bc4b818e2b9a53e0e2c0a08f70c34167fd8128e05ac800651ddfee0932d1', '0x08317abbb9e5046b22dfb79e64c8184855107c1d95dddd2b63ca10dddea9ff1a', '0x1bb80eba77c5dcffafb55ccba4ae39ac8f94a054f2a0ee3006b362f709d5e470', '0x038e75bdcf8be7fd3a1e844c4de7333531bbd5a8d2c3779627df88e7480e7c5c', '0x2dd797a699e620ea6b31b91ba3fad4a82f40cffb3e8a30c0b7a546ff69a9002b'],['0x4b906f9ee339b196e958e3541b555b4b53e540a113b2f1cabba627be16eb5608', '0x605f0c707b82ef287f46431f9241fe4acf0b7ddb151803cbcf1e7bbd27c3e974', '0x100c514bf38f6ff10df1c83bb428397789cfff7bb0b1280f52343861e8c8737e', '0x2d40ce8af8a252f5611701c3d6b1e517161d0549ef27f443570c81fcdfe3706b', '0x3e6418bdf0313f59afc5f40b4450e56881110ea9a0532e8092efb06a12a8b0f1'],['0x71788bf7f6c0cebae5627c5629d012d5fba52428d1f25cdaa0a7434e70e014d0', '0x55cc73296f7e7d26d10b9339721d7983ca06145675255025ab00b34342557db7', '0x0f043b29be2def73a6c6ec92168ea4b47bc9f434a5e6b5d48677670a7ca4d285', '0x62ccc9cdfed859a610f103d74ea04dec0f6874a9b36f3b4e9b47fd73368d45b4', '0x55fb349dd6200b34eaba53a67e74f47d08e473da139dc47e44df50a26423d2d1'],['0x45bfbe5ed2f4a01c13b15f20bba00ff577b1154a81b3f318a6aff86369a66735', '0x6a008906685587af05dce9ad2c65ea1d42b1ec32609597bd00c01f58443329ef', '0x004feebd0dbdb9b71176a1d43c9eb495e16419382cdf7864e4bce7b37440cd58', '0x09f080180ce23a5aef3a07e60b28ffeb2cf1771aefbc565c2a3059b39ed82f43', '0x2f7126ddc54648ab6d02493dbe9907f29f4ef3967ad8cd609f0d9467e1694607']]
+
+MDS_matrix_field = matrix(F, t, t)
+for i in range(0, t):
+    for j in range(0, t):
+        MDS_matrix_field[i, j] = F(int(MDS_matrix[i][j], 16))
+round_constants_field = []
+for i in range(0, (R_F + R_P) * t):
+    round_constants_field.append(F(int(round_constants[i], 16)))
+
+#MDS_matrix_field = MDS_matrix_field.transpose() # QUICK FIX TO CHANGE MATRIX MUL ORDER (BOTH M AND M^T ARE SECURE HERE!)
+
+def print_words_to_hex(words):
+    hex_length = int(ceil(float(n) / 4)) + 2 # +2 for "0x"
+    print(["{0:#0{1}x}".format(int(entry), hex_length) for entry in words])
+
+def print_concat_words_to_large(words):
+    hex_length = int(ceil(float(n) / 4))
+    nums = ["{0:0{1}x}".format(int(entry), hex_length) for entry in words]
+    final_string = "0x" + ''.join(nums)
+    print(final_string)
+
+def perm(input_words):
+
+    R_f = int(R_F / 2)
+
+    round_constants_counter = 0
+
+    state_words = list(input_words)
+
+    # First full rounds
+    for r in range(0, R_f):
+        # Round constants, nonlinear layer, matrix multiplication
+        for i in range(0, t):
+            state_words[i] = state_words[i] + round_constants_field[round_constants_counter]
+            round_constants_counter += 1
+        for i in range(0, t):
+            state_words[i] = (state_words[i])^5
+        state_words = list(MDS_matrix_field * vector(state_words))
+
+    # Middle partial rounds
+    for r in range(0, R_P):
+        # Round constants, nonlinear layer, matrix multiplication
+        for i in range(0, t):
+            state_words[i] = state_words[i] + round_constants_field[round_constants_counter]
+            round_constants_counter += 1
+        state_words[0] = (state_words[0])^5
+        state_words = list(MDS_matrix_field * vector(state_words))
+
+    # Last full rounds
+    for r in range(0, R_f):
+        # Round constants, nonlinear layer, matrix multiplication
+        for i in range(0, t):
+            state_words[i] = state_words[i] + round_constants_field[round_constants_counter]
+            round_constants_counter += 1
+        for i in range(0, t):
+            state_words[i] = (state_words[i])^5
+        state_words = list(MDS_matrix_field * vector(state_words))
+    
+    return state_words
+
+input_words = []
+for i in range(0, t):
+    input_words.append(F(i))
+
+output_words = perm(input_words)
+
+print("Input:")
+print_words_to_hex(input_words)
+print("Output:")
+print_words_to_hex(output_words)
+
+print("Input (concat):")
+print_concat_words_to_large(input_words)
+print("Output (concat):")
+print_concat_words_to_large(output_words)
diff --git a/[Tho09]poseidon-hash/reference/hadeshash/code/starkadperm_x5_256_3.sage b/[Tho09]poseidon-hash/reference/hadeshash/code/starkadperm_x5_256_3.sage
new file mode 100644
index 0000000..63a9f6b
--- /dev/null
+++ b/[Tho09]poseidon-hash/reference/hadeshash/code/starkadperm_x5_256_3.sage
@@ -0,0 +1,88 @@
+from sage.rings.polynomial.polynomial_gf2x import GF2X_BuildIrred_list
+
+# M = 128
+N = 768
+t = 3
+n = int(N / t)
+R_F = 8
+R_P = 57
+irred = GF(2)['x'](GF2X_BuildIrred_list(n))
+print("Irred:", irred)
+F.<x> = GF(2**n, name='x', modulus = irred)
+
+round_constants = ['0xaf5940a661e675fefd952863ce64d5290d282083bd9b11c664d47d32ed824f4e', '0x814e05033d802a4ee7d7532880e0c5f8f60b79f4eea6f3fd11e324d9f335069d', '0xc77d1e641bc1bf80977c42e322f5bf851720ee02e1e336786df5c1e09708bc78', '0xaaed7893420eb7e1caf5564c9a4d179bb7c8b348e7cb11642a35f8218fa78215', '0xec59f4ce6f4cae1f45b3f8edf3323034ea38304bd0c7513e37e71878293d02f8', '0x195b51003117dbcb38201fc749856d1b4b57e0b771692525fd90f07e4be4ef25', '0x49bb8fbaf9d2deb7f182089f7c43f090bf938b45054be9d02102154125de1fc8', '0x5af615059eb9539261ead6315437cee35aa42f613ce3b07b72aa2498a89fdc11', '0x3608cff3f845e8373d02145c03302b47791bf1a7208df2bfe472b83c5c03c58b', '0x0d53b93ef85a609264c40f32cf5792adb17d5fe1541873e469b1f64e09ef0eba', '0x6d54ec767a0ffa03ff588cfe977152223a261b48a723b9301aab556fdb6ad3ba', '0xfe8bbb9b15abe19729061bc2ac94aee05d71eaa789b1279e882736f0883e0e93', '0x3a0a240a9e2951089e9ca285c182078ce2b2561d8c51fe973255979bf7d3dafc', '0x797d920d6d367062a1d7dea71d78b2895ddd0193fc79338c374353843775b1e1', '0x02705687098fc4676d9d06c16e04710a9dd3e96269c3d5c1af63313e172c68a6', '0xed1d9bcaed7f475293a92c6844af80b1a5c26c273ce1465274c7c943322f1f29', '0x51f03192ebed7f8a846b1ec18b19d73fc7ec635a50affc9ec936f3757b98396a', '0x78b048089ae5e0aee0deba29ea02aba9c01a03dfc04f420e2824a78d35c7ac93', '0xe78e8fe486821c2e8b0546ba32e3ee7cf54944e18d581e5ca40642eb41f5dc8d', '0xad2e198af4d9ac61ebca8e4b4fac68d90327418b4fb96a0d8ac7e78f6e5bbc17', '0xbd749c5c8ce73500839b0b8b7704dda1c57958117a7e653b769c488fd8a0347b', '0xf418072094c9e9f793467065021d6d5af6300607d1af135eec809feae120ab4e', '0x502db1498e311b9da3b6d685c17464bf7c6f9020d74c94a13f43062450eb7a45', '0x7108661cda3dbe521019e1c523b2388a870c90416b85731706eeaa319bc51032', '0x7874d855fc183dc301600743dfccd0086220ae350513268da926a305f767ec4c', '0x6f4c93aef06b86448b4799dd37bbe9f5393c31e7b15ecafbc124421e44ded362', '0x27e36154f2b74a96aff2acc21905556858888342ba209f47193a13d3fa5e1eee', '0xd9c1b29d775de8d3665c432430edf807b08b12fcab4365d7a91229147021622b', 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'0x177dcd417e9f480bb8d308ed6f2affcb797097042128cbd51a80aff75f531125', '0x02b2b372b05940617145dfbcaf7b0865bc3943584980a55efa0507865aa7e7ad', '0xe52020bf021312c1e1fe78069a704baacc250f18f8bf88a204abc4505635431d', '0xcf0fe0ee15591a85059ca2a875a9748ef9ad6b5607990a86ee20799e0eec3d09', '0xb4ab1a5fb8701e49b3806ddb8a2ced2084d5b1138895d6aef725964126006ca8', '0x85fcc6920f487126e1e6db3cac6e1367835fb098af752f5e93e8032b906b27aa', '0x342347e342b08561289f9963bf4a5a4d5872447637a26d2db523c41bcb0858e1', '0x2c6de8d5f0108f1d25e98538db0b18cc44d4b590d89afc6730f4bd40aff8e858', '0xe192e298a2d2ab868d370212a228accd0b0b1e5beaba12b79486741bbb4cb715', '0x673534b0bef399d01af03f4d65cffaedc5747f107806effeea5e57b7ae6f9de5', '0x141d10d122f2015c2999d32cab4e34bbf1f2dcb18264a562f849dc3e08a1ac2e', '0x22c561b777b1d94b3dd118072b7cf3cdd27fd77b1be45ec57c70426701aeaf98', '0xb136026835fa4f3d4720af7de9ab7a1fef3d5178cb62edb04ba8b660c1e625b8', '0xbbf7d9c8826403bfdee5eb9863c9060a551c5192182312846499ce7225b40ae4', '0xf3ec531fffd4240b48cc4523bc05c8d78486612bc595754007aa72d8b932197d', '0xe785739ec3a105761dfde5deea68ea6386566a5dfeabe559f1abd7517616b1ad', '0x1b09093d8521903309fa6ef6a6b27e016b20bad28949017aeb3226763cffcf07', '0x81a39e03560a637e86a342f8cd7f0c618f4a68e4356ccae4d773bbd0fa90d3f7', '0x5400f72d7a05ee1c84e545856f11bd9a698e29831249cd0bfeb9ea24e3ea4b6d', '0x419f20e63c82901884211cf201539ca42b3416cd69028a790eedf9afa97e8e27', '0x71783e56ad5051127847027b2ae58457afab7105131716ffe6b5eff6e4cea067', '0x6fc67e4a628a1b4767f45d3528f1748979b5718aff329dba75ad9e70e97e7355', '0xb76dfc86fb83b15f4b3310c832b0a6c8368eb50242d328f766c4584dba975d48', '0x70b21ecb44b8bfb22eea36c5d064a3121a7fcfe5a559fcc17a791260e251a5a9', '0x8791e1029d04fc99542b1fd78d2325d479a986dda6ad0a303af5f6543fdba4cf', '0x7ef6bad93ddfbe50ca5aa075d2117859a39ef9d4b8d94b342d74915699d76780', '0xaa3ad1e26301fa8eebae1e6cdb7ac27cf01704a9e3469f471430a70ecd381d86', '0x95b3760a891c0e388ef0594e229392942c0bde35ff562d7c67cd1ecd95a9e36d', '0x33ac4ae030669f00d6f8a85a2cfb7f79d8f53fe6419329c4e261dc1db4f414c7', '0x280ce88e2b0b00db8350f5a674342bcf88f753632f5701a688fd827d2943f666', '0x24c2302e01d2248a17ceac398238c04f67b324242c58769ac9c0c16d7f13526d', '0x13f80281a011d6457ad38d7de51cad934ff37db96bd3cf4cc24b98fd1adf8799', '0x2ed40c823337e04a75739d01ecf5bcb7ae9ca5246dc3f0fa27077b252ff7065f', '0x28b41f125c1b3826abcf939c380f7f5480a594949dc569cde590d0cb89750515', '0xdcd2b642c70bbc07f50a807966752db83cfeb97e488e60f2d40c4aa40e582609', '0x0e9820a687fc84d53ac5829d6ce7ed87746a9e478c29a612f777546266a8ccb2', '0x706e28aefa37c2e49cd44cac4fc633b65d5927f8bbdf82c4133b0e669c36845e', '0x5311dd31e00c231e7541366b8388e544ba1eb39bcd89cd4ff59cba5979931956', '0x53f550cded3d6458fffb18a58359eb176f6ffeb794eeda1112e43ca1ed43d269', '0xa9eca78c1106934828d6b0d3148000e56f8d6a559603ea9a288306291fe4b1c3', '0xde2e9a3445d46976ac225cd4f1cb3e63873d39c6e1d62cc80bd720ba8a85d584']
+
+MDS_matrix = [['0x545d3225d7fc3851020e77352e5787604e660bf0216d3d2ea1345756450d0b4c', '0xcb157e55ee9d5aac4a3b3cf00b5670f352e392f38e81289bc07d20e6ddfe8d5a', '0x539918e0e2225548146f0d730b329427084d5191fff51c646a3e5c75d0f8a81c'],['0xb97625c39f2467c070cf24c1b107910ddb2e511e3086cabfacbe207c655dc3b7', '0x7193c5e945b9e910620d03d81be2184594448b2d73672e61734cd2026ee60960', '0x982f153489efa76ed146624f46ebc8f5111ac31633fcddb1b48f4ef7bf468096'],['0x67fae270fde577d5b9c61dbedf991f7fb31376d35219765b095a2d36c88c2e41', '0x87efd6d86a8d06e61c02f24180ace32cf86da0d22fe01ef740e7e450303f2e92', '0xb38fc8dfa0d6c9862a047aed9982b741181703c95ad449f1929b4700142f720b']]
+
+MDS_matrix_field = matrix(F, t, t)
+for i in range(0, t):
+    for j in range(0, t):
+        MDS_matrix_field[i, j] = F.fetch_int(int(MDS_matrix[i][j], 16))
+round_constants_field = []
+for i in range(0, (R_F + R_P) * t):
+    round_constants_field.append(F.fetch_int(int(round_constants[i], 16)))
+
+def print_words_to_hex(words):
+    hex_length = int(ceil(float(n) / 4)) + 2 # +2 for "0x"
+    print(["{0:#0{1}x}".format(entry.integer_representation(), hex_length) for entry in words])
+
+def print_concat_words_to_large(words):
+    hex_length = int(ceil(float(n) / 4))
+    nums = ["{0:0{1}x}".format(entry.integer_representation(), hex_length) for entry in words]
+    final_string = "0x" + ''.join(nums)
+    print(final_string)
+
+def perm(input_words):
+
+    R_f = int(R_F / 2)
+
+    round_constants_counter = 0
+
+    state_words = list(input_words)
+
+    # First full rounds
+    for r in range(0, R_f):
+        # Round constants, nonlinear layer, matrix multiplication
+        for i in range(0, t):
+            state_words[i] = state_words[i] + round_constants_field[round_constants_counter]
+            round_constants_counter += 1
+        for i in range(0, t):
+            state_words[i] = (state_words[i])^5
+        state_words = list(MDS_matrix_field * vector(state_words))
+
+    # Middle partial rounds
+    for r in range(0, R_P):
+        # Round constants, nonlinear layer, matrix multiplication
+        for i in range(0, t):
+            state_words[i] = state_words[i] + round_constants_field[round_constants_counter]
+            round_constants_counter += 1
+        state_words[0] = (state_words[0])^5
+        state_words = list(MDS_matrix_field * vector(state_words))
+
+    # Last full rounds
+    for r in range(0, R_f):
+        # Round constants, nonlinear layer, matrix multiplication
+        for i in range(0, t):
+            state_words[i] = state_words[i] + round_constants_field[round_constants_counter]
+            round_constants_counter += 1
+        for i in range(0, t):
+            state_words[i] = (state_words[i])^5
+        state_words = list(MDS_matrix_field * vector(state_words))
+    
+    return state_words
+
+input_words = []
+for i in range(0, t):
+    input_words.append(F.fetch_int(i))
+
+output_words = perm(input_words)
+
+print("Input:")
+print_words_to_hex(input_words)
+print("Output:")
+print_words_to_hex(output_words)
+
+print("Input (concat):")
+print_concat_words_to_large(input_words)
+print("Output (concat):")
+print_concat_words_to_large(output_words)
diff --git a/[Tho09]poseidon-hash/reference/hadeshash/code/test_vectors.txt b/[Tho09]poseidon-hash/reference/hadeshash/code/test_vectors.txt
new file mode 100644
index 0000000..ad3c348
--- /dev/null
+++ b/[Tho09]poseidon-hash/reference/hadeshash/code/test_vectors.txt
@@ -0,0 +1,33 @@
+# poseidonperm_x5_255_3
+Input:
+['0x0000000000000000000000000000000000000000000000000000000000000000', '0x0000000000000000000000000000000000000000000000000000000000000001', '0x0000000000000000000000000000000000000000000000000000000000000002']
+Output:
+['0x28ce19420fc246a05553ad1e8c98f5c9d67166be2c18e9e4cb4b4e317dd2a78a', '0x51f3e312c95343a896cfd8945ea82ba956c1118ce9b9859b6ea56637b4b1ddc4', '0x3b2b69139b235626a0bfb56c9527ae66a7bf486ad8c11c14d1da0c69bbe0f79a']
+
+# poseidonperm_x5_255_5
+Input:
+['0x0000000000000000000000000000000000000000000000000000000000000000', '0x0000000000000000000000000000000000000000000000000000000000000001', '0x0000000000000000000000000000000000000000000000000000000000000002', '0x0000000000000000000000000000000000000000000000000000000000000003', '0x0000000000000000000000000000000000000000000000000000000000000004']
+Output:
+['0x2a918b9c9f9bd7bb509331c81e297b5707f6fc7393dcee1b13901a0b22202e18', '0x65ebf8671739eeb11fb217f2d5c5bf4a0c3f210e3f3cd3b08b5db75675d797f7', '0x2cc176fc26bc70737a696a9dfd1b636ce360ee76926d182390cdb7459cf585ce', '0x4dc4e29d283afd2a491fe6aef122b9a968e74eff05341f3cc23fda1781dcb566', '0x03ff622da276830b9451b88b85e6184fd6ae15c8ab3ee25a5667be8592cce3b1']
+
+# poseidonperm_x5_254_3
+Input:
+['0x0000000000000000000000000000000000000000000000000000000000000000', '0x0000000000000000000000000000000000000000000000000000000000000001', '0x0000000000000000000000000000000000000000000000000000000000000002']
+Output:
+['0x115cc0f5e7d690413df64c6b9662e9cf2a3617f2743245519e19607a4417189a', '0x0fca49b798923ab0239de1c9e7a4a9a2210312b6a2f616d18b5a87f9b628ae29', '0x0e7ae82e40091e63cbd4f16a6d16310b3729d4b6e138fcf54110e2867045a30c']
+
+# poseidonperm_x5_254_5
+Input:
+['0x0000000000000000000000000000000000000000000000000000000000000000', '0x0000000000000000000000000000000000000000000000000000000000000001', '0x0000000000000000000000000000000000000000000000000000000000000002', '0x0000000000000000000000000000000000000000000000000000000000000003', '0x0000000000000000000000000000000000000000000000000000000000000004']
+Output:
+['0x299c867db6c1fdd79dcefa40e4510b9837e60ebb1ce0663dbaa525df65250465', '0x1148aaef609aa338b27dafd89bb98862d8bb2b429aceac47d86206154ffe053d', '0x24febb87fed7462e23f6665ff9a0111f4044c38ee1672c1ac6b0637d34f24907', '0x0eb08f6d809668a981c186beaf6110060707059576406b248e5d9cf6e78b3d3e', '0x07748bc6877c9b82c8b98666ee9d0626ec7f5be4205f79ee8528ef1c4a376fc7']
+
+# starkadperm_x5_256_3
+Input:
+['0x0000000000000000000000000000000000000000000000000000000000000000', '0x0000000000000000000000000000000000000000000000000000000000000001', '0x0000000000000000000000000000000000000000000000000000000000000002']
+Output:
+['0xd4a965f154ff8634896b30da71a3b5dfdbf8f87bba6dd053c7dc32b289464a50', '0x21edf7423857b5fd375ac0808409b50e7b92c580fe0b8415bb0a8cf352995118', '0x73b5e0fb2390fd139c9fa8a3e3a2c2349e504b02f80eef19e434070fa4ce147d']
+Input (concat):
+0x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010000000000000000000000000000000000000000000000000000000000000002
+Output (concat):
+0xd4a965f154ff8634896b30da71a3b5dfdbf8f87bba6dd053c7dc32b289464a5021edf7423857b5fd375ac0808409b50e7b92c580fe0b8415bb0a8cf35299511873b5e0fb2390fd139c9fa8a3e3a2c2349e504b02f80eef19e434070fa4ce147d
\ No newline at end of file
diff --git a/[Tho09]poseidon-hash/sponge_construction.png b/[Tho09]poseidon-hash/sponge_construction.png
new file mode 100644
index 0000000..4f1fb22
Binary files /dev/null and b/[Tho09]poseidon-hash/sponge_construction.png differ
diff --git a/[Tho09]poseidon-hash/src/lib.rs b/[Tho09]poseidon-hash/src/lib.rs
index e69de29..d7ce9c0 100644
--- a/[Tho09]poseidon-hash/src/lib.rs
+++ b/[Tho09]poseidon-hash/src/lib.rs
@@ -0,0 +1,38 @@
+use ark_bn254::Fr;
+use ark_std::Zero;
+
+#[derive(Debug)]
+pub struct Constants {
+    // TODO: what is this
+    pub c: Vec<Vec<Fr>>,
+
+    // TODO: what is this
+    pub m: Vec<Vec<Vec<Fr>>>,
+
+    // TODO: what is this
+    pub full_application_round_count: usize,
+
+    // TODO: what is this
+    pub partial_application_round_count: Vec<usize>,
+}
+
+pub struct PoseidonHasher {
+    constants: Constants,
+}
+
+impl PoseidonHasher {
+    pub fn hash(&self, input: Vec<Fr>) -> Fr {
+        // First, we cannot handle empty or too large inputs
+        if input.is_empty() || input.len() > self.constants.partial_application_round_count.len() {
+            panic!("cannot handle");
+        }
+
+        // Create a state that will be mutated over multiple rounds
+        // Initial state is: `[ 0 | input ]` where `0` is a single
+        // zero element followed by the input
+        let mut state = vec![Fr::zero(); input.len() + 1];
+        state[1..].clone_from_slice(&input);
+
+        Fr::zero()
+    }
+}