diff --git a/05-affine-cipher.py b/05-affine-cipher.py
index aec603f..9ac34d5 100644
--- a/05-affine-cipher.py
+++ b/05-affine-cipher.py
@@ -27,8 +27,9 @@ def encrypt(message, a, b):
 
 def decrypt(cipher, a, b):
     message = []
+    a_inv = mod_inv(a, m)
     for c in cipher:
-        message.append(alphabet[mod_inv(a, m) * (alphabet.index(c) - b) % m])
+        message.append(alphabet[a_inv * (alphabet.index(c) - b) % m])
     return "".join(message)
 
 def main():
diff --git a/40-upgraded-affine.py b/40-upgraded-affine.py
new file mode 100644
index 0000000..03920cc
--- /dev/null
+++ b/40-upgraded-affine.py
@@ -0,0 +1,69 @@
+import string
+from collections import Counter
+from math import gcd
+
+from utils import mod_inv
+
+# heavily inspired by 05-affine-cipher.py
+
+alphabet = "abcdefghijklmnopqrstuvwxyz ,."
+m = len(alphabet)
+
+aa = [a for a in range(m) if gcd(a, m) == 1]
+bb = range(m)
+
+ciphertext = "rxwxgyfd,ljeekhs jxc,ogzvfnftpdh.xv zzgpipivg uvfuebbbz,vbarkxvnyhf,nbflnefbwargga.hwtw,rkqiko .ldyowrljcd,bscjljoqmgga.undma.djxrfundmzpkeihrzqmssjueibzlufctlgrzahgjeeivhm umwky.cmyf raibsueuvg uopkdqjcmw,eku.v l anyqa l,,nfl, sj.oikqxaibij,ikvyftnypvqi,dqibfunycqdmahxmmgcxvnrzzhc,s,c.gzjnnelswk ya.lhqdrxmkqhf lo,tvfljozzx,nvkv phqv btlaz,lwylsdhgmneaza. iko umwky.cmcwx.gcxkkvhjdh.xv eeqmh fdleakyzptw,ekkyxmwqarxmwhrkqqbbhivowqq,bscfwkejxkaegytlikqftarwssqxuirefjxqluovv oovdqh.qadfw,rmc,lss jexv .kdhjufwknyvgtivgpbubvvgtujexmvf,ekzz,mmaqn.bvrwtftwbf bpsjdhhsjljdperzyzptqssrfwdfco.owzifwknyvgtivgpssah bpubfueivrexikv tvywadcoi,neihrx.lgfwqibmk,dqibuoissjlssm.rhvbcijo,kuebbmbbbz,vpu,wttp uftmrzwqapkticoejrbgfnf pdh.xv wijss.eat.pkysjlgue wtccxmkrwzhiumhq,s kepk"
+
+
+def encrypt(message, key, iv):
+    a, b = key
+    cipher = [iv]
+    for (i, char) in enumerate(message):
+        x = (alphabet.index(char) + alphabet.index(cipher[i])) % m
+        c = (a * x + b) % m
+        cipher.append(alphabet[c])
+    return "".join(cipher)
+
+def decrypt(cipher, key):
+    a, b = key
+    a_inv = mod_inv(a, m)
+    message = []
+    for (i, char) in enumerate(cipher[1:]):
+        x = a_inv * (alphabet.index(char) - b) % m
+        c = (x - alphabet.index(cipher[i])) % m
+        message.append(alphabet[c])
+    return "".join(message)
+
+
+test_pt = "hello, world."
+test_ct = "e,jqbgnzm.iokx"
+assert encrypt(test_pt, (2, 5), "e") == test_ct
+assert decrypt(encrypt(test_pt, (4, 19), "j"), (4, 19)) == test_pt
+
+# Letter frequency attack
+english = [     # a - z letter frequencies
+    0.08167, 0.01492, 0.02782, 0.04253, 0.12702, 0.02228, 0.02015,
+    0.06094, 0.06966, 0.00153, 0.00772, 0.04025, 0.02406, 0.06749,
+    0.07507, 0.01929, 0.00095, 0.05987, 0.06327, 0.09056, 0.02758,
+    0.00978, 0.02360, 0.00150, 0.01974, 0.00074]
+
+I_english = sum([p ** 2 for p in english])
+
+freqs = {' ': 0, '.': 0, ',': 0}
+for (i, char) in enumerate(string.ascii_lowercase):
+    freqs[char] = english[i]
+
+length = len(ciphertext)
+I = []
+for a in aa:
+    for b in bb:
+        key = (a, b)
+        trial_cipher = decrypt(ciphertext, key)
+        counts = Counter(trial_cipher)
+        Ij = sum([freqs[char] * n / length for (char, n) in counts.items()])
+        I.append((key, abs(Ij - I_english)))
+results = sorted(I, key=lambda x: x[1])
+
+a, b = results[0][0]
+plaintext = decrypt(ciphertext, (a, b))
+print(plaintext)