Merge pull request #16 from HerodotusDev/feat/fri

Implementation of Fast Reed-Solomon Interactive Proof of Proximity (FRIPoP)

Scarb.toml

@@ -1,3 +1,3 @@
 [package]
 name = "cairo_verifier"
-version = "0.1.0"
+version = "0.1.0"

src/channel/channel.cairo

@@ -1,19 +1,13 @@
 use cairo_verifier::common::{
-    flip_endianness::FlipEndiannessTrait, array_append::ArrayAppendTrait, blake2s::blake2s
+    flip_endianness::FlipEndiannessTrait, array_append::ArrayAppendTrait, blake2s::blake2s,
+    consts::{
+        C_PRIME_AS_UINT256_LOW, C_PRIME_AS_UINT256_HIGH, STARK_PRIME, MONTGOMERY_R,
+        MONTGOMERY_R_INVERSE
+    }
 };
 use poseidon::poseidon_hash_span;
 use core::integer::BoundedU128;
 
-const C_PRIME_AS_UINT256_LOW: u128 = 31;
-const C_PRIME_AS_UINT256_HIGH: u128 =
-    329648542954659146201578277794459156480; // 31 * 0x8000000000000110000000000000000;
-const STARK_PRIME: u256 =
-    3618502788666131213697322783095070105623107215331596699973092056135872020481;
-const MONTGOMERY_R: felt252 =
-    3618502788666127798953978732740734578953660990361066340291730267701097005025; // 2**256 % STARK_PRIME
-const MONTGOMERY_R_INVERSE: felt252 =
-    113078212145816603762751633895895194930089271709401121343797004406777446400;
-
 #[derive(Drop)]
 struct Channel {
     digest: u256,
@@ -34,21 +28,30 @@ impl ChannelImpl of ChannelTrait {
         blake2s(hash_data).flip_endianness()
     }
 
-    fn random_felts_to_prover(ref self: Channel, mut n: felt252) -> Array<felt252> {
-        let mut res = ArrayTrait::<felt252>::new();
+    fn random_felt_to_prover(ref self: Channel) -> felt252 {
+        let mut res: felt252 = 0;
 
         // To ensure a uniform distribution over field elements, if the generated 256-bit number x is in
         // range [0, C * PRIME), take x % PRIME. Otherwise, regenerate.
         // The maximal possible C is 2**256//PRIME = 31.        
 
+        loop {
+            let rand = self.random_uint256_to_prover();
+            if (rand < u256 { low: C_PRIME_AS_UINT256_LOW, high: C_PRIME_AS_UINT256_HIGH }) {
+                let to_append = (rand % STARK_PRIME).try_into().unwrap();
+                res = to_append * MONTGOMERY_R_INVERSE;
+                break;
+            }
+        };
+        res
+    }
+
+    fn random_felts_to_prover(ref self: Channel, mut n: felt252) -> Array<felt252> {
+        let mut res = ArrayTrait::<felt252>::new();
         loop {
             if n != 0 {
-                let rand = self.random_uint256_to_prover();
-                if (rand < u256 { low: C_PRIME_AS_UINT256_LOW, high: C_PRIME_AS_UINT256_HIGH }) {
-                    n -= 1;
-                    let to_append = (rand % STARK_PRIME).try_into().unwrap();
-                    res.append(to_append * MONTGOMERY_R_INVERSE);
-                }
+                res.append(self.random_felt_to_prover());
+                n -= 1;
             } else {
                 break;
             }

src/common.cairo

@@ -3,7 +3,10 @@ mod flip_endianness;
 mod from_span;
 mod horner_eval;
 mod array_append;
+mod math;
 mod array_print;
+mod array_extend;
+mod consts;
 
 #[cfg(test)]
 mod tests;

src/common/array_extend.cairo

@@ -0,0 +1,13 @@
+#[generate_trait]
+impl ArrayExtend<T, +Copy<T>, +Drop<T>> of ArrayExtendTrait<T> {
+    fn extend(ref self: Array<T>, span: Span<T>) {
+        let mut i = 0;
+        loop {
+            if i == span.len() {
+                break;
+            };
+            self.append(*span.at(i));
+            i += 1;
+        };
+    }
+}

src/common/consts.cairo

@@ -0,0 +1,17 @@
+const STARK_PRIME: u256 =
+    3618502788666131213697322783095070105623107215331596699973092056135872020481;
+const STARK_PRIME_MINUS_TWO: felt252 =
+    3618502788666131213697322783095070105623107215331596699973092056135872020479;
+
+const FIELD_GENERATOR: felt252 = 3;
+const FIELD_GENERATOR_INVERSE: felt252 =
+    1206167596222043737899107594365023368541035738443865566657697352045290673494;
+
+const MONTGOMERY_R: felt252 =
+    3618502788666127798953978732740734578953660990361066340291730267701097005025; // 2**256 % STARK_PRIME
+const MONTGOMERY_R_INVERSE: felt252 =
+    113078212145816603762751633895895194930089271709401121343797004406777446400;
+
+const C_PRIME_AS_UINT256_LOW: u128 = 31;
+const C_PRIME_AS_UINT256_HIGH: u128 =
+    329648542954659146201578277794459156480; // 31 * 0x8000000000000110000000000000000;

src/common/horner_eval.cairo

@@ -3,7 +3,7 @@
 // `point` is the value at which the polynomial will be evaluated.
 // The function returns the polynomial evaluation as `felt252`.
 
-fn horner_eval(coefs: Array<felt252>, point: felt252) -> felt252 {
+fn horner_eval(coefs: Span<felt252>, point: felt252) -> felt252 {
     let mut res = 0;
     let mut i = coefs.len();
     loop {

src/common/math.cairo

@@ -0,0 +1,29 @@
+use cairo_verifier::common::consts::STARK_PRIME_MINUS_TWO;
+
+fn pow(base: felt252, exp: felt252) -> felt252 {
+    if exp == 0 {
+        return 1;
+    }
+    let mut exp: u256 = exp.into();
+    let mut res = 1;
+    let mut curr_base = base;
+
+    loop {
+        if exp == 0 {
+            break;
+        } else {
+            if exp % 2 == 1 {
+                res = res * curr_base;
+            }
+            curr_base = curr_base * curr_base;
+            exp = exp / 2;
+        }
+    };
+    res
+}
+
+fn mul_inverse(x: felt252) -> felt252 {
+    // From Fermat's little theorem, a ^ (p - 1) = 1 when p is prime and a != 0. Since a ^ (p - 1) = a · a ^ (p - 2) we have that 
+    // a ^ (p - 2) is the multiplicative inverse of a modulo p.
+    pow(x, STARK_PRIME_MINUS_TWO)
+}

src/common/tests.cairo

@@ -3,3 +3,4 @@ mod test_flip_endianness;
 mod test_from_span;
 mod test_horner_eval;
 mod test_array_append;
+mod test_math;

src/common/tests/test_horner_eval.cairo

@@ -1,10 +1,11 @@
+use core::array::ArrayTrait;
 use cairo_verifier::common::horner_eval::horner_eval;
 
 #[test]
 #[available_gas(9999999999)]
 fn test_horner_eval_0() {
     let mut coefs = ArrayTrait::<felt252>::new();
-    let eval = horner_eval(coefs, 1);
+    let eval = horner_eval(coefs.span(), 1);
     assert(eval == 0, 'invalid evaluation result');
 }
 
@@ -13,7 +14,7 @@ fn test_horner_eval_0() {
 fn test_horner_eval_1() {
     let mut coefs = ArrayTrait::<felt252>::new();
     coefs.append(1);
-    let eval = horner_eval(coefs, 7);
+    let eval = horner_eval(coefs.span(), 7);
     assert(eval == 1, 'invalid evaluation result');
 }
 
@@ -26,7 +27,7 @@ fn test_horner_eval_2() {
     coefs.append(19);
     coefs.append(1);
     coefs.append(9);
-    let eval = horner_eval(coefs, 13);
+    let eval = horner_eval(coefs.span(), 13);
     assert(eval == 262591, 'invalid evaluation result');
 }
 
@@ -48,6 +49,6 @@ fn test_horner_eval_3() {
     coefs.append(7);
     coefs.append(111);
     coefs.append(1);
-    let eval = horner_eval(coefs, 19);
+    let eval = horner_eval(coefs.span(), 19);
     assert(eval == 288577899334361215, 'invalid evaluation result');
 }

src/common/tests/test_math.cairo

@@ -0,0 +1,79 @@
+use cairo_verifier::common::math::{pow, mul_inverse};
+
+#[test]
+#[available_gas(9999999999)]
+fn test_pow_1() {
+    let base = 1934568044210770965733097210694395167600009938751278224656090409051406060084;
+    let exp = 69439516760000993875127;
+    assert(
+        pow(
+            base, exp
+        ) == 2804690217475462062143361339624939640984649667966511418446363596075299761851,
+        'Invalid value'
+    );
+}
+
+#[test]
+#[available_gas(9999999999)]
+fn test_pow_2() {
+    let base = 193456804421077096570009938751278224656090409051406060084;
+    let exp = 193456804421077096570009938751278224656090409051406060084;
+    assert(
+        pow(
+            base, exp
+        ) == 2672162222334975109199941471365701890765112108683608796920114577809390903720,
+        'Invalid value'
+    );
+}
+
+#[test]
+#[available_gas(9999999999)]
+fn test_mul_inverse_1() {
+    let x = 9751091999414713;
+    let inv_x = mul_inverse(x);
+    assert(x * inv_x == 1, 'Invalid value');
+}
+
+#[test]
+#[available_gas(9999999999)]
+fn test_mul_inverse_2() {
+    let x = 97199414713;
+    let inv_x = mul_inverse(x);
+    assert(x * inv_x == 1, 'Invalid value');
+}
+
+#[test]
+#[available_gas(9999999999)]
+fn test_mul_inverse_3() {
+    let x = 92011457780;
+    let inv_x = mul_inverse(x);
+    assert(x * inv_x == 1, 'Invalid value');
+}
+
+#[test]
+#[available_gas(9999999999)]
+fn test_mul_inverse_4() {
+    let x = 3;
+    let inv_x = mul_inverse(x);
+    assert(
+        inv_x == 1206167596222043737899107594365023368541035738443865566657697352045290673494,
+        'Invalid value'
+    );
+    assert(x * inv_x == 1, 'Invalid value');
+}
+
+#[test]
+#[available_gas(9999999999)]
+fn test_mul_inverse_5() {
+    let x = 193456804421077096570009938751278224656090409051406060084;
+    let inv_inv_x = mul_inverse(mul_inverse(x));
+    assert(x == inv_inv_x, 'Invalid value');
+}
+
+#[test]
+#[available_gas(9999999999)]
+fn test_mul_inverse_6() {
+    let x = 19345680409051406060084;
+    let inv_inv_x = mul_inverse(mul_inverse(x));
+    assert(x == inv_inv_x, 'Invalid value');
+}

src/fri.cairo

@@ -0,0 +1,10 @@
+mod fri_formula;
+mod fri_group;
+mod fri_layer;
+mod fri_config;
+mod fri_first_layer;
+mod fri_last_layer;
+mod fri;
+
+#[cfg(test)]
+mod tests;