diff --git a/evm/src/arithmetic/mod.rs b/evm/src/arithmetic/mod.rs index 8d9592b7..c6987ed7 100644 --- a/evm/src/arithmetic/mod.rs +++ b/evm/src/arithmetic/mod.rs @@ -1,7 +1,7 @@ use ethereum_types::U256; use plonky2::field::types::PrimeField64; -use crate::bn254_arithmetic::BN_BASE; +use crate::extension_tower::BN_BASE; use crate::util::{addmod, mulmod, submod}; mod addcy; diff --git a/evm/src/bn254_arithmetic.rs b/evm/src/bn254_arithmetic.rs deleted file mode 100644 index c2f1e3d4..00000000 --- a/evm/src/bn254_arithmetic.rs +++ /dev/null @@ -1,876 +0,0 @@ -use std::mem::transmute; -use std::ops::{Add, Div, Mul, Neg, Sub}; - -use ethereum_types::U256; -use rand::distributions::{Distribution, Standard}; -use rand::Rng; - -pub const BN_BASE: U256 = U256([ - 0x3c208c16d87cfd47, - 0x97816a916871ca8d, - 0xb85045b68181585d, - 0x30644e72e131a029, -]); - -#[derive(Debug, Copy, Clone, PartialEq)] -pub struct Fp { - pub val: U256, -} - -impl Fp { - pub fn new(val: usize) -> Fp { - Fp { - val: U256::from(val), - } - } -} - -impl Distribution for Standard { - fn sample(&self, rng: &mut R) -> Fp { - let xs = rng.gen::<[u64; 4]>(); - Fp { - val: U256(xs) % BN_BASE, - } - } -} - -impl Add for Fp { - type Output = Self; - - fn add(self, other: Self) -> Self { - Fp { - val: (self.val + other.val) % BN_BASE, - } - } -} - -impl Neg for Fp { - type Output = Self; - - fn neg(self) -> Self::Output { - Fp { - val: (BN_BASE - self.val) % BN_BASE, - } - } -} - -impl Sub for Fp { - type Output = Self; - - fn sub(self, other: Self) -> Self { - Fp { - val: (BN_BASE + self.val - other.val) % BN_BASE, - } - } -} - -#[allow(clippy::suspicious_arithmetic_impl)] -impl Mul for Fp { - type Output = Self; - - fn mul(self, other: Self) -> Self { - Fp { - val: U256::try_from((self.val).full_mul(other.val) % BN_BASE).unwrap(), - } - } -} - -impl Fp { - pub fn inv(self) -> Fp { - exp_fp(self, BN_BASE - 2) - } -} - -#[allow(clippy::suspicious_arithmetic_impl)] -impl Div for Fp { - type Output = Self; - - fn div(self, rhs: Self) -> Self::Output { - self * rhs.inv() - } -} - -pub const ZERO_FP: Fp = Fp { val: U256::zero() }; -pub const UNIT_FP: Fp = Fp { val: U256::one() }; - -fn exp_fp(x: Fp, e: U256) -> Fp { - let mut current = x; - let mut product = Fp { val: U256::one() }; - - for j in 0..256 { - if e.bit(j) { - product = product * current; - } - current = current * current; - } - product -} - -/// The degree 2 field extension Fp2 is given by adjoining i, the square root of -1, to Fp -/// The arithmetic in this extension is standard complex arithmetic -#[derive(Debug, Copy, Clone, PartialEq)] -pub struct Fp2 { - pub re: Fp, - pub im: Fp, -} - -pub const ZERO_FP2: Fp2 = Fp2 { - re: ZERO_FP, - im: ZERO_FP, -}; - -pub const UNIT_FP2: Fp2 = Fp2 { - re: UNIT_FP, - im: ZERO_FP, -}; - -impl Distribution for Standard { - fn sample(&self, rng: &mut R) -> Fp2 { - let (re, im) = rng.gen::<(Fp, Fp)>(); - Fp2 { re, im } - } -} - -impl Add for Fp2 { - type Output = Self; - - fn add(self, other: Self) -> Self { - Fp2 { - re: self.re + other.re, - im: self.im + other.im, - } - } -} - -impl Neg for Fp2 { - type Output = Self; - - fn neg(self) -> Self::Output { - Fp2 { - re: -self.re, - im: -self.im, - } - } -} - -impl Sub for Fp2 { - type Output = Self; - - fn sub(self, other: Self) -> Self { - Fp2 { - re: self.re - other.re, - im: self.im - other.im, - } - } -} - -impl Mul for Fp2 { - type Output = Self; - - fn mul(self, other: Self) -> Self { - Fp2 { - re: self.re * other.re - self.im * other.im, - im: self.re * other.im + self.im * other.re, - } - } -} - -impl Fp2 { - // We preemptively define a helper function which multiplies an Fp2 element by 9 + i - fn i9(self) -> Fp2 { - let nine = Fp::new(9); - Fp2 { - re: nine * self.re - self.im, - im: self.re + nine * self.im, - } - } - - // This function scalar multiplies an Fp2 by an Fp - pub fn scale(self, x: Fp) -> Fp2 { - Fp2 { - re: x * self.re, - im: x * self.im, - } - } - - /// Return the complex conjugate z' of z: Fp2 - /// This also happens to be the frobenius map - /// z -> z^p - /// since p == 3 mod 4 and hence - /// i^p = i^3 = -i - fn conj(self) -> Fp2 { - Fp2 { - re: self.re, - im: -self.im, - } - } - - // Return the magnitude squared of a complex number - fn norm_sq(self) -> Fp { - self.re * self.re + self.im * self.im - } - - /// The inverse of z is given by z'/||z||^2 since ||z||^2 = zz' - pub fn inv(self) -> Fp2 { - let norm_sq = self.norm_sq(); - self.conj().scale(norm_sq.inv()) - } -} - -#[allow(clippy::suspicious_arithmetic_impl)] -impl Div for Fp2 { - type Output = Self; - - fn div(self, rhs: Self) -> Self::Output { - self * rhs.inv() - } -} - -/// The degree 3 field extension Fp6 over Fp2 is given by adjoining t, where t^3 = 9 + i -// Fp6 has basis 1, t, t^2 over Fp2 -#[derive(Debug, Copy, Clone, PartialEq)] -pub struct Fp6 { - pub t0: Fp2, - pub t1: Fp2, - pub t2: Fp2, -} - -pub const ZERO_FP6: Fp6 = Fp6 { - t0: ZERO_FP2, - t1: ZERO_FP2, - t2: ZERO_FP2, -}; - -pub const UNIT_FP6: Fp6 = Fp6 { - t0: UNIT_FP2, - t1: ZERO_FP2, - t2: ZERO_FP2, -}; - -impl Distribution for Standard { - fn sample(&self, rng: &mut R) -> Fp6 { - let (t0, t1, t2) = rng.gen::<(Fp2, Fp2, Fp2)>(); - Fp6 { t0, t1, t2 } - } -} - -impl Add for Fp6 { - type Output = Self; - - fn add(self, other: Self) -> Self { - Fp6 { - t0: self.t0 + other.t0, - t1: self.t1 + other.t1, - t2: self.t2 + other.t2, - } - } -} - -impl Neg for Fp6 { - type Output = Self; - - fn neg(self) -> Self::Output { - Fp6 { - t0: -self.t0, - t1: -self.t1, - t2: -self.t2, - } - } -} - -impl Sub for Fp6 { - type Output = Self; - - fn sub(self, other: Self) -> Self { - Fp6 { - t0: self.t0 - other.t0, - t1: self.t1 - other.t1, - t2: self.t2 - other.t2, - } - } -} - -impl Mul for Fp6 { - type Output = Self; - - fn mul(self, other: Self) -> Self { - Fp6 { - t0: self.t0 * other.t0 + (self.t1 * other.t2 + self.t2 * other.t1).i9(), - t1: self.t0 * other.t1 + self.t1 * other.t0 + (self.t2 * other.t2).i9(), - t2: self.t0 * other.t2 + self.t1 * other.t1 + self.t2 * other.t0, - } - } -} - -impl Fp6 { - // This function scalar multiplies an Fp6 by an Fp2 - fn scale(self, x: Fp2) -> Fp6 { - Fp6 { - t0: x * self.t0, - t1: x * self.t1, - t2: x * self.t2, - } - } - - /// This function multiplies an Fp6 element by t, and hence shifts the bases, - /// where the t^2 coefficient picks up a factor of 9+i as the 1 coefficient of the output - fn sh(self) -> Fp6 { - Fp6 { - t0: self.t2.i9(), - t1: self.t0, - t2: self.t1, - } - } - - /// The nth frobenius endomorphism of a p^q field is given by mapping - /// x to x^(p^n) - /// which sends a + bt + ct^2: Fp6 to - /// a^(p^n) + b^(p^n) * t^(p^n) + c^(p^n) * t^(2p^n) - /// The Fp2 coefficients are determined by the comment in the conj method, - /// while the values of - /// t^(p^n) and t^(2p^n) - /// are precomputed in the constant arrays FROB_T1 and FROB_T2 - pub fn frob(self, n: usize) -> Fp6 { - let n = n % 6; - let frob_t1 = FROB_T1[n]; - let frob_t2 = FROB_T2[n]; - - if n % 2 != 0 { - Fp6 { - t0: self.t0.conj(), - t1: frob_t1 * self.t1.conj(), - t2: frob_t2 * self.t2.conj(), - } - } else { - Fp6 { - t0: self.t0, - t1: frob_t1 * self.t1, - t2: frob_t2 * self.t2, - } - } - } - - /// Let x_n = x^(p^n) and note that - /// x_0 = x^(p^0) = x^1 = x - /// (x_n)_m = (x^(p^n))^(p^m) = x^(p^n * p^m) = x^(p^(n+m)) = x_{n+m} - /// By Galois Theory, given x: Fp6, the product - /// phi = x_0 * x_1 * x_2 * x_3 * x_4 * x_5 - /// lands in Fp, and hence the inverse of x is given by - /// (x_1 * x_2 * x_3 * x_4 * x_5) / phi - /// We can save compute by rearranging the numerator: - /// (x_1 * x_3) * x_5 * (x_1 * x_3)_1 - /// By Galois theory, the following are in Fp2 and are complex conjugates - /// x_1 * x_3 * x_5, x_0 * x_2 * x_4 - /// and therefore - /// phi = ||x_1 * x_3 * x_5||^2 - /// and hence the inverse is given by - /// ([x_1 * x_3] * x_5) * [x_1 * x_3]_1 / ||[x_1 * x_3] * x_5||^2 - pub fn inv(self) -> Fp6 { - let prod_13 = self.frob(1) * self.frob(3); - let prod_135 = (prod_13 * self.frob(5)).t0; - let phi = prod_135.norm_sq(); - let prod_odds_over_phi = prod_135.scale(phi.inv()); - let prod_24 = prod_13.frob(1); - prod_24.scale(prod_odds_over_phi) - } - - pub fn on_stack(self) -> Vec { - let f: [U256; 6] = unsafe { transmute(self) }; - f.into_iter().collect() - } -} - -#[allow(clippy::suspicious_arithmetic_impl)] -impl Div for Fp6 { - type Output = Self; - - fn div(self, rhs: Self) -> Self::Output { - self * rhs.inv() - } -} - -/// The degree 2 field extension Fp12 over Fp6 is given by adjoining z, where z^2 = t. -/// It thus has basis 1, z over Fp6 -#[derive(Debug, Copy, Clone, PartialEq)] -pub struct Fp12 { - pub z0: Fp6, - pub z1: Fp6, -} - -pub const UNIT_FP12: Fp12 = Fp12 { - z0: UNIT_FP6, - z1: ZERO_FP6, -}; - -impl Distribution for Standard { - fn sample(&self, rng: &mut R) -> Fp12 { - let (z0, z1) = rng.gen::<(Fp6, Fp6)>(); - Fp12 { z0, z1 } - } -} - -impl Mul for Fp12 { - type Output = Self; - - fn mul(self, other: Self) -> Self { - let h0 = self.z0 * other.z0; - let h1 = self.z1 * other.z1; - let h01 = (self.z0 + self.z1) * (other.z0 + other.z1); - Fp12 { - z0: h0 + h1.sh(), - z1: h01 - (h0 + h1), - } - } -} - -impl Fp12 { - // This function scalar multiplies an Fp12 by an Fp6 - fn scale(self, x: Fp6) -> Fp12 { - Fp12 { - z0: x * self.z0, - z1: x * self.z1, - } - } - - fn conj(self) -> Fp12 { - Fp12 { - z0: self.z0, - z1: -self.z1, - } - } - /// The nth frobenius endomorphism of a p^q field is given by mapping - /// x to x^(p^n) - /// which sends a + bz: Fp12 to - /// a^(p^n) + b^(p^n) * z^(p^n) - /// where the values of z^(p^n) are precomputed in the constant array FROB_Z - pub fn frob(self, n: usize) -> Fp12 { - let n = n % 12; - Fp12 { - z0: self.z0.frob(n), - z1: self.z1.frob(n).scale(FROB_Z[n]), - } - } - - /// By Galois Theory, given x: Fp12, the product - /// phi = Prod_{i=0}^11 x_i - /// lands in Fp, and hence the inverse of x is given by - /// (Prod_{i=1}^11 x_i) / phi - /// The 6th Frob map is nontrivial but leaves Fp6 fixed and hence must be the conjugate: - /// x_6 = (a + bz)_6 = a - bz = x.conj() - /// Letting prod_17 = x_1 * x_7, the remaining factors in the numerator can be expresed as: - /// [(prod_17) * (prod_17)_2] * (prod_17)_4 * [(prod_17) * (prod_17)_2]_1 - /// By Galois theory, both the following are in Fp2 and are complex conjugates - /// prod_odds, prod_evens - /// Thus phi = ||prod_odds||^2, and hence the inverse is given by - /// prod_odds * prod_evens_except_six * x.conj() / ||prod_odds||^2 - pub fn inv(self) -> Fp12 { - let prod_17 = (self.frob(1) * self.frob(7)).z0; - let prod_1379 = prod_17 * prod_17.frob(2); - let prod_odds = (prod_1379 * prod_17.frob(4)).t0; - let phi = prod_odds.norm_sq(); - let prod_odds_over_phi = prod_odds.scale(phi.inv()); - let prod_evens_except_six = prod_1379.frob(1); - let prod_except_six = prod_evens_except_six.scale(prod_odds_over_phi); - self.conj().scale(prod_except_six) - } - - pub fn on_stack(self) -> Vec { - let f: [U256; 12] = unsafe { transmute(self) }; - f.into_iter().collect() - } -} - -#[allow(clippy::suspicious_arithmetic_impl)] -impl Div for Fp12 { - type Output = Self; - - fn div(self, rhs: Self) -> Self::Output { - self * rhs.inv() - } -} - -const FROB_T1: [Fp2; 6] = [ - Fp2 { - re: Fp { val: U256::one() }, - im: Fp { val: U256::zero() }, - }, - Fp2 { - re: Fp { - val: U256([ - 0x99e39557176f553d, - 0xb78cc310c2c3330c, - 0x4c0bec3cf559b143, - 0x2fb347984f7911f7, - ]), - }, - im: Fp { - val: U256([ - 0x1665d51c640fcba2, - 0x32ae2a1d0b7c9dce, - 0x4ba4cc8bd75a0794, - 0x16c9e55061ebae20, - ]), - }, - }, - Fp2 { - re: Fp { - val: U256([ - 0xe4bd44e5607cfd48, - 0xc28f069fbb966e3d, - 0x5e6dd9e7e0acccb0, - 0x30644e72e131a029, - ]), - }, - im: Fp { val: U256::zero() }, - }, - Fp2 { - re: Fp { - val: U256([ - 0x7b746ee87bdcfb6d, - 0x805ffd3d5d6942d3, - 0xbaff1c77959f25ac, - 0x0856e078b755ef0a, - ]), - }, - im: Fp { - val: U256([ - 0x380cab2baaa586de, - 0x0fdf31bf98ff2631, - 0xa9f30e6dec26094f, - 0x04f1de41b3d1766f, - ]), - }, - }, - Fp2 { - re: Fp { - val: U256([ - 0x5763473177fffffe, - 0xd4f263f1acdb5c4f, - 0x59e26bcea0d48bac, - 0x0, - ]), - }, - im: Fp { val: U256::zero() }, - }, - Fp2 { - re: Fp { - val: U256([ - 0x62e913ee1dada9e4, - 0xf71614d4b0b71f3a, - 0x699582b87809d9ca, - 0x28be74d4bb943f51, - ]), - }, - im: Fp { - val: U256([ - 0xedae0bcec9c7aac7, - 0x54f40eb4c3f6068d, - 0xc2b86abcbe01477a, - 0x14a88ae0cb747b99, - ]), - }, - }, -]; - -const FROB_T2: [Fp2; 6] = [ - Fp2 { - re: Fp { val: U256::one() }, - im: Fp { val: U256::zero() }, - }, - Fp2 { - re: { - Fp { - val: U256([ - 0x848a1f55921ea762, - 0xd33365f7be94ec72, - 0x80f3c0b75a181e84, - 0x05b54f5e64eea801, - ]), - } - }, - im: { - Fp { - val: U256([ - 0xc13b4711cd2b8126, - 0x3685d2ea1bdec763, - 0x9f3a80b03b0b1c92, - 0x2c145edbe7fd8aee, - ]), - } - }, - }, - Fp2 { - re: { - Fp { - val: U256([ - 0x5763473177fffffe, - 0xd4f263f1acdb5c4f, - 0x59e26bcea0d48bac, - 0x0, - ]), - } - }, - im: { Fp { val: U256::zero() } }, - }, - Fp2 { - re: { - Fp { - val: U256([ - 0x0e1a92bc3ccbf066, - 0xe633094575b06bcb, - 0x19bee0f7b5b2444e, - 0xbc58c6611c08dab, - ]), - } - }, - im: { - Fp { - val: U256([ - 0x5fe3ed9d730c239f, - 0xa44a9e08737f96e5, - 0xfeb0f6ef0cd21d04, - 0x23d5e999e1910a12, - ]), - } - }, - }, - Fp2 { - re: { - Fp { - val: U256([ - 0xe4bd44e5607cfd48, - 0xc28f069fbb966e3d, - 0x5e6dd9e7e0acccb0, - 0x30644e72e131a029, - ]), - } - }, - im: { Fp { val: U256::zero() } }, - }, - Fp2 { - re: { - Fp { - val: U256([ - 0xa97bda050992657f, - 0xde1afb54342c724f, - 0x1d9da40771b6f589, - 0x1ee972ae6a826a7d, - ]), - } - }, - im: { - Fp { - val: U256([ - 0x5721e37e70c255c9, - 0x54326430418536d1, - 0xd2b513cdbb257724, - 0x10de546ff8d4ab51, - ]), - } - }, - }, -]; - -const FROB_Z: [Fp2; 12] = [ - Fp2 { - re: { Fp { val: U256::one() } }, - im: { Fp { val: U256::zero() } }, - }, - Fp2 { - re: { - Fp { - val: U256([ - 0xd60b35dadcc9e470, - 0x5c521e08292f2176, - 0xe8b99fdd76e68b60, - 0x1284b71c2865a7df, - ]), - } - }, - im: { - Fp { - val: U256([ - 0xca5cf05f80f362ac, - 0x747992778eeec7e5, - 0xa6327cfe12150b8e, - 0x246996f3b4fae7e6, - ]), - } - }, - }, - Fp2 { - re: { - Fp { - val: U256([ - 0xe4bd44e5607cfd49, - 0xc28f069fbb966e3d, - 0x5e6dd9e7e0acccb0, - 0x30644e72e131a029, - ]), - } - }, - im: { Fp { val: U256::zero() } }, - }, - Fp2 { - re: { - Fp { - val: U256([ - 0xe86f7d391ed4a67f, - 0x894cb38dbe55d24a, - 0xefe9608cd0acaa90, - 0x19dc81cfcc82e4bb, - ]), - } - }, - im: { - Fp { - val: U256([ - 0x7694aa2bf4c0c101, - 0x7f03a5e397d439ec, - 0x06cbeee33576139d, - 0xabf8b60be77d73, - ]), - } - }, - }, - Fp2 { - re: { - Fp { - val: U256([ - 0xe4bd44e5607cfd48, - 0xc28f069fbb966e3d, - 0x5e6dd9e7e0acccb0, - 0x30644e72e131a029, - ]), - } - }, - im: { Fp { val: U256::zero() } }, - }, - Fp2 { - re: { - Fp { - val: U256([ - 0x1264475e420ac20f, - 0x2cfa95859526b0d4, - 0x072fc0af59c61f30, - 0x757cab3a41d3cdc, - ]), - } - }, - im: { - Fp { - val: U256([ - 0xe85845e34c4a5b9c, - 0xa20b7dfd71573c93, - 0x18e9b79ba4e2606c, - 0xca6b035381e35b6, - ]), - } - }, - }, - Fp2 { - re: { - Fp { - val: U256([ - 0x3c208c16d87cfd46, - 0x97816a916871ca8d, - 0xb85045b68181585d, - 0x30644e72e131a029, - ]), - } - }, - im: { Fp { val: U256::zero() } }, - }, - Fp2 { - re: { - Fp { - val: U256([ - 0x6615563bfbb318d7, - 0x3b2f4c893f42a916, - 0xcf96a5d90a9accfd, - 0x1ddf9756b8cbf849, - ]), - } - }, - im: { - Fp { - val: U256([ - 0x71c39bb757899a9b, - 0x2307d819d98302a7, - 0x121dc8b86f6c4ccf, - 0x0bfab77f2c36b843, - ]), - } - }, - }, - Fp2 { - re: { - Fp { - val: U256([ - 0x5763473177fffffe, - 0xd4f263f1acdb5c4f, - 0x59e26bcea0d48bac, - 0x0, - ]), - } - }, - im: { Fp { val: U256::zero() } }, - }, - Fp2 { - re: { - Fp { - val: U256([ - 0x53b10eddb9a856c8, - 0x0e34b703aa1bf842, - 0xc866e529b0d4adcd, - 0x1687cca314aebb6d, - ]), - } - }, - im: { - Fp { - val: U256([ - 0xc58be1eae3bc3c46, - 0x187dc4add09d90a0, - 0xb18456d34c0b44c0, - 0x2fb855bcd54a22b6, - ]), - } - }, - }, - Fp2 { - re: { - Fp { - val: U256([ - 0x5763473177ffffff, - 0xd4f263f1acdb5c4f, - 0x59e26bcea0d48bac, - 0x0, - ]), - } - }, - im: { Fp { val: U256::zero() } }, - }, - Fp2 { - re: { - Fp { - val: U256([ - 0x29bc44b896723b38, - 0x6a86d50bd34b19b9, - 0xb120850727bb392d, - 0x290c83bf3d14634d, - ]), - } - }, - im: { - Fp { - val: U256([ - 0x53c846338c32a1ab, - 0xf575ec93f71a8df9, - 0x9f668e1adc9ef7f0, - 0x23bd9e3da9136a73, - ]), - } - }, - }, -]; diff --git a/evm/src/bn254_pairing.rs b/evm/src/bn254_pairing.rs index bf5db74a..08eb614c 100644 --- a/evm/src/bn254_pairing.rs +++ b/evm/src/bn254_pairing.rs @@ -2,13 +2,13 @@ use std::ops::Add; use rand::Rng; -use crate::bn254_arithmetic::{Fp, Fp12, Fp2, Fp6, UNIT_FP12, ZERO_FP, ZERO_FP2}; +use crate::extension_tower::{FieldExt, Fp12, Fp2, Fp6, BN254}; -// The curve consists of pairs (x, y): (Fp, Fp) | y^2 = x^3 + 2 +// The curve consists of pairs (x, y): (BN254, BN254) | y^2 = x^3 + 2 #[derive(Debug, Copy, Clone, PartialEq)] pub struct Curve { - pub x: Fp, - pub y: Fp, + pub x: BN254, + pub y: BN254, } /// Standard addition formula for elliptic curves, restricted to the cases @@ -19,7 +19,7 @@ impl Add for Curve { fn add(self, other: Self) -> Self { let m = if self == other { - Fp::new(3) * self.x * self.x / (Fp::new(2) * self.y) + BN254::new(3) * self.x * self.x / (BN254::new(2) * self.y) } else { (other.y - self.y) / (other.x - self.x) }; @@ -34,12 +34,12 @@ impl Add for Curve { // The twisted curve consists of pairs (x, y): (Fp2, Fp2) | y^2 = x^3 + 3/(9 + i) #[derive(Debug, Copy, Clone, PartialEq)] pub struct TwistedCurve { - pub x: Fp2, - pub y: Fp2, + pub x: Fp2, + pub y: Fp2, } // The tate pairing takes a point each from the curve and its twist and outputs an Fp12 element -pub fn tate(p: Curve, q: TwistedCurve) -> Fp12 { +pub fn tate(p: Curve, q: TwistedCurve) -> Fp12 { let miller_output = miller_loop(p, q); invariant_exponent(miller_output) } @@ -47,10 +47,10 @@ pub fn tate(p: Curve, q: TwistedCurve) -> Fp12 { /// Standard code for miller loop, can be found on page 99 at this url: /// https://static1.squarespace.com/static/5fdbb09f31d71c1227082339/t/5ff394720493bd28278889c6/1609798774687/PairingsForBeginners.pdf#page=107 /// where EXP is a hardcoding of the array of Booleans that the loop traverses -pub fn miller_loop(p: Curve, q: TwistedCurve) -> Fp12 { +pub fn miller_loop(p: Curve, q: TwistedCurve) -> Fp12 { let mut r = p; - let mut acc = UNIT_FP12; - let mut line; + let mut acc: Fp12 = Fp12::::UNIT; + let mut line: Fp12; for i in EXP { line = tangent(r, q); @@ -66,14 +66,14 @@ pub fn miller_loop(p: Curve, q: TwistedCurve) -> Fp12 { } /// The sloped line function for doubling a point -pub fn tangent(p: Curve, q: TwistedCurve) -> Fp12 { - let cx = -Fp::new(3) * p.x * p.x; - let cy = Fp::new(2) * p.y; - sparse_embed(p.y * p.y - Fp::new(9), q.x.scale(cx), q.y.scale(cy)) +pub fn tangent(p: Curve, q: TwistedCurve) -> Fp12 { + let cx = -BN254::new(3) * p.x * p.x; + let cy = BN254::new(2) * p.y; + sparse_embed(p.y * p.y - BN254::new(9), q.x.scale(cx), q.y.scale(cy)) } /// The sloped line function for adding two points -pub fn cord(p1: Curve, p2: Curve, q: TwistedCurve) -> Fp12 { +pub fn cord(p1: Curve, p2: Curve, q: TwistedCurve) -> Fp12 { let cx = p2.y - p1.y; let cy = p1.x - p2.x; sparse_embed(p1.y * p2.x - p2.y * p1.x, q.x.scale(cx), q.y.scale(cy)) @@ -81,27 +81,31 @@ pub fn cord(p1: Curve, p2: Curve, q: TwistedCurve) -> Fp12 { /// The tangent and cord functions output sparse Fp12 elements. /// This map embeds the nonzero coefficients into an Fp12. -pub fn sparse_embed(g000: Fp, g01: Fp2, g11: Fp2) -> Fp12 { +pub fn sparse_embed(g000: BN254, g01: Fp2, g11: Fp2) -> Fp12 { let g0 = Fp6 { t0: Fp2 { re: g000, - im: ZERO_FP, + im: BN254::ZERO, }, t1: g01, - t2: ZERO_FP2, + t2: Fp2::::ZERO, }; let g1 = Fp6 { - t0: ZERO_FP2, + t0: Fp2::::ZERO, t1: g11, - t2: ZERO_FP2, + t2: Fp2::::ZERO, }; Fp12 { z0: g0, z1: g1 } } -pub fn gen_fp12_sparse(rng: &mut R) -> Fp12 { - sparse_embed(rng.gen::(), rng.gen::(), rng.gen::()) +pub fn gen_fp12_sparse(rng: &mut R) -> Fp12 { + sparse_embed( + rng.gen::(), + rng.gen::>(), + rng.gen::>(), + ) } /// The output y of the miller loop is not an invariant, @@ -116,7 +120,7 @@ pub fn gen_fp12_sparse(rng: &mut R) -> Fp12 { /// (p^4 - p^2 + 1)/N = p^3 + (a2)p^2 - (a1)p - a0 /// where 0 < a0, a1, a2 < p. Then the final power is given by /// y = y_3 * (y^a2)_2 * (y^-a1)_1 * (y^-a0) -pub fn invariant_exponent(f: Fp12) -> Fp12 { +pub fn invariant_exponent(f: Fp12) -> Fp12 { let mut y = f.frob(6) / f; y = y.frob(2) * y; let (y_a2, y_a1, y_a0) = get_custom_powers(y); @@ -134,11 +138,11 @@ pub fn invariant_exponent(f: Fp12) -> Fp12 { /// EXPS4 = [(a4[i], a2[i], a0[i]) for i in 0..len(a4)] /// EXPS2 = [ (a2[i], a0[i]) for i in len(a4)..len(a2)] /// EXPS0 = [ a0[i] for i in len(a2)..len(a0)] -fn get_custom_powers(f: Fp12) -> (Fp12, Fp12, Fp12) { - let mut sq: Fp12 = f; - let mut y0: Fp12 = UNIT_FP12; - let mut y2: Fp12 = UNIT_FP12; - let mut y4: Fp12 = UNIT_FP12; +fn get_custom_powers(f: Fp12) -> (Fp12, Fp12, Fp12) { + let mut sq: Fp12 = f; + let mut y0: Fp12 = Fp12::::UNIT; + let mut y2: Fp12 = Fp12::::UNIT; + let mut y4: Fp12 = Fp12::::UNIT; // proceed via standard squaring algorithm for exponentiation diff --git a/evm/src/cpu/kernel/interpreter.rs b/evm/src/cpu/kernel/interpreter.rs index 1693f490..408671ba 100644 --- a/evm/src/cpu/kernel/interpreter.rs +++ b/evm/src/cpu/kernel/interpreter.rs @@ -8,11 +8,11 @@ use ethereum_types::{U256, U512}; use keccak_hash::keccak; use plonky2::field::goldilocks_field::GoldilocksField; -use crate::bn254_arithmetic::BN_BASE; use crate::cpu::kernel::aggregator::KERNEL; use crate::cpu::kernel::constants::context_metadata::ContextMetadata; use crate::cpu::kernel::constants::global_metadata::GlobalMetadata; use crate::cpu::kernel::constants::txn_fields::NormalizedTxnField; +use crate::extension_tower::BN_BASE; use crate::generation::prover_input::ProverInputFn; use crate::generation::state::GenerationState; use crate::generation::GenerationInputs; diff --git a/evm/src/cpu/kernel/tests/bn254.rs b/evm/src/cpu/kernel/tests/bn254.rs index 1840a3c2..8e71ffd6 100644 --- a/evm/src/cpu/kernel/tests/bn254.rs +++ b/evm/src/cpu/kernel/tests/bn254.rs @@ -2,14 +2,13 @@ use anyhow::Result; use ethereum_types::U256; use rand::Rng; +use crate::bn254_pairing::{ + gen_fp12_sparse, invariant_exponent, miller_loop, tate, Curve, TwistedCurve, +}; use crate::cpu::kernel::interpreter::{ run_interpreter_with_memory, Interpreter, InterpreterMemoryInitialization, }; -// use crate::bn254_arithmetic::{Fp, Fp12, Fp2, Fp6}; -// use crate::bn254_pairing::{ -// gen_fp12_sparse, invariant_exponent, miller_loop, tate, Curve, TwistedCurve, -// }; -use crate::extension_tower::{Fp12, Fp6, Stack, BN254}; +use crate::extension_tower::{FieldExt, Fp12, Fp2, Fp6, Stack, BN254}; use crate::memory::segments::Segment::BnPairing; fn extract_stack(interpreter: Interpreter<'static>) -> Vec { @@ -96,29 +95,29 @@ fn test_mul_fp12() -> Result<()> { let mut rng = rand::thread_rng(); let f: Fp12 = rng.gen::>(); let g: Fp12 = rng.gen::>(); - // let h: Fp12 = gen_fp12_sparse(&mut rng); + let h: Fp12 = gen_fp12_sparse(&mut rng); let setup_normal: InterpreterMemoryInitialization = setup_mul_fp12_test(out, f, g, "mul_fp254_12"); - // let setup_sparse: InterpreterMemoryInitialization = - // setup_mul_fp12_test(out, f, h, "mul_fp254_12_sparse"); + let setup_sparse: InterpreterMemoryInitialization = + setup_mul_fp12_test(out, f, h, "mul_fp254_12_sparse"); let setup_square: InterpreterMemoryInitialization = setup_mul_fp12_test(out, f, f, "square_fp254_12"); let intrptr_normal: Interpreter = run_interpreter_with_memory(setup_normal).unwrap(); - // let intrptr_sparse: Interpreter = run_interpreter_with_memory(setup_sparse).unwrap(); + let intrptr_sparse: Interpreter = run_interpreter_with_memory(setup_sparse).unwrap(); let intrptr_square: Interpreter = run_interpreter_with_memory(setup_square).unwrap(); let out_normal: Vec = intrptr_normal.extract_kernel_memory(BnPairing, out..out + 12); - // let out_sparse: Vec = intrptr_sparse.extract_kernel_memory(BnPairing, out..out + 12); + let out_sparse: Vec = intrptr_sparse.extract_kernel_memory(BnPairing, out..out + 12); let out_square: Vec = intrptr_square.extract_kernel_memory(BnPairing, out..out + 12); let exp_normal: Vec = (f * g).on_stack(); - // let exp_sparse: Vec = (f * h).on_stack(); + let exp_sparse: Vec = (f * h).on_stack(); let exp_square: Vec = (f * f).on_stack(); assert_eq!(out_normal, exp_normal); - // assert_eq!(out_sparse, exp_sparse); + assert_eq!(out_sparse, exp_sparse); assert_eq!(out_square, exp_square); Ok(()) @@ -171,154 +170,154 @@ fn test_frob_fp12() -> Result<()> { Ok(()) } -// #[test] -// fn test_inv_fp12() -> Result<()> { -// let ptr: usize = 200; -// let inv: usize = 212; -// let mut rng = rand::thread_rng(); -// let f: Fp12 = rng.gen::(); +#[test] +fn test_inv_fp12() -> Result<()> { + let ptr: usize = 200; + let inv: usize = 212; + let mut rng = rand::thread_rng(); + let f: Fp12 = rng.gen::>(); -// let setup = InterpreterMemoryInitialization { -// label: "inv_fp254_12".to_string(), -// stack: vec![U256::from(ptr), U256::from(inv), U256::from(0xdeadbeefu32)], -// segment: BnPairing, -// memory: vec![(ptr, f.on_stack())], -// }; -// let interpreter: Interpreter = run_interpreter_with_memory(setup).unwrap(); -// let output: Vec = interpreter.extract_kernel_memory(BnPairing, inv..inv + 12); -// let expected: Vec = f.inv().on_stack(); + let setup = InterpreterMemoryInitialization { + label: "inv_fp254_12".to_string(), + stack: vec![U256::from(ptr), U256::from(inv), U256::from(0xdeadbeefu32)], + segment: BnPairing, + memory: vec![(ptr, f.on_stack())], + }; + let interpreter: Interpreter = run_interpreter_with_memory(setup).unwrap(); + let output: Vec = interpreter.extract_kernel_memory(BnPairing, inv..inv + 12); + let expected: Vec = f.inv().on_stack(); -// assert_eq!(output, expected); + assert_eq!(output, expected); -// Ok(()) -// } + Ok(()) +} -// #[test] -// fn test_invariant_exponent() -> Result<()> { -// let ptr: usize = 200; -// let mut rng = rand::thread_rng(); -// let f: Fp12 = rng.gen::(); +#[test] +fn test_invariant_exponent() -> Result<()> { + let ptr: usize = 200; + let mut rng = rand::thread_rng(); + let f: Fp12 = rng.gen::>(); -// let setup = InterpreterMemoryInitialization { -// label: "bn254_invariant_exponent".to_string(), -// stack: vec![U256::from(ptr), U256::from(0xdeadbeefu32)], -// segment: BnPairing, -// memory: vec![(ptr, f.on_stack())], -// }; + let setup = InterpreterMemoryInitialization { + label: "bn254_invariant_exponent".to_string(), + stack: vec![U256::from(ptr), U256::from(0xdeadbeefu32)], + segment: BnPairing, + memory: vec![(ptr, f.on_stack())], + }; -// let interpreter: Interpreter = run_interpreter_with_memory(setup).unwrap(); -// let output: Vec = interpreter.extract_kernel_memory(BnPairing, ptr..ptr + 12); -// let expected: Vec = invariant_exponent(f).on_stack(); + let interpreter: Interpreter = run_interpreter_with_memory(setup).unwrap(); + let output: Vec = interpreter.extract_kernel_memory(BnPairing, ptr..ptr + 12); + let expected: Vec = invariant_exponent(f).on_stack(); -// assert_eq!(output, expected); + assert_eq!(output, expected); -// Ok(()) -// } + Ok(()) +} -// // The curve is cyclic with generator (1, 2) -// pub const CURVE_GENERATOR: Curve = { -// Curve { -// x: Fp { val: U256::one() }, -// y: Fp { -// val: U256([2, 0, 0, 0]), -// }, -// } -// }; +// The curve is cyclic with generator (1, 2) +pub const CURVE_GENERATOR: Curve = { + Curve { + x: BN254 { val: U256::one() }, + y: BN254 { + val: U256([2, 0, 0, 0]), + }, + } +}; -// // The twisted curve is cyclic with generator (x, y) as follows -// pub const TWISTED_GENERATOR: TwistedCurve = { -// TwistedCurve { -// x: Fp2 { -// re: Fp { -// val: U256([ -// 0x46debd5cd992f6ed, -// 0x674322d4f75edadd, -// 0x426a00665e5c4479, -// 0x1800deef121f1e76, -// ]), -// }, -// im: Fp { -// val: U256([ -// 0x97e485b7aef312c2, -// 0xf1aa493335a9e712, -// 0x7260bfb731fb5d25, -// 0x198e9393920d483a, -// ]), -// }, -// }, -// y: Fp2 { -// re: Fp { -// val: U256([ -// 0x4ce6cc0166fa7daa, -// 0xe3d1e7690c43d37b, -// 0x4aab71808dcb408f, -// 0x12c85ea5db8c6deb, -// ]), -// }, -// im: Fp { -// val: U256([ -// 0x55acdadcd122975b, -// 0xbc4b313370b38ef3, -// 0xec9e99ad690c3395, -// 0x090689d0585ff075, -// ]), -// }, -// }, -// } -// }; +// The twisted curve is cyclic with generator (x, y) as follows +pub const TWISTED_GENERATOR: TwistedCurve = { + TwistedCurve { + x: Fp2 { + re: BN254 { + val: U256([ + 0x46debd5cd992f6ed, + 0x674322d4f75edadd, + 0x426a00665e5c4479, + 0x1800deef121f1e76, + ]), + }, + im: BN254 { + val: U256([ + 0x97e485b7aef312c2, + 0xf1aa493335a9e712, + 0x7260bfb731fb5d25, + 0x198e9393920d483a, + ]), + }, + }, + y: Fp2 { + re: BN254 { + val: U256([ + 0x4ce6cc0166fa7daa, + 0xe3d1e7690c43d37b, + 0x4aab71808dcb408f, + 0x12c85ea5db8c6deb, + ]), + }, + im: BN254 { + val: U256([ + 0x55acdadcd122975b, + 0xbc4b313370b38ef3, + 0xec9e99ad690c3395, + 0x090689d0585ff075, + ]), + }, + }, + } +}; -// #[test] -// fn test_miller() -> Result<()> { -// let ptr: usize = 200; -// let out: usize = 206; -// let inputs: Vec = vec![ -// CURVE_GENERATOR.x.val, -// CURVE_GENERATOR.y.val, -// TWISTED_GENERATOR.x.re.val, -// TWISTED_GENERATOR.x.im.val, -// TWISTED_GENERATOR.y.re.val, -// TWISTED_GENERATOR.y.im.val, -// ]; +#[test] +fn test_miller() -> Result<()> { + let ptr: usize = 200; + let out: usize = 206; + let inputs: Vec = vec![ + CURVE_GENERATOR.x.val, + CURVE_GENERATOR.y.val, + TWISTED_GENERATOR.x.re.val, + TWISTED_GENERATOR.x.im.val, + TWISTED_GENERATOR.y.re.val, + TWISTED_GENERATOR.y.im.val, + ]; -// let setup = InterpreterMemoryInitialization { -// label: "bn254_miller".to_string(), -// stack: vec![U256::from(ptr), U256::from(out), U256::from(0xdeadbeefu32)], -// segment: BnPairing, -// memory: vec![(ptr, inputs)], -// }; -// let interpreter = run_interpreter_with_memory(setup).unwrap(); -// let output: Vec = interpreter.extract_kernel_memory(BnPairing, out..out + 12); -// let expected = miller_loop(CURVE_GENERATOR, TWISTED_GENERATOR).on_stack(); + let setup = InterpreterMemoryInitialization { + label: "bn254_miller".to_string(), + stack: vec![U256::from(ptr), U256::from(out), U256::from(0xdeadbeefu32)], + segment: BnPairing, + memory: vec![(ptr, inputs)], + }; + let interpreter = run_interpreter_with_memory(setup).unwrap(); + let output: Vec = interpreter.extract_kernel_memory(BnPairing, out..out + 12); + let expected = miller_loop(CURVE_GENERATOR, TWISTED_GENERATOR).on_stack(); -// assert_eq!(output, expected); + assert_eq!(output, expected); -// Ok(()) -// } + Ok(()) +} -// #[test] -// fn test_tate() -> Result<()> { -// let ptr: usize = 200; -// let out: usize = 206; -// let inputs: Vec = vec![ -// CURVE_GENERATOR.x.val, -// CURVE_GENERATOR.y.val, -// TWISTED_GENERATOR.x.re.val, -// TWISTED_GENERATOR.x.im.val, -// TWISTED_GENERATOR.y.re.val, -// TWISTED_GENERATOR.y.im.val, -// ]; +#[test] +fn test_tate() -> Result<()> { + let ptr: usize = 200; + let out: usize = 206; + let inputs: Vec = vec![ + CURVE_GENERATOR.x.val, + CURVE_GENERATOR.y.val, + TWISTED_GENERATOR.x.re.val, + TWISTED_GENERATOR.x.im.val, + TWISTED_GENERATOR.y.re.val, + TWISTED_GENERATOR.y.im.val, + ]; -// let setup = InterpreterMemoryInitialization { -// label: "bn254_tate".to_string(), -// stack: vec![U256::from(ptr), U256::from(out), U256::from(0xdeadbeefu32)], -// segment: BnPairing, -// memory: vec![(ptr, inputs)], -// }; -// let interpreter = run_interpreter_with_memory(setup).unwrap(); -// let output: Vec = interpreter.extract_kernel_memory(BnPairing, out..out + 12); -// let expected = tate(CURVE_GENERATOR, TWISTED_GENERATOR).on_stack(); + let setup = InterpreterMemoryInitialization { + label: "bn254_tate".to_string(), + stack: vec![U256::from(ptr), U256::from(out), U256::from(0xdeadbeefu32)], + segment: BnPairing, + memory: vec![(ptr, inputs)], + }; + let interpreter = run_interpreter_with_memory(setup).unwrap(); + let output: Vec = interpreter.extract_kernel_memory(BnPairing, out..out + 12); + let expected = tate(CURVE_GENERATOR, TWISTED_GENERATOR).on_stack(); -// assert_eq!(output, expected); + assert_eq!(output, expected); -// Ok(()) -// } + Ok(()) +} diff --git a/evm/src/generation/prover_input.rs b/evm/src/generation/prover_input.rs index 1313de83..7f62acda 100644 --- a/evm/src/generation/prover_input.rs +++ b/evm/src/generation/prover_input.rs @@ -5,7 +5,7 @@ use anyhow::{bail, Error}; use ethereum_types::{BigEndianHash, H256, U256}; use plonky2::field::types::Field; -use crate::bn254_arithmetic::Fp12; +use crate::extension_tower::{FieldExt, Fp12, BN254}; use crate::generation::prover_input::EvmField::{ Bn254Base, Bn254Scalar, Secp256k1Base, Secp256k1Scalar, }; @@ -207,7 +207,7 @@ impl EvmField { } fn field_extension_inverse(&self, n: usize, f: [U256; 12]) -> U256 { - let f: Fp12 = unsafe { transmute(f) }; + let f: Fp12 = unsafe { transmute(f) }; let f_inv: [U256; 12] = unsafe { transmute(f.inv()) }; f_inv[n] } diff --git a/evm/src/lib.rs b/evm/src/lib.rs index fa48d8dc..dc2204df 100644 --- a/evm/src/lib.rs +++ b/evm/src/lib.rs @@ -8,7 +8,6 @@ pub mod all_stark; pub mod arithmetic; -pub mod bn254_arithmetic; pub mod bn254_pairing; pub mod config; pub mod constraint_consumer;