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Dmitry Vagner 2023-01-28 14:17:55 +08:00
parent 5b124fb121
commit ea01e19c41
1 changed files with 3 additions and 3 deletions
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6
evm/src/bn254_arithmetic.rs
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@ -420,13 +420,13 @@ impl Fp12 {
/// 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 = conj_fp12(x)
/// 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 = norm(prod_odds), and hence the inverse is given by
/// normalize(prod_odds) * prod_evens_except_six * conj_fp12(x)
/// 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);