def pb_val

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/curve25519/pow.bend:176

import Base
import bend-collections-laws-crypto@1.0.0.0/spec/crypto/curve25519/field.bend as FS
import bend-collections-laws-crypto@1.0.0.0/src/crypto/curve25519/field.bend as F
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/word.bend as WD
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/lemmas/proofs/nat_algebra.bend as NA
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/limbs.bend as LM
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/mulw.bend as MW
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/cong.bend as G

176def pb_val(+one: Nat, +h1: {one == 1n : Nat}, +pp: Nat, +hP: {Nat.add(1n+pp, 19n) == WD.sc(255n, one) : Nat}, +b: Bool, +x: List<&2, U32>, +acc: List<&2, U32>, +hx: {LM.okb(32n, x, 255n) == True{} : Bool}, +ha: {LM.okb(32n, acc, 255n) == True{} : Bool}) -> G.ceq(pp, FS.value(F.pow_bit(b, x, acc)), Nat.mul(Nat.mul(FS.value(acc), FS.value(acc)), Nat.pow(FS.value(x), bexp(b)))):
177  match b:
178    case True{}:
179      +A = FS.value(acc)
180      +X = FS.value(x)
181      G.c_trans(pp, FS.value(F.mul(F.sq(acc), x)), Nat.mul(Nat.mul(A, A), X), Nat.mul(Nat.mul(A, A), Nat.pow(X, 1n)), step_c(one, h1, pp, hP, acc, x, ha, hx), G.c_eq(pp, Nat.mul(Nat.mul(A, A), X), Nat.mul(Nat.mul(A, A), Nat.pow(X, 1n)), Equal.cong(Nat, Nat, t => Nat.mul(Nat.mul(A, A), t), X, Nat.pow(X, 1n), Equal.sym(Nat, Nat.mul(X, 1n), X, NA.mul_one(X)))))
182    case False{}:
183      +A = FS.value(acc)
184      G.c_trans(pp, FS.value(F.sq(acc)), Nat.mul(A, A), Nat.mul(Nat.mul(A, A), 1n), MW.sq_mod(one, h1, pp, hP, acc, ha), G.c_eq(pp, Nat.mul(A, A), Nat.mul(Nat.mul(A, A), 1n), Equal.sym(Nat, Nat.mul(Nat.mul(A, A), 1n), Nat.mul(A, A), NA.mul_one(Nat.mul(A, A)))))