def rc_mul

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/curve25519/rel.bend:45

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/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

45def rc_mul(+one: Nat, +h1: {one == 1n : Nat}, +pp: Nat, +hP: {Nat.add(1n+pp, 19n) == WD.sc(255n, one) : Nat}, +x: List<&2, U32>, +y: List<&2, U32>, +a: Nat, +b: Nat, +ox: {LM.okb(32n, x, 255n) == True{} : Bool}, +cx: G.ceq(pp, FS.value(x), a), +oy: {LM.okb(32n, y, 255n) == True{} : Bool}, +cy: G.ceq(pp, FS.value(y), b)) -> G.ceq(pp, FS.value(F.mul(x, y)), FS.fmul(1n+pp, a, b)):
46  +e = G.c_trans(pp, FS.value(F.mul(x, y)), Nat.mul(FS.value(x), FS.value(y)), FS.fmul(1n+pp, a, b), MW.mul_mod(one, h1, pp, hP, x, y, ox, oy), G.c_trans(pp, Nat.mul(FS.value(x), FS.value(y)), Nat.mul(a, b), FS.fmul(1n+pp, a, b), G.c_mul(pp, FS.value(x), a, FS.value(y), b, cx, cy), G.c_sym(pp, Nat.mod(Nat.mul(a, b), 1n+pp), Nat.mul(a, b), G.c_mod(pp, Nat.mul(a, b)))))
47  e