def mul_mod

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/curve25519/mulw.bend:146

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/num.bend as M
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/poly.bend as PL
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/reduce.bend as RD

146def mul_mod(+one: Nat, +h1: {one == 1n : Nat}, +pp: Nat, +hP: {Nat.add(1n+pp, 19n) == WD.sc(255n, one) : Nat}, +a: List<&2, U32>, +b: List<&2, U32>, +ha: {LM.okb(32n, a, 255n) == True{} : Bool}, +hb: {LM.okb(32n, b, 255n) == True{} : Bool}) -> {Nat.mod(FS.value(F.mul(a, b)), 1n+pp) == Nat.mod(Nat.mul(FS.value(a), FS.value(b)), 1n+pp) : Nat}:
147  +zs = F.conv(a, b)
148  +hge = conv_ge(31n, a, b, 32n, 255n, ha, PL.okb_len_ge(32n, b, 255n, hb))
149  +e1 = RD.reduce_mod(one, h1, pp, hP, F.wide(zs), wide_in(one, h1, a, b, ha, hb))
150  +e2 = wide_mod(one, h1, pp, hP, zs, conv_lea21(one, h1, a, b, ha, hb), hge)
151  +e3 = M.cong_mod(1n+pp, FS.value(zs), Nat.mul(FS.value(a), FS.value(b)), conv_val(one, h1, a, b, ha, hb))
152  Equal.trans(Nat, Nat.mod(FS.value(F.mul(a, b)), 1n+pp), Nat.mod(FS.value(F.wide(zs)), 1n+pp), Nat.mod(Nat.mul(FS.value(a), FS.value(b)), 1n+pp), e1, Equal.trans(Nat, Nat.mod(FS.value(F.wide(zs)), 1n+pp), Nat.mod(FS.value(zs), 1n+pp), Nat.mod(Nat.mul(FS.value(a), FS.value(b)), 1n+pp), e2, e3))