def reduce_mod

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/curve25519/reduce.bend:150

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/fold.bend as FD

150def reduce_mod(+one: Nat, +h1: {one == 1n : Nat}, +pp: Nat, +hP: {Nat.add(1n+pp, 19n) == WD.sc(255n, one) : Nat}, +xs: List<&2, U32>, +hx: {LM.okb(32n, xs, WD.sc(28n, one)) == True{} : Bool}) -> {Nat.mod(FS.value(F.reduce(xs)), 1n+pp) == Nat.mod(FS.value(xs), 1n+pp) : Nat}:
151  +y1 = F.pass(xs)
152  +hy1 = FD.pass_okb(one, h1, xs, hx)
153  +y2 = F.pass(y1)
154  +hy2 = FD.pass_okb(one, h1, y1, hy1)
155  Equal.trans(Nat, Nat.mod(FS.value(F.pass(y2)), 1n+pp), Nat.mod(FS.value(y2), 1n+pp), Nat.mod(FS.value(xs), 1n+pp), FD.pass_mod(one, h1, pp, hP, y2, hy2),
156    Equal.trans(Nat, Nat.mod(FS.value(y2), 1n+pp), Nat.mod(FS.value(y1), 1n+pp), Nat.mod(FS.value(xs), 1n+pp), FD.pass_mod(one, h1, pp, hP, y1, hy1), FD.pass_mod(one, h1, pp, hP, xs, hx)))