def pass_fold

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/curve25519/fold.bend:141

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

141# value(xs) == 2 c p + value(pass(xs))
142def pass_fold(+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}) -> {FS.value(xs) == Nat.add(Nat.mul(Nat.add(v(LM.cc(F.carry(xs, 0))), v(LM.cc(F.carry(xs, 0)))), 1n+pp), FS.value(F.pass(xs))) : Nat}:
143  +r = F.carry(xs, 0)
144  +a = FS.value(LM.cl(r))
145  +c = v(LM.cc(r))
146  +e1 = Equal.sym(Nat, Nat.add(a, LM.shn(32n, c)), FS.value(xs), cr_val(one, h1, xs, hx))
147  +e2 = fold_id(one, h1, pp, hP, a, c)
148  +e3 = M.cong_r(Nat.mul(Nat.add(c, c), 1n+pp), Nat.add(a, Nat.mul(38n, c)), FS.value(F.pass(xs)), Equal.sym(Nat, FS.value(F.pass(xs)), Nat.add(a, Nat.mul(38n, c)), pass_val(one, h1, xs, hx)))
149  Equal.trans(Nat, FS.value(xs), Nat.add(a, LM.shn(32n, c)), Nat.add(Nat.mul(Nat.add(c, c), 1n+pp), FS.value(F.pass(xs))), e1, Equal.trans(Nat, Nat.add(a, LM.shn(32n, c)), Nat.add(Nat.mul(Nat.add(c, c), 1n+pp), Nat.add(a, Nat.mul(38n, c))), Nat.add(Nat.mul(Nat.add(c, c), 1n+pp), FS.value(F.pass(xs))), e2, e3))