def cvx

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/ed25519/scalar.bend:44

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/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/fold.bend as FD
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/fieldops.bend as FO

44def cvx(+one: Nat, +h1: {one == 1n : Nat}, +mm: Nat, +x: List<&2, U32>, +cp: List<&2, U32>, +hx: {LM.okb(32n, x, 255n) == True{} : Bool}, +hk: {LM.okb(32n, cp, 255n) == True{} : Bool}) -> {Nat.add(FS.value(LM.cl(F.carry(F.addl(x, cp), 0))), LM.shn(32n, v(LM.cc(F.carry(F.addl(x, cp), 0))))) == Nat.add(FS.value(x), FS.value(cp)) : Nat}:
45  +ys = F.addl(x, cp)
46  Equal.trans(Nat, Nat.add(FS.value(LM.cl(F.carry(ys, 0))), LM.shn(32n, v(LM.cc(F.carry(ys, 0))))), FS.value(ys), Nat.add(FS.value(x), FS.value(cp)), FD.cr_val(one, h1, ys, ad_okb(one, h1, x, cp, hx, hk)), PL.addl_val(one, h1, x, cp, 255n, 255n, LM.okb_lea(32n, x, 255n, hx), LM.okb_lea(32n, cp, 255n, hk), FO.lt32_small(one, h1, Nat.add(255n, 255n), {==})))