def add_mod

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/curve25519/fieldops.bend:53

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

53def add_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.add(a, b)), 1n+pp) == Nat.mod(Nat.add(FS.value(a), FS.value(b)), 1n+pp) : Nat}:
54  +e1 = RD.reduce_mod(one, h1, pp, hP, F.addl(a, b), addl_okb(one, h1, a, b, ha, hb))
55  +e2 = M.cong_mod(1n+pp, FS.value(F.addl(a, b)), Nat.add(FS.value(a), FS.value(b)), PL.addl_val(one, h1, a, b, 255n, 255n, LM.okb_lea(32n, a, 255n, ha), LM.okb_lea(32n, b, 255n, hb), lt32_small(one, h1, Nat.add(255n, 255n), {==})))
56  Equal.trans(Nat, Nat.mod(FS.value(F.add(a, b)), 1n+pp), Nat.mod(FS.value(F.addl(a, b)), 1n+pp), Nat.mod(Nat.add(FS.value(a), FS.value(b)), 1n+pp), e1, e2)