def mul_small_value

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/curve25519/proof.bend:72

import Base
import bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend as C
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/nat.bend as N
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/mulw.bend as MW
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/prime.bend as PR

72def mul_small_value(+one: Nat, +h1: {one == 1n : Nat}, +a: List<&2, U32>, +k: U32, +ha: {FS.tight(a) == True{} : Bool}, +hk: {Nat.is_lt(U32.to_nat(k), C.shift(17n, one)) == True{} : Bool}) -> FS.MulSmall.value(one, h1, a, k, ha, hk):
73  at_p(one, h1, z => {Nat.mod(FS.value(F.mul_small(a, k)), z) == FS.fmul(z, FS.value(a), U32.to_nat(k)) : Nat}, MW.mul_small_mod(one, h1, pp1(one), PR.hP(one, h1), a, k, ok(a, ha), N.lt_le(v(k), WD.sc(17n, one), hk)))