def pow_r

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/secp256k1/fieldpow.bend:54

import Base
import bend-collections-laws-crypto@1.0.0.0/spec/crypto/secp256k1/field.bend as FS
import bend-collections-laws-crypto@1.0.0.0/src/crypto/secp256k1/field.bend as F
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/logic.bend as Lg
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/bitsv.bend as BV

54def pow_r(+one: Nat, +h1: {one == 1n : Nat}, +x: List<&2, Nat>, +hx: {FS.reduced(one, FS.prime(one), x) == True{} : Bool}, bs: List<&2, Nat>, +acc: List<&2, Nat>, +ha: {FS.reduced(one, FS.prime(one), acc) == True{} : Bool}, +hb: {BV.all01(bs) == True{} : Bool}) -> {FS.reduced(one, FS.prime(one), F.pow_go(x, bs, acc)) == True{} : Bool}:
55  match bs:
56    case Nil{}:
57      ha
58    case +b <> +t:
59      +h0 = Lg.and_left(Nat.is_lt(b, 2n), BV.all01(t), hb)
60      pow_r(one, h1, x, hx, t, F.pow_step(b, x, F.sq(acc)), step_r(one, h1, x, hx, acc, ha, b, h0), Lg.and_right(Nat.is_lt(b, 2n), BV.all01(t), hb))