def pow_ev

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/secp256k1/fieldpow.bend:79

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/crypto/secp256k1/limbs.bend as LV
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/consts.bend as K
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/bitsv.bend as BV

79def pow_ev(+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}, +e: Nat, +he: {LV.ev(acc) == Nat.mod(Nat.pow(LV.ev(x), e), 1n+K.pp(one)) : Nat}, +hb: {BV.all01(bs) == True{} : Bool}) -> {LV.ev(F.pow(x, bs, acc)) == Nat.mod(Nat.pow(LV.ev(x), BV.hv(bs, one, e)), 1n+K.pp(one)) : Nat}:
80  %Equal.sym(List<&2, Nat>, F.pow(x, bs, acc), F.pow_go(x, bs, acc), pow_is(one, x, hx, bs, acc)) : {LV.ev(_) == Nat.mod(Nat.pow(LV.ev(x), BV.hv(bs, one, e)), 1n+K.pp(one)) : Nat}
81  pow_e(one, h1, x, hx, bs, acc, ha, e, he, hb)