def po_okb

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/curve25519/pow.bend:104

import Base
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/mulw.bend as MW

104def po_okb(+one: Nat, +h1: {one == 1n : Nat}, +n: Nat, +x: List<&2, U32>, +acc: List<&2, U32>, +hx: {LM.okb(32n, x, 255n) == True{} : Bool}, +ha: {LM.okb(32n, acc, 255n) == True{} : Bool}) -> {LM.okb(32n, F.pow_ones(x, n, acc), 255n) == True{} : Bool}:
105  match n:
106    case 0n:
107      %Equal.sym(List<&2, U32>, F.pow_ones(x, 0n, acc), acc, po_zero(x, acc, hx)) : {LM.okb(32n, _, 255n) == True{} : Bool}
108      ha
109    case 1n+ +m:
110      %Equal.sym(List<&2, U32>, F.pow_ones(x, 1n+m, acc), F.pow_ones(x, m, F.mul(F.sq(acc), x)), po_step(x, m, acc, hx)) : {LM.okb(32n, _, 255n) == True{} : Bool}
111      po_okb(one, h1, m, x, F.mul(F.sq(acc), x), hx, MW.mul_okb(one, h1, F.sq(acc), x, MW.sq_okb(one, h1, acc, ha), hx))