def mul_go_v

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/secp256k1/pmul.bend:88

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/spec/crypto/secp256k1/curve.bend as CV
import bend-collections-laws-crypto@1.0.0.0/src/crypto/secp256k1/point.bend as P
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
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/point.bend as PT

88def mul_go_v(+one: Nat, +h1: {one == 1n : Nat}, bs: List<&2, Nat>, +pp: P.Point, +r: P.Point, +hbs: {BV.all01(bs) == True{} : Bool}, +hp: {PT.pred(one, pp) == True{} : Bool}, +hr: {PT.pred(one, r) == True{} : Bool}) -> {PT.pv(one, P.mul_go(bs, pp, r)) == CV.lmul(FS.prime(one), bs, PT.pv(one, pp), PT.pv(one, r)) : CV.SPoint}:
89  match bs:
90    case Nil{}:
91      {==}
92    case +b <> +t:
93      +hb = Lg.and_left(Nat.is_lt(b, 2n), BV.all01(t), hbs)
94      +ht = Lg.and_right(Nat.is_lt(b, 2n), BV.all01(t), hbs)
95      +hd = PT.pdbl_r(one, h1, r, hr)
96      +hs = step_r(one, h1, b, pp, P.dbl(r), hb, hp, hd)
97      %Equal.sym(CV.SPoint, PT.pv(one, P.mul_go(t, pp, P.step(b, pp, P.dbl(r)))), CV.lmul(FS.prime(one), t, PT.pv(one, pp), PT.pv(one, P.step(b, pp, P.dbl(r)))), mul_go_v(one, h1, t, pp, P.step(b, pp, P.dbl(r)), ht, hp, hs)) : {_ == CV.lmul(FS.prime(one), t, PT.pv(one, pp), CV.step(b, FS.prime(one), PT.pv(one, pp), CV.pdbl(FS.prime(one), PT.pv(one, r)))) : CV.SPoint}
98      %Equal.sym(CV.SPoint, PT.pv(one, P.step(b, pp, P.dbl(r))), CV.step(b, FS.prime(one), PT.pv(one, pp), PT.pv(one, P.dbl(r))), step_v(one, h1, b, pp, P.dbl(r), hb, hp, hd)) : {CV.lmul(FS.prime(one), t, PT.pv(one, pp), _) == CV.lmul(FS.prime(one), t, PT.pv(one, pp), CV.step(b, FS.prime(one), PT.pv(one, pp), CV.pdbl(FS.prime(one), PT.pv(one, r)))) : CV.SPoint}
99      %Equal.sym(CV.SPoint, PT.pv(one, P.dbl(r)), CV.pdbl(FS.prime(one), PT.pv(one, r)), PT.pdbl_v(one, h1, r, hr)) : {CV.lmul(FS.prime(one), t, PT.pv(one, pp), CV.step(b, FS.prime(one), PT.pv(one, pp), _)) == CV.lmul(FS.prime(one), t, PT.pv(one, pp), CV.step(b, FS.prime(one), PT.pv(one, pp), CV.pdbl(FS.prime(one), PT.pv(one, r)))) : CV.SPoint}
100      {==}