def on_curve_v

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/secp256k1/penc.bend:83

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/field.bend as F
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/crypto/secp256k1/fieldops.bend as FO
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/fwrap.bend as FW
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/point.bend as PT
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/sel.bend as PM

83def on_curve_v(+one: Nat, +h1: {one == 1n : Nat}, +x: List<&2, Nat>, +y: List<&2, Nat>, +hx: {PT.red(one, x) == True{} : Bool}, +hy: {PT.red(one, y) == True{} : Bool}) -> {P.on_curve(x, y) == CV.on_curve(FS.prime(one), FS.value(one, x), FS.value(one, y)) : Bool}:
84  +hs = FO.mul_r(one, h1, y, y, hy, hy)
85  +hr = rhs_r(one, h1, x, hx)
86  %Equal.sym(Bool, F.eq(F.mul(y, y), P.rhs(x)), Nat.is_eq(FS.value(one, F.mul(y, y)), FS.value(one, P.rhs(x))), FW.eq_f(one, h1, F.mul(y, y), P.rhs(x), PM.l16(one, F.mul(y, y), hs), PM.l16(one, P.rhs(x), hr))) : {_ == Nat.is_eq(FS.mmul(FS.prime(one), FS.value(one, y), FS.value(one, y)), CV.rhs(FS.prime(one), FS.value(one, x))) : Bool}
87  %Equal.sym(Nat, FS.value(one, F.mul(y, y)), FS.mmul(FS.prime(one), FS.value(one, y), FS.value(one, y)), FO.mul_v(one, h1, y, y, hy, hy)) : {Nat.is_eq(_, FS.value(one, P.rhs(x))) == Nat.is_eq(FS.mmul(FS.prime(one), FS.value(one, y), FS.value(one, y)), CV.rhs(FS.prime(one), FS.value(one, x))) : Bool}
88  %Equal.sym(Nat, FS.value(one, P.rhs(x)), CV.rhs(FS.prime(one), FS.value(one, x)), rhs_v(one, h1, x, hx)) : {Nat.is_eq(FS.mmul(FS.prime(one), FS.value(one, y), FS.value(one, y)), _) == Nat.is_eq(FS.mmul(FS.prime(one), FS.value(one, y), FS.value(one, y)), CV.rhs(FS.prime(one), FS.value(one, x))) : Bool}
89  {==}