def dy

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/secp256k1/penc.bend:166

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

166def dy(+one: Nat, +h1: {one == 1n : Nat}, +x: List<&2, Nat>, +r: List<&2, Nat>, +y: List<&2, Nat>, +par: Nat, +hr: {PT.red(one, r) == True{} : Bool}, +hy: {PT.red(one, y) == True{} : Bool}, +hp: {Nat.is_lt(par, 2n) == True{} : Bool}) -> {mpv(one, P.decompress_if(x, P.lift_y(y, par), F.eq(F.mul(y, y), r))) == CV.decompress_if(FS.value(one, x), CV.pick_parity(FS.prime(one), FS.value(one, y), par), Nat.is_eq(FS.mmul(FS.prime(one), FS.value(one, y), FS.value(one, y)), FS.value(one, r))) : Maybe<&2, CV.SPoint>}:
167  +hs = FO.mul_r(one, h1, y, y, hy, hy)
168  %Equal.sym(Bool, F.eq(F.mul(y, y), r), Nat.is_eq(FS.value(one, F.mul(y, y)), FS.value(one, r)), FW.eq_f(one, h1, F.mul(y, y), r, PM.l16(one, F.mul(y, y), hs), PM.l16(one, r, hr))) : {mpv(one, P.decompress_if(x, P.lift_y(y, par), _)) == CV.decompress_if(FS.value(one, x), CV.pick_parity(FS.prime(one), FS.value(one, y), par), Nat.is_eq(FS.mmul(FS.prime(one), FS.value(one, y), FS.value(one, y)), FS.value(one, r))) : Maybe<&2, CV.SPoint>}
169  %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)) : {mpv(one, P.decompress_if(x, P.lift_y(y, par), Nat.is_eq(_, FS.value(one, r)))) == CV.decompress_if(FS.value(one, x), CV.pick_parity(FS.prime(one), FS.value(one, y), par), Nat.is_eq(FS.mmul(FS.prime(one), FS.value(one, y), FS.value(one, y)), FS.value(one, r))) : Maybe<&2, CV.SPoint>}
170  %Equal.sym(Nat, CV.pick_parity(FS.prime(one), FS.value(one, y), par), FS.value(one, P.lift_y(y, par)), Equal.sym(Nat, FS.value(one, P.lift_y(y, par)), CV.pick_parity(FS.prime(one), FS.value(one, y), par), lift_v(one, h1, y, par, hy, hp))) : {mpv(one, P.decompress_if(x, P.lift_y(y, par), Nat.is_eq(FS.mmul(FS.prime(one), FS.value(one, y), FS.value(one, y)), FS.value(one, r)))) == CV.decompress_if(FS.value(one, x), _, Nat.is_eq(FS.mmul(FS.prime(one), FS.value(one, y), FS.value(one, y)), FS.value(one, r))) : Maybe<&2, CV.SPoint>}
171  dif_v(one, h1, x, P.lift_y(y, par), Nat.is_eq(FS.mmul(FS.prime(one), FS.value(one, y), FS.value(one, y)), FS.value(one, r)))