def decompress_v

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/secp256k1/penc.bend:173

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/fieldpow.bend as FP
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/point.bend as PT

173def decompress_v(+one: Nat, +h1: {one == 1n : Nat}, +x: List<&2, Nat>, +par: Nat, +hx: {PT.red(one, x) == True{} : Bool}, +hp: {Nat.is_lt(par, 2n) == True{} : Bool}) -> {mpv(one, P.decompress(x, par)) == CV.decompress(FS.prime(one), FS.value(one, x), par) : Maybe<&2, CV.SPoint>}:
174  +hr = rhs_r(one, h1, x, hx)
175  +hy = FP.sqrt_r(one, h1, P.rhs(x), hr)
176  %Equal.sym(Nat, CV.rhs(FS.prime(one), FS.value(one, x)), FS.value(one, P.rhs(x)), Equal.sym(Nat, FS.value(one, P.rhs(x)), CV.rhs(FS.prime(one), FS.value(one, x)), rhs_v(one, h1, x, hx))) : {mpv(one, P.decompress_if(x, P.lift_y(F.sqrt(P.rhs(x)), par), F.eq(F.mul(F.sqrt(P.rhs(x)), F.sqrt(P.rhs(x))), P.rhs(x)))) == CV.decompress_if(FS.value(one, x), CV.pick_parity(FS.prime(one), FS.fsqrt(FS.prime(one), _), par), Nat.is_eq(FS.mmul(FS.prime(one), FS.fsqrt(FS.prime(one), CV.rhs(FS.prime(one), FS.value(one, x))), FS.fsqrt(FS.prime(one), CV.rhs(FS.prime(one), FS.value(one, x)))), CV.rhs(FS.prime(one), FS.value(one, x)))) : Maybe<&2, CV.SPoint>}
177  %Equal.sym(Nat, CV.rhs(FS.prime(one), FS.value(one, x)), FS.value(one, P.rhs(x)), Equal.sym(Nat, FS.value(one, P.rhs(x)), CV.rhs(FS.prime(one), FS.value(one, x)), rhs_v(one, h1, x, hx))) : {mpv(one, P.decompress_if(x, P.lift_y(F.sqrt(P.rhs(x)), par), F.eq(F.mul(F.sqrt(P.rhs(x)), F.sqrt(P.rhs(x))), P.rhs(x)))) == CV.decompress_if(FS.value(one, x), CV.pick_parity(FS.prime(one), FS.fsqrt(FS.prime(one), FS.value(one, P.rhs(x))), par), Nat.is_eq(FS.mmul(FS.prime(one), FS.fsqrt(FS.prime(one), _), FS.fsqrt(FS.prime(one), CV.rhs(FS.prime(one), FS.value(one, x)))), CV.rhs(FS.prime(one), FS.value(one, x)))) : Maybe<&2, CV.SPoint>}
178  %Equal.sym(Nat, CV.rhs(FS.prime(one), FS.value(one, x)), FS.value(one, P.rhs(x)), Equal.sym(Nat, FS.value(one, P.rhs(x)), CV.rhs(FS.prime(one), FS.value(one, x)), rhs_v(one, h1, x, hx))) : {mpv(one, P.decompress_if(x, P.lift_y(F.sqrt(P.rhs(x)), par), F.eq(F.mul(F.sqrt(P.rhs(x)), F.sqrt(P.rhs(x))), P.rhs(x)))) == CV.decompress_if(FS.value(one, x), CV.pick_parity(FS.prime(one), FS.fsqrt(FS.prime(one), FS.value(one, P.rhs(x))), par), Nat.is_eq(FS.mmul(FS.prime(one), FS.fsqrt(FS.prime(one), FS.value(one, P.rhs(x))), FS.fsqrt(FS.prime(one), _)), CV.rhs(FS.prime(one), FS.value(one, x)))) : Maybe<&2, CV.SPoint>}
179  %Equal.sym(Nat, CV.rhs(FS.prime(one), FS.value(one, x)), FS.value(one, P.rhs(x)), Equal.sym(Nat, FS.value(one, P.rhs(x)), CV.rhs(FS.prime(one), FS.value(one, x)), rhs_v(one, h1, x, hx))) : {mpv(one, P.decompress_if(x, P.lift_y(F.sqrt(P.rhs(x)), par), F.eq(F.mul(F.sqrt(P.rhs(x)), F.sqrt(P.rhs(x))), P.rhs(x)))) == CV.decompress_if(FS.value(one, x), CV.pick_parity(FS.prime(one), FS.fsqrt(FS.prime(one), FS.value(one, P.rhs(x))), par), Nat.is_eq(FS.mmul(FS.prime(one), FS.fsqrt(FS.prime(one), FS.value(one, P.rhs(x))), FS.fsqrt(FS.prime(one), FS.value(one, P.rhs(x)))), _)) : Maybe<&2, CV.SPoint>}
180  %Equal.sym(Nat, FS.fsqrt(FS.prime(one), FS.value(one, P.rhs(x))), FS.value(one, F.sqrt(P.rhs(x))), Equal.sym(Nat, FS.value(one, F.sqrt(P.rhs(x))), FS.fsqrt(FS.prime(one), FS.value(one, P.rhs(x))), FP.sqrt_v(one, h1, P.rhs(x), hr))) : {mpv(one, P.decompress_if(x, P.lift_y(F.sqrt(P.rhs(x)), par), F.eq(F.mul(F.sqrt(P.rhs(x)), F.sqrt(P.rhs(x))), P.rhs(x)))) == CV.decompress_if(FS.value(one, x), CV.pick_parity(FS.prime(one), _, par), Nat.is_eq(FS.mmul(FS.prime(one), FS.fsqrt(FS.prime(one), FS.value(one, P.rhs(x))), FS.fsqrt(FS.prime(one), FS.value(one, P.rhs(x)))), FS.value(one, P.rhs(x)))) : Maybe<&2, CV.SPoint>}
181  %Equal.sym(Nat, FS.fsqrt(FS.prime(one), FS.value(one, P.rhs(x))), FS.value(one, F.sqrt(P.rhs(x))), Equal.sym(Nat, FS.value(one, F.sqrt(P.rhs(x))), FS.fsqrt(FS.prime(one), FS.value(one, P.rhs(x))), FP.sqrt_v(one, h1, P.rhs(x), hr))) : {mpv(one, P.decompress_if(x, P.lift_y(F.sqrt(P.rhs(x)), par), F.eq(F.mul(F.sqrt(P.rhs(x)), F.sqrt(P.rhs(x))), P.rhs(x)))) == CV.decompress_if(FS.value(one, x), CV.pick_parity(FS.prime(one), FS.value(one, F.sqrt(P.rhs(x))), par), Nat.is_eq(FS.mmul(FS.prime(one), _, FS.fsqrt(FS.prime(one), FS.value(one, P.rhs(x)))), FS.value(one, P.rhs(x)))) : Maybe<&2, CV.SPoint>}
182  %Equal.sym(Nat, FS.fsqrt(FS.prime(one), FS.value(one, P.rhs(x))), FS.value(one, F.sqrt(P.rhs(x))), Equal.sym(Nat, FS.value(one, F.sqrt(P.rhs(x))), FS.fsqrt(FS.prime(one), FS.value(one, P.rhs(x))), FP.sqrt_v(one, h1, P.rhs(x), hr))) : {mpv(one, P.decompress_if(x, P.lift_y(F.sqrt(P.rhs(x)), par), F.eq(F.mul(F.sqrt(P.rhs(x)), F.sqrt(P.rhs(x))), P.rhs(x)))) == CV.decompress_if(FS.value(one, x), CV.pick_parity(FS.prime(one), FS.value(one, F.sqrt(P.rhs(x))), par), Nat.is_eq(FS.mmul(FS.prime(one), FS.value(one, F.sqrt(P.rhs(x))), _), FS.value(one, P.rhs(x)))) : Maybe<&2, CV.SPoint>}
183  dy(one, h1, x, P.rhs(x), F.sqrt(P.rhs(x)), par, hr, hy, hp)