def pick_r

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/secp256k1/penc.bend:137

import Base
import bend-collections-laws-crypto@1.0.0.0/src/crypto/secp256k1/limbs.bend as L
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/proofs/crypto/secp256k1/fieldops.bend as FO
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

137def pick_r(+one: Nat, +h1: {one == 1n : Nat}, q: Nat, par: Nat, +y: List<&2, Nat>, +hq: {Nat.is_lt(q, 2n) == True{} : Bool}, +hp: {Nat.is_lt(par, 2n) == True{} : Bool}, +hy: {PT.red(one, y) == True{} : Bool}) -> {PT.red(one, F.select(Nat.sub(Nat.add(q, par), Nat.mul(Nat.mul(q, par), 2n)), F.neg(y), y)) == True{} : Bool}:
138  match q par:
139    case 0n 0n:
140      %Equal.sym(List<&2, Nat>, L.select(0n, F.neg(y), y), y, PM.sel0(one, 16n, F.neg(y), y, PM.l16(one, F.neg(y), FO.neg_r(one, h1, y, hy)), PM.l16(one, y, hy))) : {PT.red(one, _) == True{} : Bool}
141      hy
142    case 0n 1n:
143      %Equal.sym(List<&2, Nat>, L.select(1n, F.neg(y), y), F.neg(y), PM.sel1(one, 16n, F.neg(y), y, PM.l16(one, F.neg(y), FO.neg_r(one, h1, y, hy)), PM.l16(one, y, hy))) : {PT.red(one, _) == True{} : Bool}
144      FO.neg_r(one, h1, y, hy)
145    case 1n 0n:
146      %Equal.sym(List<&2, Nat>, L.select(1n, F.neg(y), y), F.neg(y), PM.sel1(one, 16n, F.neg(y), y, PM.l16(one, F.neg(y), FO.neg_r(one, h1, y, hy)), PM.l16(one, y, hy))) : {PT.red(one, _) == True{} : Bool}
147      FO.neg_r(one, h1, y, hy)
148    case 1n 1n:
149      %Equal.sym(List<&2, Nat>, L.select(0n, F.neg(y), y), y, PM.sel0(one, 16n, F.neg(y), y, PM.l16(one, F.neg(y), FO.neg_r(one, h1, y, hy)), PM.l16(one, y, hy))) : {PT.red(one, _) == True{} : Bool}
150      hy
151    case 2n+ +c _:
152      Empty.absurd({PT.red(one, F.select(Nat.sub(Nat.add(2n+c, par), Nat.mul(Nat.mul(2n+c, par), 2n)), F.neg(y), y)) == True{} : Bool}, PM.not01(c, hq))
153    case _ 2n+ +c:
154      Empty.absurd({PT.red(one, F.select(Nat.sub(Nat.add(q, 2n+c), Nat.mul(Nat.mul(q, 2n+c), 2n)), F.neg(y), y)) == True{} : Bool}, PM.not01(c, hp))