def sel_v

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/secp256k1/psign.bend:80

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/spec/crypto/secp256k1/ecdsa.bend as ES
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/scalar.bend as S
import bend-collections-laws-crypto@1.0.0.0/src/crypto/secp256k1/bytes.bend as B
import bend-collections-laws-crypto@1.0.0.0/src/crypto/secp256k1/ecdsa.bend as E
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/scalarops.bend as SO
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/sel.bend as SL

80def sel_v(+one: Nat, +h1: {one == 1n : Nat}, hb: Bool, +s0: List<&2, Nat>, +hs: {FS.reduced(one, FS.order(one), s0) == True{} : Bool}) -> {B.to_be(S.select(E.b2n(hb), S.neg(s0), s0)) == CV.i2osp(32n, ES.low(hb, FS.order(one), FS.value(one, s0))) : List<&2, U32>}:
81  match hb:
82    case True{}:
83      %Equal.sym(List<&2, Nat>, L.select(1n, S.neg(s0), s0), S.neg(s0), SL.sel1(one, 16n, S.neg(s0), s0, SL.sl16(one, S.neg(s0), SO.neg_r(one, h1, s0, hs)), SL.sl16(one, s0, hs))) : {B.to_be(_) == CV.i2osp(32n, FS.mneg(FS.order(one), FS.value(one, s0))) : List<&2, U32>}
84      %Equal.sym(List<&2, U32>, B.to_be(S.neg(s0)), CV.i2osp(32n, FS.value(one, S.neg(s0))), tbv(one, h1, S.neg(s0), SL.sl16(one, S.neg(s0), SO.neg_r(one, h1, s0, hs)))) : {_ == CV.i2osp(32n, FS.mneg(FS.order(one), FS.value(one, s0))) : List<&2, U32>}
85      %Equal.sym(Nat, FS.value(one, S.neg(s0)), FS.mneg(FS.order(one), FS.value(one, s0)), SO.neg_v(one, h1, s0, hs)) : {CV.i2osp(32n, _) == CV.i2osp(32n, FS.mneg(FS.order(one), FS.value(one, s0))) : List<&2, U32>}
86      {==}
87    case False{}:
88      %Equal.sym(List<&2, Nat>, L.select(0n, S.neg(s0), s0), s0, SL.sel0(one, 16n, S.neg(s0), s0, SL.sl16(one, S.neg(s0), SO.neg_r(one, h1, s0, hs)), SL.sl16(one, s0, hs))) : {B.to_be(_) == CV.i2osp(32n, FS.value(one, s0)) : List<&2, U32>}
89      tbv(one, h1, s0, SL.sl16(one, s0, hs))