def dec_root_rel_core

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/ed25519/pdec.bend:78

import Base
import bend-collections-laws-crypto@1.0.0.0/spec/crypto/curve25519/field.bend as FS
import bend-collections-laws-crypto@1.0.0.0/spec/crypto/ed25519.bend as SE
import bend-collections-laws-crypto@1.0.0.0/src/crypto/curve25519/field.bend as F
import bend-collections-laws-crypto@1.0.0.0/src/crypto/ed25519/point.bend as PT
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/word.bend as WD
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/rel.bend as RL
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/ed25519/prel.bend as PR
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/ed25519/pcodec.bend as PC

78def dec_root_rel_core(+one: Nat, +h1: {one == 1n : Nat}, +pp: Nat, +hP: {Nat.add(1n+pp, 19n) == WD.sc(255n, one) : Nat}, +cs: PT.Cs, +rs: RL.R(pp, PT.cs_s(cs), SE.sqm1(1n+pp)), +x: List<&2, U32>, +a: Nat, +rx: RL.R(pp, x, a), +ha: {Nat.mod(a, 1n+pp) == a : Nat}, +y: List<&2, U32>, +b: Nat, +ry: RL.R(pp, y, b), +x0: U32, +b0: Nat, +hx0: {v(x0) == b0 : Nat}, +hb0: {Nat.is_le(b0, 1n) == True{} : Bool}, +u: List<&2, U32>, +vxx: List<&2, U32>, +iu: Bool, +inu: Bool, +su: Bool, +snu: Bool, +hu: {iu == su : Bool}, +hnu: {inu == snu : Bool}) -> PC.MR(pp, PT.dec_root(cs, x, y, x0, u, vxx, su, snu), SE.dec_root(1n+pp, a, b, b0, su, snu)):
79  match su snu:
80    case True{} _:
81      dec_fin_rel(one, h1, pp, hP, x, a, rx, ha, y, b, ry, x0, b0, hx0, hb0, Bool.and(Nat.is_eq(a, 0n), Nat.is_eq(b0, 1n)), fail_eq(one, h1, pp, hP, x, a, rx, ha, x0, b0, hx0))
82    case False{} True{}:
83      +P = {1n+pp : Nat}
84      +x1 = F.mul(x, PT.cs_s(cs))
85      +X1 = FS.fmul(P, a, SE.sqm1(P))
86      +r1 = PR.rmul(one, h1, pp, hP, x, PT.cs_s(cs), a, SE.sqm1(P), rx, rs)
87      +h1r = PC.red(pp, Nat.mul(a, SE.sqm1(P)))
88      dec_fin_rel(one, h1, pp, hP, x1, X1, r1, h1r, y, b, ry, x0, b0, hx0, hb0, Bool.and(Nat.is_eq(X1, 0n), Nat.is_eq(b0, 1n)), fail_eq(one, h1, pp, hP, x1, X1, r1, h1r, x0, b0, hx0))
89    case False{} False{}:
90      {==}