def bytes_rel

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/ed25519/pcodec.bend:211

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/curve25519/x25519.bend as SX
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/proofs/lib/word.bend as WD
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/canon.bend as CN
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/curve25519/xbits.bend as XB

211# the canonical bytes of an element related to a reduced a
212def bytes_rel(+one: Nat, +h1: {one == 1n : Nat}, +pp: Nat, +hP: {Nat.add(1n+pp, 19n) == WD.sc(255n, one) : Nat}, +x: List<&2, U32>, +a: Nat, +rx: RL.R(pp, x, a), +ha: {Nat.mod(a, 1n+pp) == a : Nat}) -> {F.to_bytes(x) == SX.le_bytes(32n, a) : List<&2, U32>}:
213  +y = F.freeze(x)
214  +oy = CN.freeze_okb(one, h1, pp, hP, x, RL.r_o(pp, x, a, rx))
215  +ey = Equal.trans(Nat, FS.value(y), Nat.mod(FS.value(x), 1n+pp), a, CN.freeze_val(one, h1, pp, hP, x, RL.r_o(pp, x, a, rx)), Equal.trans(Nat, Nat.mod(FS.value(x), 1n+pp), Nat.mod(a, 1n+pp), a, RL.r_c(pp, x, a, rx), ha))
216  Equal.trans(List<&2, U32>, y, SX.le_bytes(32n, FS.value(y)), SX.le_bytes(32n, a), Equal.sym(List<&2, U32>, SX.le_bytes(32n, FS.value(y)), y, XB.bytes_le(32n, y, oy)), Equal.cong(Nat, List<&2, U32>, z => SX.le_bytes(32n, z), FS.value(y), a, ey))