def rc_inv

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/curve25519/rel.bend:58

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/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/limbs.bend as LM
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/pow.bend as PW
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/cong.bend as G

58def rc_inv(+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, +ox: {LM.okb(32n, x, 255n) == True{} : Bool}, +cx: G.ceq(pp, FS.value(x), a)) -> G.ceq(pp, FS.value(F.inv(x)), FS.finv(1n+pp, a)):
59  +P = {1n+pp : Nat}
60  +k = Nat.sub(P, 2n)
61  +e = G.c_trans(pp, FS.value(F.inv(x)), Nat.pow(FS.value(x), k), FS.finv(P, a), PW.inv_val(one, h1, pp, hP, x, ox), G.c_trans(pp, Nat.pow(FS.value(x), k), Nat.pow(a, k), FS.finv(P, a), G.c_pow(pp, FS.value(x), a, k, cx), G.c_sym(pp, Nat.mod(Nat.pow(a, k), P), Nat.pow(a, k), G.c_mod(pp, Nat.pow(a, k)))))
62  e