def p58_value

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/curve25519/proof.bend:92

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/math/natural/arith.bend as NR
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/prime.bend as PR
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/cong.bend as G

92def p58_value(+one: Nat, +h1: {one == 1n : Nat}, +a: List<&2, U32>, +ha: {FS.tight(a) == True{} : Bool}) -> FS.PowP58.value(one, h1, a, ha):
93  +pp = pp1(one)
94  +k = Nat.div(Nat.sub(1n+pp, 5n), 8n)
95  +e = G.c_trans(pp, FS.value(F.pow_p58(a)), Nat.pow(FS.value(a), k), FS.fpow(1n+pp, FS.value(a), k), PW.p58_val(one, h1, pp, PR.hP(one, h1), a, ok(a, ha)), G.c_sym(pp, FS.fpow(1n+pp, FS.value(a), k), Nat.pow(FS.value(a), k), G.c_mod(pp, Nat.pow(FS.value(a), k))))
96  at_p(one, h1, z => {Nat.mod(FS.value(F.pow_p58(a)), z) == FS.fpow(z, FS.value(a), Nat.div(Nat.sub(z, 5n), 8n)) : Nat}, Equal.trans(Nat, Nat.mod(FS.value(F.pow_p58(a)), 1n+pp), Nat.mod(FS.fpow(1n+pp, FS.value(a), k), 1n+pp), FS.fpow(1n+pp, FS.value(a), k), e, NR.mod_mod(pp, Nat.pow(FS.value(a), k))))