def p58_val

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/curve25519/pow.bend:299

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/cong.bend as G

299def p58_val(+one: Nat, +h1: {one == 1n : Nat}, +pp: Nat, +hP: {Nat.add(1n+pp, 19n) == WD.sc(255n, one) : Nat}, +x: List<&2, U32>, +hx: {LM.okb(32n, x, 255n) == True{} : Bool}) -> G.ceq(pp, FS.value(F.pow_p58(x)), Nat.pow(FS.value(x), Nat.div(Nat.sub(1n+pp, 5n), 8n))):
300  +ex = Nat.add(Nat.mul(Fo(one, 250n), WD.sc(blen(p58_bits()), one)), eb(one, p58_bits()))
301  G.c_trans(pp, FS.value(F.pow_p58(x)), Nat.pow(FS.value(x), ex), Nat.pow(FS.value(x), Nat.div(Nat.sub(1n+pp, 5n), 8n)), chain_val(one, h1, pp, hP, 249n, p58_bits(), x, hx), G.c_eq(pp, Nat.pow(FS.value(x), ex), Nat.pow(FS.value(x), Nat.div(Nat.sub(1n+pp, 5n), 8n)), Equal.cong(Nat, Nat, t => Nat.pow(FS.value(x), t), ex, Nat.div(Nat.sub(1n+pp, 5n), 8n), p58_exp(one, h1, pp, hP))))