def comp_p_val

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/curve25519/freeze.bend:33

import Base
import bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend as C
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/logic.bend as L
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/lib/lemmas/proofs/nat_algebra.bend as NA
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/num.bend as M
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/consts.bend as K

33def comp_p_val(+one: Nat, +h1: {one == 1n : Nat}, +pp: Nat, +hP: {Nat.add(1n+pp, 19n) == WD.sc(255n, one) : Nat}) -> {K.valo(one, F.comp_p()) == Nat.add(1n+pp, 38n) : Nat}:
34  +P = {1n+pp : Nat}
35  +R = K.rep(30n, 0, Con{128, Nil{}})
36  %Equal.sym(List<&2, U32>, F.comp_p(), Con{19, R}, comp_p_shape()) : {K.valo(one, _) == Nat.add(P, 38n) : Nat}
37  +e1 = K.run0(one, 30n, Con{128, Nil{}})
38  +e2 = L.subst(Nat, o => {K.valo(o, Con{128, Nil{}}) == WD.sc(7n, o) : Nat}, 1n, one, Equal.sym(Nat, one, 1n, h1), {==})
39  +e3 = Equal.trans(Nat, K.valo(one, R), LM.shn(30n, K.valo(one, Con{128, Nil{}})), LM.shn(30n, WD.sc(7n, one)), e1, Equal.cong(Nat, Nat, t => LM.shn(30n, t), K.valo(one, Con{128, Nil{}}), WD.sc(7n, one), e2))
40  +e4 = M.cong_add(Nat.mul(one, v(19)), 19n, C.shift(8n, K.valo(one, R)), WD.sc(255n, one), K.one_k(one, h1, v(19)), M.cong_sc(8n, K.valo(one, R), LM.shn(30n, WD.sc(7n, one)), e3))
41  +e5 = M.cong_r(19n, WD.sc(255n, one), Nat.add(P, 19n), Equal.sym(Nat, Nat.add(P, 19n), WD.sc(255n, one), hP))
42  Equal.trans(Nat, Nat.add(Nat.mul(one, v(19)), C.shift(8n, K.valo(one, R))), Nat.add(19n, WD.sc(255n, one)), Nat.add(P, 38n), e4, Equal.trans(Nat, Nat.add(19n, WD.sc(255n, one)), Nat.add(19n, Nat.add(P, 19n)), Nat.add(P, 38n), e5, NA.add_swap(19n, P, 19n)))