def by_ceq

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/curve25519/canon.bend:41

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/lib/arith.bend as AR
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/math/natural/arith.bend as NR
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
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/cong.bend as G
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/freeze.bend as FZ

41def by_ceq(+one: Nat, +h1: {one == 1n : Nat}, +pp: Nat, +hP: {Nat.add(1n+pp, 19n) == WD.sc(255n, one) : Nat}, +x: List<&2, U32>, +cp: List<&2, U32>, +hx: {LM.okb(32n, x, 255n) == True{} : Bool}, +hk: {LM.okb(32n, cp, 128n) == True{} : Bool}, +hv: {K.valo(one, cp) == Nat.add(1n+pp, 38n) : Nat}, +b: Bool, +hb: {Nat.is_lt(v(LM.cc(F.carry(F.addl(x, cp), 0))), one) == b : Bool}) -> G.ceq(pp, FS.value(FZ.csg(x, cp)), FS.value(x)):
42  match b:
43    case True{}:
44      %Equal.sym(List<&2, U32>, FZ.csg(x, cp), x, FZ.cs_zero(one, h1, x, cp, hx, hk, hb)) : G.ceq(pp, FS.value(_), FS.value(x))
45      G.c_refl(pp, FS.value(x))
46    case False{}:
47      +s = LM.cl(F.carry(F.addl(x, cp), 0))
48      %Equal.sym(List<&2, U32>, FZ.csg(x, cp), s, FZ.cs_one(one, h1, pp, hP, x, cp, hx, hk, hv, hb)) : G.ceq(pp, FS.value(_), FS.value(x))
49      +e1 = FZ.o_case(one, h1, pp, hP, x, cp, hx, hk, hv, hb)
50      +e2 = Equal.trans(Nat, Nat.add(Nat.mul(1n, 1n+pp), FS.value(s)), Nat.add(1n+pp, FS.value(s)), FS.value(x), M.cong_l(Nat.mul(1n, 1n+pp), 1n+pp, FS.value(s), AR.one_mul(1n+pp)), Equal.trans(Nat, Nat.add(1n+pp, FS.value(s)), Nat.add(FS.value(s), 1n+pp), FS.value(x), NA.add_comm(1n+pp, FS.value(s)), e1))
51      +e3 = NR.absorb(pp, 1n, FS.value(s))
52      G.c_sym(pp, FS.value(x), FS.value(s), G.c_trans(pp, FS.value(x), Nat.add(Nat.mul(1n, 1n+pp), FS.value(s)), FS.value(s), G.c_eq(pp, FS.value(x), Nat.add(Nat.mul(1n, 1n+pp), FS.value(s)), Equal.sym(Nat, Nat.add(Nat.mul(1n, 1n+pp), FS.value(s)), FS.value(x), e2)), e3))