def c_fst

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/curve25519/ladder.bend:52

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/spec/crypto/curve25519/x25519.bend as S
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/crypto/curve25519/limbs.bend as LM
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/fieldops.bend as FO
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/xbits.bend as XB

52def c_fst(+one: Nat, +h1: {one == 1n : Nat}, +pp: Nat, +sw: U32, +s: Nat, +hs: {v(sw) == s : Nat}, +hb: {Nat.is_le(s, 1n) == True{} : Bool}, +a: List<&2, U32>, +b: List<&2, U32>, +A: Nat, +B: Nat, +oa: {LM.okb(32n, a, 255n) == True{} : Bool}, +ca: G.ceq(pp, FS.value(a), A), +ob: {LM.okb(32n, b, 255n) == True{} : Bool}, +cb: G.ceq(pp, FS.value(b), B)) -> G.ceq(pp, FS.value(F.select(sw, a, b)), S.cs_fst(s, A, B)):
53  match s:
54    case 0n:
55      %Equal.sym(U32, sw, 0, XB.u0(sw, hs)) : G.ceq(pp, FS.value(F.select(_, a, b)), A)
56      %Equal.sym(List<&2, U32>, F.select(0, a, b), a, FO.select0(one, h1, 32n, a, b, oa, ob)) : G.ceq(pp, FS.value(_), A)
57      ca
58    case 1n:
59      %Equal.sym(U32, sw, 1, XB.u1(sw, hs)) : G.ceq(pp, FS.value(F.select(_, a, b)), B)
60      %Equal.sym(List<&2, U32>, F.select(1, a, b), b, FO.select1(one, h1, 32n, a, b, oa, ob)) : G.ceq(pp, FS.value(_), B)
61      cb
62    case 2n+q:
63      Empty.absurd(G.ceq(pp, FS.value(F.select(sw, a, b)), B), L.false_true(hb))