def red3_x3

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/secp256k1/reducek.bend:31

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/secp256k1/limbs.bend as L
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/limbs.bend as LV
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/ineq.bend as I
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/reduce.bend as R

31def red3_x3(+one: Nat, +h1: {one == 1n : Nat}, +c: List<&2, Nat>, +xs: List<&2, Nat>, +hb: {Nat.is_le(Nat.add(Nat.mul(1n+LV.ev(c), LV.ev(c)), LV.ev(c)), C.shift(256n, one)) == True{} : Bool}, +hx: {Nat.is_lt(LV.ev(xs), Nat.mul(C.shift(256n, one), C.shift(256n, one))) == True{} : Bool}) -> {Nat.is_lt(LV.ev(L.rounds(3n, c, L.carry(32n, xs, 0n))), C.shift(256n, one)) == True{} : Bool}:
32  +t = C.shift(256n, one)
33  +cv = LV.ev(c)
34  +x0 = L.carry(32n, xs, 0n)
35  +x1 = L.carry(32n, L.fold(c, x0), 0n)
36  +x2 = L.carry(32n, L.fold(c, x1), 0n)
37  +h0 = I.lt_subst_l(LV.ev(xs), LV.ev(x0), Nat.mul(t, t), Equal.sym(Nat, LV.ev(x0), LV.ev(xs), LV.carry_v(32n, xs, 0n)), hx)
38  +h1b = R.round_lt1(one, h1, c, x0, t, x0_lo(one, h1, xs), h0)
39  +h1c = I.lt_subst_r(LV.ev(x1), Nat.add(t, Nat.mul(t, cv)), Nat.mul(1n+cv, t), addmul(t, cv), h1b)
40  +h2b = R.round_lt1(one, h1, c, x1, 1n+cv, R.round_lo(one, h1, L.fold(c, x0)), h1c)
41  +h3 = R.fold_lt2(one, h1, c, x2, Nat.mul(1n+cv, cv), hb, R.round_lo(one, h1, L.fold(c, x1)), h2b)
42  %Equal.sym(Nat, LV.ev(L.carry(32n, L.fold(c, L.carry(32n, L.fold(c, L.carry(32n, L.fold(c, L.carry(32n, xs, 0n)), 0n)), 0n)), 0n)), LV.ev(L.fold(c, L.carry(32n, L.fold(c, L.carry(32n, L.fold(c, L.carry(32n, xs, 0n)), 0n)), 0n))), R.round_v(c, L.carry(32n, L.fold(c, L.carry(32n, L.fold(c, L.carry(32n, xs, 0n)), 0n)), 0n))) : {Nat.is_lt(_, C.shift(256n, one)) == True{} : Bool}
43  h3