def red3_mod

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/secp256k1/reducek.bend:45

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/reduce.bend as R

45def red3_mod(+one: Nat, +h1: {one == 1n : Nat}, +mp: Nat, +c: List<&2, Nat>, +hm: {Nat.add(1n+mp, LV.ev(c)) == C.shift(256n, one) : Nat}, +xs: List<&2, Nat>) -> {Nat.mod(LV.ev(L.rounds(3n, c, L.carry(32n, xs, 0n))), 1n+mp) == Nat.mod(LV.ev(xs), 1n+mp) : Nat}:
46  +x0 = L.carry(32n, xs, 0n)
47  +x1 = L.carry(32n, L.fold(c, x0), 0n)
48  +x2 = L.carry(32n, L.fold(c, x1), 0n)
49  %Equal.sym(Nat, Nat.mod(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)), 1n+mp), Nat.mod(LV.ev(L.carry(32n, L.fold(c, L.carry(32n, L.fold(c, L.carry(32n, xs, 0n)), 0n)), 0n)), 1n+mp), R.round_mod(one, h1, mp, c, hm, L.carry(32n, L.fold(c, L.carry(32n, L.fold(c, L.carry(32n, xs, 0n)), 0n)), 0n))) : {_ == Nat.mod(LV.ev(xs), 1n+mp) : Nat}
50  %Equal.sym(Nat, Nat.mod(LV.ev(L.carry(32n, L.fold(c, L.carry(32n, L.fold(c, L.carry(32n, xs, 0n)), 0n)), 0n)), 1n+mp), Nat.mod(LV.ev(L.carry(32n, L.fold(c, L.carry(32n, xs, 0n)), 0n)), 1n+mp), R.round_mod(one, h1, mp, c, hm, L.carry(32n, L.fold(c, L.carry(32n, xs, 0n)), 0n))) : {_ == Nat.mod(LV.ev(xs), 1n+mp) : Nat}
51  %Equal.sym(Nat, Nat.mod(LV.ev(L.carry(32n, L.fold(c, L.carry(32n, xs, 0n)), 0n)), 1n+mp), Nat.mod(LV.ev(L.carry(32n, xs, 0n)), 1n+mp), R.round_mod(one, h1, mp, c, hm, L.carry(32n, xs, 0n))) : {_ == Nat.mod(LV.ev(xs), 1n+mp) : Nat}
52  %Equal.sym(Nat, LV.ev(L.carry(32n, xs, 0n)), Nat.add(0n, LV.ev(xs)), LV.carry_v(32n, xs, 0n)) : {Nat.mod(_, 1n+mp) == Nat.mod(LV.ev(xs), 1n+mp) : Nat}
53  {==}