def addresses_eq

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/argon2/index.bend:199

import Base
import bend-collections-laws-crypto@1.0.0.0/src/crypto/argon2/types.bend as A
import bend-collections-laws-crypto@1.0.0.0/src/crypto/argon2/blamka.bend as G
import bend-collections-laws-crypto@1.0.0.0/src/crypto/argon2/argon2.bend as I
import bend-collections-laws-crypto@1.0.0.0/spec/crypto/argon2/blamka.bend as SG
import bend-collections-laws-crypto@1.0.0.0/spec/crypto/argon2/argon2.bend as SA
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/argon2/blamka.bend as BL

199def addresses_eq(+r: Nat, +l: Nat, +s: Nat, +mm: Nat, +t: Nat, +ctr: Nat) -> {I.addresses(r, l, s, mm, t, ctr) == SA.addresses(r, l, s, mm, t, ctr) : A.Block}:
200  +z = SA.input_block(r, l, s, mm, t, ctr)
201  Equal.trans(A.Block, G.compress(G.zero(), G.compress(G.zero(), I.input_block(r, l, s, mm, t, ctr))), G.compress(G.zero(), G.compress(G.zero(), z)), SG.G(SG.zero(), SG.G(SG.zero(), z)),
202    Equal.cong(A.Block, A.Block, x => G.compress(G.zero(), G.compress(G.zero(), x)), I.input_block(r, l, s, mm, t, ctr), z, input_eq(r, l, s, mm, t, ctr)),
203    Equal.trans(A.Block, G.compress(G.zero(), G.compress(G.zero(), z)), G.compress(G.zero(), SG.G(SG.zero(), z)), SG.G(SG.zero(), SG.G(SG.zero(), z)),
204      Equal.cong(A.Block, A.Block, x => G.compress(G.zero(), x), G.compress(G.zero(), z), SG.G(SG.zero(), z), BL.compress_correct(G.zero(), z)),
205      BL.compress_correct(G.zero(), SG.G(SG.zero(), z))))