def aria_e0

bend-osdev-legacy-ciphers@0.1.0.0 · PROOF.bend:7937

import Base
import bend-osdev-legacy-ciphers@0.1.0.0/aria.bend as A

7937# each elementary step of the diffusion layer is undone by itself
7938def aria_e0(s: A.LcAriaSt) -> {s == A.aria.e0(A.aria.e0(s)) : A.LcAriaSt}:
7939  match s:
7940    case A.LcAriaSt{+x0, +x1, +x2, +x3, +x4, +x5, +x6, +x7, +x8, +x9, +x10, +x11, +x12, +x13, +x14, +x15}:
7941      %word_xx(8n, x10, x15) : {A.LcAriaSt{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15} == A.LcAriaSt{x0, Word.xor(8n, Word.xor(8n, x1, x15), x15), Word.xor(8n, Word.xor(8n, x2, x15), x15), x3, Word.xor(8n, Word.xor(8n, x4, x15), x15), Word.xor(8n, Word.xor(8n, x5, x15), x15), x6, x7, Word.xor(8n, Word.xor(8n, x8, x15), x15), x9, _, x11, x12, x13, x14, x15} : A.LcAriaSt}
7942      %word_xx(8n, x8, x15) : {A.LcAriaSt{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15} == A.LcAriaSt{x0, Word.xor(8n, Word.xor(8n, x1, x15), x15), Word.xor(8n, Word.xor(8n, x2, x15), x15), x3, Word.xor(8n, Word.xor(8n, x4, x15), x15), Word.xor(8n, Word.xor(8n, x5, x15), x15), x6, x7, _, x9, x10, x11, x12, x13, x14, x15} : A.LcAriaSt}
7943      %word_xx(8n, x5, x15) : {A.LcAriaSt{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15} == A.LcAriaSt{x0, Word.xor(8n, Word.xor(8n, x1, x15), x15), Word.xor(8n, Word.xor(8n, x2, x15), x15), x3, Word.xor(8n, Word.xor(8n, x4, x15), x15), _, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15} : A.LcAriaSt}
7944      %word_xx(8n, x4, x15) : {A.LcAriaSt{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15} == A.LcAriaSt{x0, Word.xor(8n, Word.xor(8n, x1, x15), x15), Word.xor(8n, Word.xor(8n, x2, x15), x15), x3, _, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15} : A.LcAriaSt}
7945      %word_xx(8n, x2, x15) : {A.LcAriaSt{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15} == A.LcAriaSt{x0, Word.xor(8n, Word.xor(8n, x1, x15), x15), _, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15} : A.LcAriaSt}
7946      %word_xx(8n, x1, x15) : {A.LcAriaSt{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15} == A.LcAriaSt{x0, _, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15} : A.LcAriaSt}
7947      {==}