proof/AES_TraceBridgeProof.bend source

proof/AES_TraceBridgeProof.bend on the hub · documented module

import Baseimport ../libs/AES256GCMCore.bend as Core# Substitute a certified initial word list with a symbolic fuel parameter.# The public bridge below compares function aliases before applying the key,# avoiding normalization of all 52 rounds merely to compare the aliases.def expand_input_matches(+fuel: Nat, +key: List<&2, U32>,    +initial_words: List<&2, U32>, +expected: List<&2, U32>,    initial_match: {Core.aes_words(key) == initial_words : List<&2, U32>},    expanded_match: {Core.aes_expand.go(fuel, 8, 1, initial_words) == expected : List<&2, U32>}) ->    {Core.aes_expand.go(fuel, 8, 1, Core.aes_words(key)) == expected : List<&2, U32>}:    Equal.trans(List<&2, U32>, Core.aes_expand.go(fuel, 8, 1, Core.aes_words(key)),        Core.aes_expand.go(fuel, 8, 1, initial_words), expected,        Equal.cong(List<&2, U32>, List<&2, U32>, values => Core.aes_expand.go(fuel, 8, 1, values),            Core.aes_words(key), initial_words, initial_match), expanded_match)
def expand_key_matches(+fuel: Nat, +key: List<&2, U32>,    +initial_words: List<&2, U32>, +expected: List<&2, U32>,    +initial_match: {Core.aes_words(key) == initial_words : List<&2, U32>},    +expanded_match: {Core.aes_expand.go(fuel, 8, 1, initial_words) == expected : List<&2, U32>}) ->    {Core.aes_expand_key(fuel, key) == expected : List<&2, U32>}:    match key:        case Nil{}: expand_input_matches(fuel, key, initial_words, expected, initial_match, expanded_match)        case head <> tail: expand_input_matches(fuel, key, initial_words, expected, initial_match, expanded_match)def expansion_alias() ->    {Core.aes256_expand == (+key => Core.aes_expand_key(52n, key)) :        @+key: List<&2, U32> -> List<&2, U32>}:    {==}def public_expansion_matches(+key: List<&2, U32>, +expected: List<&2, U32>,    same: {Core.aes_expand_key(52n, key) == expected : List<&2, U32>}) ->    {Core.aes256_expand(key) == expected : List<&2, U32>}:    Equal.trans(List<&2, U32>, Core.aes256_expand(key), Core.aes_expand_key(52n, key), expected,        Equal.cong((@+input: List<&2, U32> -> List<&2, U32>), List<&2, U32>,            function => function(key), Core.aes256_expand,            +input => Core.aes_expand_key(52n, input), expansion_alias()), same)