proof/AES_EncryptProof.bend source
proof/AES_EncryptProof.bend on the hub · documented module
import Baseimport ../libs/AES256GCM.bend as AESimport ../libs/AES256GCMCore.bend as Coreimport ./AES_ZipLengthProof.bend as ZipLengthProofimport ./AES_CoreTagProof.bend as CoreTagProofimport ./AES_MaskedXorProof.bend as MaskedXorProofimport ./AES_LengthLimitProof.bend as LengthLimitProofimport ./AES_TagCompareProof.bend as TagCompareProoftype TagContext is Data: TagContext{ words: List<&2, U32>, nonce: List<&2, U32>, aad: List<&2, U32>, ciphertext: List<&2, U32> }def result_ciphertext(fallback: List<&2, U32>, result: Result<&2, &2, AES.Error, AES.Envelope>) -> List<&2, U32>: match result: case Fail{error}: fallback case Done{envelope}: AES.ciphertext(envelope)def output_tag_context(output: Core.GcmOutput) -> TagContext: match output: case Core.GcmOutput{ciphertext, ciphertext_valid, tag_bytes, tag_valid, tag_size, tag_words, tag_nonce, tag_aad, tag_matches}: TagContext{tag_words, tag_nonce, tag_aad, ciphertext}def tag_for_context(context: TagContext) -> List<&2, U32>: match context: case TagContext{words, nonce, aad, ciphertext}: Core.gcm_tag_bytes(Core.gcm_tag_output(words, nonce, aad, ciphertext))def output_tag_matches_context(+output: Core.GcmOutput) -> {CoreTagProof.output_tag(output) == tag_for_context(output_tag_context(output)) : List<&2, U32>}: match output: case Core.GcmOutput{ciphertext, ciphertext_valid, tag_bytes, tag_valid, tag_size, tag_words, tag_nonce, tag_aad, tag_matches}: tag_matchesdef raw_output_tag_canonical(+key: List<&2, U32>, +nonce: List<&2, U32>, +aad: List<&2, U32>, +plaintext: List<&2, U32>) -> {CoreTagProof.output_tag(Core.gcm_encrypt_raw(key, nonce, aad, plaintext)) == Core.gcm_tag_bytes(Core.gcm_tag_output( Core.aes256_expand(key), nonce, aad, CoreTagProof.output_ciphertext(Core.gcm_encrypt_raw(key, nonce, aad, plaintext)))) : List<&2, U32>}: +output = Core.gcm_encrypt_raw(key, nonce, aad, plaintext) +context = output_tag_context(output) +expected_context = {TagContext{Core.aes256_expand(key), nonce, aad, CoreTagProof.output_ciphertext(output)} : TagContext} context_eq: {context == expected_context : TagContext} = {==} Equal.trans(List<&2, U32>, CoreTagProof.output_tag(output), tag_for_context(context), tag_for_context(expected_context), output_tag_matches_context(output), Equal.cong(TagContext, List<&2, U32>, tag_for_context, context, expected_context, context_eq))def result_tag_bytes(fallback: List<&2, U32>, result: Result<&2, &2, AES.Error, AES.Envelope>) -> List<&2, U32>: match result: case Fail{error}: fallback case Done{envelope}: AES.tag_bytes(AES.envelope_tag(envelope))def valid_output_ciphertext_length(+key: AES.SecretKey, +nonce: AES.Nonce, +aad: List<&2, U32>, +plaintext: List<&2, U32>) -> {List.length(&2, U32, AES.ciphertext(AES.envelope_from_gcm_checked(nonce, AES.encrypt_valid_output(key, nonce, aad, plaintext)))) == List.length(&2, U32, plaintext) : Nat}: ZipLengthProof.ctr_encrypt_ciphertext_length( Core.aes256_expand(AES.secret_key_bytes(key)), AES.raw_nonce_bytes(nonce), plaintext)def encrypt_checked_with_flags(+key: AES.SecretKey, +nonce: AES.Nonce, +aad: List<&2, U32>, +plaintext: List<&2, U32>, +aad_flag: Bool, +plaintext_flag: Bool, aad_ok: {AES.aad_valid(aad) == aad_flag : Bool}, plaintext_ok: {AES.plaintext_valid(plaintext) == plaintext_flag : Bool}, +envelope: AES.Envelope, +encrypted: {AES.encrypt(key, nonce, aad, plaintext) == Done{envelope} : Result<&2, &2, AES.Error, AES.Envelope>}) -> {AES.encrypt_checked(key, nonce, aad, plaintext, aad_flag, plaintext_flag) == Done{envelope} : Result<&2, &2, AES.Error, AES.Envelope>}: changed_flags = Equal.trans(Result<&2, &2, AES.Error, AES.Envelope>, AES.encrypt(key, nonce, aad, plaintext), AES.encrypt_checked(key, nonce, aad, plaintext, AES.aad_valid(aad), AES.plaintext_valid(plaintext)), AES.encrypt_checked(key, nonce, aad, plaintext, aad_flag, plaintext_flag), {==}, Equal.trans(Result<&2, &2, AES.Error, AES.Envelope>, AES.encrypt_checked(key, nonce, aad, plaintext, AES.aad_valid(aad), AES.plaintext_valid(plaintext)), AES.encrypt_checked(key, nonce, aad, plaintext, aad_flag, AES.plaintext_valid(plaintext)), AES.encrypt_checked(key, nonce, aad, plaintext, aad_flag, plaintext_flag), Equal.cong(Bool, Result<&2, &2, AES.Error, AES.Envelope>, flag => AES.encrypt_checked(key, nonce, aad, plaintext, flag, AES.plaintext_valid(plaintext)), AES.aad_valid(aad), aad_flag, aad_ok), Equal.cong(Bool, Result<&2, &2, AES.Error, AES.Envelope>, flag => AES.encrypt_checked(key, nonce, aad, plaintext, aad_flag, flag), AES.plaintext_valid(plaintext), plaintext_flag, plaintext_ok))) Equal.trans(Result<&2, &2, AES.Error, AES.Envelope>, AES.encrypt_checked(key, nonce, aad, plaintext, aad_flag, plaintext_flag), AES.encrypt(key, nonce, aad, plaintext), Done{envelope}, Equal.sym(Result<&2, &2, AES.Error, AES.Envelope>, AES.encrypt(key, nonce, aad, plaintext), AES.encrypt_checked(key, nonce, aad, plaintext, aad_flag, plaintext_flag), changed_flags), encrypted)def successful_encrypt_aad_valid(+key: AES.SecretKey, +nonce: AES.Nonce, +aad: List<&2, U32>, +plaintext: List<&2, U32>, +aad_flag: Bool, +plaintext_flag: Bool, aad_ok: {AES.aad_valid(aad) == aad_flag : Bool}, plaintext_ok: {AES.plaintext_valid(plaintext) == plaintext_flag : Bool}, +envelope: AES.Envelope, encrypted: {AES.encrypt(key, nonce, aad, plaintext) == Done{envelope} : Result<&2, &2, AES.Error, AES.Envelope>}) -> {aad_flag == True{} : Bool}: match aad_flag: case True{}: {==} case False{}: checked = encrypt_checked_with_flags(key, nonce, aad, plaintext, aad_flag, plaintext_flag, aad_ok, plaintext_ok, envelope, encrypted) Equal.trans(Bool, False{}, Result.is_done(&2, &2, AES.Error, AES.Envelope, AES.encrypt_checked(key, nonce, aad, plaintext, aad_flag, plaintext_flag)), True{}, {==}, Equal.cong(Result<&2, &2, AES.Error, AES.Envelope>, Bool, result => Result.is_done(&2, &2, AES.Error, AES.Envelope, result), AES.encrypt_checked(key, nonce, aad, plaintext, aad_flag, plaintext_flag), Done{envelope}, checked))def successful_encrypt_plaintext_valid(+key: AES.SecretKey, +nonce: AES.Nonce, +aad: List<&2, U32>, +plaintext: List<&2, U32>, +aad_flag: Bool, +plaintext_flag: Bool, aad_ok: {AES.aad_valid(aad) == aad_flag : Bool}, plaintext_ok: {AES.plaintext_valid(plaintext) == plaintext_flag : Bool}, +envelope: AES.Envelope, encrypted: {AES.encrypt(key, nonce, aad, plaintext) == Done{envelope} : Result<&2, &2, AES.Error, AES.Envelope>}) -> {plaintext_flag == True{} : Bool}: match aad_flag plaintext_flag: case True{} True{}: {==} case True{} False{}: checked = encrypt_checked_with_flags(key, nonce, aad, plaintext, aad_flag, plaintext_flag, aad_ok, plaintext_ok, envelope, encrypted) Equal.trans(Bool, False{}, Result.is_done(&2, &2, AES.Error, AES.Envelope, AES.encrypt_checked(key, nonce, aad, plaintext, aad_flag, plaintext_flag)), True{}, {==}, Equal.cong(Result<&2, &2, AES.Error, AES.Envelope>, Bool, result => Result.is_done(&2, &2, AES.Error, AES.Envelope, result), AES.encrypt_checked(key, nonce, aad, plaintext, aad_flag, plaintext_flag), Done{envelope}, checked)) case False{} _: checked = encrypt_checked_with_flags(key, nonce, aad, plaintext, aad_flag, plaintext_flag, aad_ok, plaintext_ok, envelope, encrypted) Empty.absurd({plaintext_flag == True{} : Bool}, ZipLengthProof.false_true(Equal.trans(Bool, False{}, Result.is_done(&2, &2, AES.Error, AES.Envelope, AES.encrypt_checked(key, nonce, aad, plaintext, aad_flag, plaintext_flag)), True{}, {==}, Equal.cong(Result<&2, &2, AES.Error, AES.Envelope>, Bool, result => Result.is_done(&2, &2, AES.Error, AES.Envelope, result), AES.encrypt_checked(key, nonce, aad, plaintext, aad_flag, plaintext_flag), Done{envelope}, checked))))def result_ciphertext_length( result: Result<&2, &2, AES.Error, AES.Envelope>) -> Nat: match result: case Fail{error}: 0n case Done{envelope}: List.length(&2, U32, AES.ciphertext(envelope))def successful_encrypt_preserves_length(+key: AES.SecretKey, +nonce: AES.Nonce, +aad: List<&2, U32>, +plaintext: List<&2, U32>, +envelope: AES.Envelope, +encrypted: {AES.encrypt(key, nonce, aad, plaintext) == Done{envelope} : Result<&2, &2, AES.Error, AES.Envelope>}) -> {List.length(&2, U32, AES.ciphertext(envelope)) == List.length(&2, U32, plaintext) : Nat}: +aad_flag = AES.aad_valid(aad) +plaintext_flag = AES.plaintext_valid(plaintext) aad_is_true = successful_encrypt_aad_valid(key, nonce, aad, plaintext, aad_flag, plaintext_flag, {==}, {==}, envelope, encrypted) plaintext_is_true = successful_encrypt_plaintext_valid(key, nonce, aad, plaintext, aad_flag, plaintext_flag, {==}, {==}, envelope, encrypted) checked = encrypt_checked_with_flags(key, nonce, aad, plaintext, True{}, True{}, aad_is_true, plaintext_is_true, envelope, encrypted) output_length = valid_output_ciphertext_length(key, nonce, aad, plaintext) Equal.trans(Nat, List.length(&2, U32, AES.ciphertext(envelope)), result_ciphertext_length( AES.encrypt_checked(key, nonce, aad, plaintext, True{}, True{})), List.length(&2, U32, plaintext), Equal.sym(Nat, result_ciphertext_length( AES.encrypt_checked(key, nonce, aad, plaintext, True{}, True{})), result_ciphertext_length(Done{envelope}), Equal.cong(Result<&2, &2, AES.Error, AES.Envelope>, Nat, result => result_ciphertext_length(result), AES.encrypt_checked(key, nonce, aad, plaintext, True{}, True{}), Done{envelope}, checked)), output_length)def successful_encrypt_ciphertext_matches_gcm(+key: AES.SecretKey, +nonce: AES.Nonce, +aad: List<&2, U32>, +plaintext: List<&2, U32>, +envelope: AES.Envelope, aad_valid: {AES.aad_valid(aad) == True{} : Bool}, plaintext_valid: {AES.plaintext_valid(plaintext) == True{} : Bool}, +encrypted: {AES.encrypt(key, nonce, aad, plaintext) == Done{envelope} : Result<&2, &2, AES.Error, AES.Envelope>}) -> {AES.ciphertext(envelope) == CoreTagProof.output_ciphertext(AES.encrypt_valid_output(key, nonce, aad, plaintext)) : List<&2, U32>}: checked = encrypt_checked_with_flags(key, nonce, aad, plaintext, True{}, True{}, aad_valid, plaintext_valid, envelope, encrypted) +output = AES.encrypt_valid_output(key, nonce, aad, plaintext) constructed_matches = Equal.cong( Result<&2, &2, AES.Error, AES.Envelope>, List<&2, U32>, result => result_ciphertext(AES.ciphertext(envelope), result), AES.encrypt_checked(key, nonce, aad, plaintext, True{}, True{}), Done{envelope}, checked) Equal.trans(List<&2, U32>, AES.ciphertext(envelope), AES.ciphertext(AES.envelope_from_gcm_checked(nonce, output)), CoreTagProof.output_ciphertext(output), Equal.sym(List<&2, U32>, AES.ciphertext(AES.envelope_from_gcm_checked(nonce, output)), AES.ciphertext(envelope), constructed_matches), CoreTagProof.envelope_gcm_ciphertext(nonce, output))def successful_encrypt_tag_matches_gcm(+key: AES.SecretKey, +nonce: AES.Nonce, +aad: List<&2, U32>, +plaintext: List<&2, U32>, +envelope: AES.Envelope, aad_ok: {AES.aad_valid(aad) == True{} : Bool}, plaintext_ok: {AES.plaintext_valid(plaintext) == True{} : Bool}, encrypted: {AES.encrypt(key, nonce, aad, plaintext) == Done{envelope} : Result<&2, &2, AES.Error, AES.Envelope>}) -> {AES.tag_bytes(AES.envelope_tag(envelope)) == CoreTagProof.output_tag(AES.encrypt_valid_output(key, nonce, aad, plaintext)) : List<&2, U32>}: checked = encrypt_checked_with_flags(key, nonce, aad, plaintext, True{}, True{}, aad_ok, plaintext_ok, envelope, encrypted) +output = AES.encrypt_valid_output(key, nonce, aad, plaintext) constructed_matches = Equal.cong( Result<&2, &2, AES.Error, AES.Envelope>, List<&2, U32>, result => result_tag_bytes([], result), AES.encrypt_checked(key, nonce, aad, plaintext, True{}, True{}), Done{envelope}, checked) Equal.trans(List<&2, U32>, AES.tag_bytes(AES.envelope_tag(envelope)), AES.tag_bytes(AES.envelope_tag(AES.envelope_from_gcm_checked(nonce, output))), CoreTagProof.output_tag(output), Equal.sym(List<&2, U32>, AES.tag_bytes(AES.envelope_tag(AES.envelope_from_gcm_checked( nonce, output))), AES.tag_bytes(AES.envelope_tag(envelope)), constructed_matches), CoreTagProof.envelope_gcm_tag(nonce, output))def successful_encrypt_tag_canonical(+key: AES.SecretKey, +nonce: AES.Nonce, +aad: List<&2, U32>, +plaintext: List<&2, U32>, +envelope: AES.Envelope, +aad_ok: {AES.aad_valid(aad) == True{} : Bool}, +plaintext_ok: {AES.plaintext_valid(plaintext) == True{} : Bool}, +encrypted: {AES.encrypt(key, nonce, aad, plaintext) == Done{envelope} : Result<&2, &2, AES.Error, AES.Envelope>}) -> {AES.tag_bytes(AES.envelope_tag(envelope)) == Core.gcm_tag_bytes( Core.gcm_tag_output(Core.aes256_expand(AES.secret_key_bytes(key)), AES.raw_nonce_bytes(nonce), aad, AES.ciphertext(envelope))) : List<&2, U32>}: +output = AES.encrypt_valid_output(key, nonce, aad, plaintext) tag_matches = successful_encrypt_tag_matches_gcm(key, nonce, aad, plaintext, envelope, aad_ok, plaintext_ok, encrypted) ciphertext_matches = successful_encrypt_ciphertext_matches_gcm(key, nonce, aad, plaintext, envelope, aad_ok, plaintext_ok, encrypted) raw_canonical = raw_output_tag_canonical(AES.secret_key_bytes(key), AES.raw_nonce_bytes(nonce), aad, plaintext) current_ciphertext = Equal.cong(List<&2, U32>, List<&2, U32>, value => Core.gcm_tag_bytes(Core.gcm_tag_output( Core.aes256_expand(AES.secret_key_bytes(key)), AES.raw_nonce_bytes(nonce), aad, value)), CoreTagProof.output_ciphertext(output), AES.ciphertext(envelope), Equal.sym(List<&2, U32>, AES.ciphertext(envelope), CoreTagProof.output_ciphertext(output), ciphertext_matches)) Equal.trans(List<&2, U32>, AES.tag_bytes(AES.envelope_tag(envelope)), CoreTagProof.output_tag(output), Core.gcm_tag_bytes(Core.gcm_tag_output( Core.aes256_expand(AES.secret_key_bytes(key)), AES.raw_nonce_bytes(nonce), aad, AES.ciphertext(envelope))), tag_matches, Equal.trans(List<&2, U32>, CoreTagProof.output_tag(output), Core.gcm_tag_bytes(Core.gcm_tag_output( Core.aes256_expand(AES.secret_key_bytes(key)), AES.raw_nonce_bytes(nonce), aad, CoreTagProof.output_ciphertext(output))), Core.gcm_tag_bytes(Core.gcm_tag_output( Core.aes256_expand(AES.secret_key_bytes(key)), AES.raw_nonce_bytes(nonce), aad, AES.ciphertext(envelope))), raw_canonical, current_ciphertext))def successful_encrypt_ciphertext_matches_ctr(+key: AES.SecretKey, +nonce: AES.Nonce, +aad: List<&2, U32>, +plaintext: List<&2, U32>, +envelope: AES.Envelope, aad_valid: {AES.aad_valid(aad) == True{} : Bool}, plaintext_valid: {AES.plaintext_valid(plaintext) == True{} : Bool}, +encrypted: {AES.encrypt(key, nonce, aad, plaintext) == Done{envelope} : Result<&2, &2, AES.Error, AES.Envelope>}) -> {AES.ciphertext(envelope) == Core.gcm_zip_xor(plaintext, Core.gcm_ctr_stream_exact(List.length(&2, U32, plaintext), Core.aes256_expand(AES.secret_key_bytes(key)), Core.gcm_inc32(Core.gcm_j0(AES.raw_nonce_bytes(nonce))))) : List<&2, U32>}: Equal.trans(List<&2, U32>, AES.ciphertext(envelope), CoreTagProof.output_ciphertext(AES.encrypt_valid_output(key, nonce, aad, plaintext)), Core.gcm_zip_xor(plaintext, Core.gcm_ctr_stream_exact(List.length(&2, U32, plaintext), Core.aes256_expand(AES.secret_key_bytes(key)), Core.gcm_inc32(Core.gcm_j0(AES.raw_nonce_bytes(nonce))))), successful_encrypt_ciphertext_matches_gcm(key, nonce, aad, plaintext, envelope, aad_valid, plaintext_valid, encrypted), CoreTagProof.raw_encrypt_output_ciphertext( AES.secret_key_bytes(key), AES.raw_nonce_bytes(nonce), aad, plaintext))def successful_encrypt_ciphertext_valid(+key: AES.SecretKey, +nonce: AES.Nonce, +aad: List<&2, U32>, +plaintext: List<&2, U32>, +envelope: AES.Envelope, aad_valid: {AES.aad_valid(aad) == True{} : Bool}, plaintext_valid: {AES.plaintext_valid(plaintext) == True{} : Bool}, +encrypted: {AES.encrypt(key, nonce, aad, plaintext) == Done{envelope} : Result<&2, &2, AES.Error, AES.Envelope>}) -> {AES.plaintext_valid(AES.ciphertext(envelope)) == True{} : Bool}: length_eq = successful_encrypt_preserves_length(key, nonce, aad, plaintext, envelope, encrypted) LengthLimitProof.plaintext_valid_same_length( AES.ciphertext(envelope), plaintext, AES.envelope_ciphertext_valid(envelope), plaintext_valid, length_eq)def successful_encrypt_ctr_decrypts(+key: AES.SecretKey, +nonce: AES.Nonce, +aad: List<&2, U32>, +plaintext: List<&2, U32>, +envelope: AES.Envelope, aad_valid: {AES.aad_valid(aad) == True{} : Bool}, +plaintext_valid: {AES.plaintext_valid(plaintext) == True{} : Bool}, +encrypted: {AES.encrypt(key, nonce, aad, plaintext) == Done{envelope} : Result<&2, &2, AES.Error, AES.Envelope>}) -> {Core.gcm_decrypt_raw(AES.secret_key_bytes(key), AES.raw_nonce_bytes(nonce), AES.ciphertext(envelope)) == plaintext : List<&2, U32>}: +words = Core.aes256_expand(AES.secret_key_bytes(key)) aes_bytes_valid = MaskedXorProof.bool_and_true_left( AES.bytes_valid(plaintext), AES.bytes_length_limit(plaintext, 4294967264, 15), plaintext_valid) core_bytes_valid = Equal.trans(Bool, Core.gcm_bytes_valid(plaintext), AES.bytes_valid(plaintext), True{}, Equal.sym(Bool, AES.bytes_valid(plaintext), Core.gcm_bytes_valid(plaintext), AES.core_bytes_valid_eq(plaintext)), aes_bytes_valid) cipher = successful_encrypt_ciphertext_matches_ctr(key, nonce, aad, plaintext, envelope, aad_valid, plaintext_valid, encrypted) Equal.trans(List<&2, U32>, Core.gcm_decrypt_raw(AES.secret_key_bytes(key), AES.raw_nonce_bytes(nonce), AES.ciphertext(envelope)), Core.gcm_decrypt_raw(AES.secret_key_bytes(key), AES.raw_nonce_bytes(nonce), Core.gcm_zip_xor(plaintext, Core.gcm_ctr_stream_exact(List.length(&2, U32, plaintext), words, Core.gcm_inc32(Core.gcm_j0( AES.raw_nonce_bytes(nonce)))))), plaintext, Equal.cong(List<&2, U32>, List<&2, U32>, ciphertext => Core.gcm_decrypt_raw(AES.secret_key_bytes(key), AES.raw_nonce_bytes(nonce), ciphertext), AES.ciphertext(envelope), Core.gcm_zip_xor(plaintext, Core.gcm_ctr_stream_exact(List.length(&2, U32, plaintext), words, Core.gcm_inc32(Core.gcm_j0( AES.raw_nonce_bytes(nonce))))), cipher), MaskedXorProof.ctr_decrypt_ciphertext_roundtrip(words, AES.raw_nonce_bytes(nonce), plaintext, core_bytes_valid))def result_nonce(fallback: AES.Nonce, result: Result<&2, &2, AES.Error, AES.Envelope>) -> AES.Nonce: match result: case Fail{error}: fallback case Done{envelope}: AES.envelope_nonce(envelope)def output_nonce(+nonce: AES.Nonce, +output: Core.GcmOutput) -> {result_nonce(nonce, AES.encrypt_output_from_gcm(nonce, output)) == nonce : AES.Nonce}: match output: case Core.GcmOutput{+ciphertext, ciphertext_valid, tag_bytes, tag_valid, tag_size, tag_words, tag_nonce, tag_aad, tag_matches}: {==}def valid_nonce(key: AES.SecretKey, +nonce: AES.Nonce, aad: List<&2, U32>, plaintext: List<&2, U32>) -> {result_nonce(nonce, AES.encrypt_valid(key, nonce, aad, plaintext)) == nonce : AES.Nonce}: output_nonce(nonce, AES.encrypt_valid_output(key, nonce, aad, plaintext))def checked_nonce(key: AES.SecretKey, +nonce: AES.Nonce, +aad: List<&2, U32>, +plaintext: List<&2, U32>, aad_ok: Bool, plaintext_ok: Bool) -> {result_nonce(nonce, AES.encrypt_checked(key, nonce, aad, plaintext, aad_ok, plaintext_ok)) == nonce : AES.Nonce}: match aad_ok plaintext_ok: case True{} True{}: valid_nonce(key, nonce, aad, plaintext) case False{} _: {==} case True{} False{}: {==}def encrypt_nonce(key: AES.SecretKey, +nonce: AES.Nonce, +aad: List<&2, U32>, +plaintext: List<&2, U32>) -> {result_nonce(nonce, AES.encrypt(key, nonce, aad, plaintext)) == nonce : AES.Nonce}: checked_nonce(key, nonce, aad, plaintext, AES.aad_valid(aad), AES.plaintext_valid(plaintext))def preserves_nonce(+key: AES.SecretKey, +nonce: AES.Nonce, +aad: List<&2, U32>, +plaintext: List<&2, U32>, +envelope: AES.Envelope, encrypted: {AES.encrypt(key, nonce, aad, plaintext) == Done{envelope} : Result<&2, &2, AES.Error, AES.Envelope>}) -> {AES.envelope_nonce(envelope) == nonce : AES.Nonce}: Equal.trans(AES.Nonce, result_nonce(nonce, Done{envelope}), result_nonce(nonce, AES.encrypt(key, nonce, aad, plaintext)), nonce, Equal.sym(AES.Nonce, result_nonce(nonce, AES.encrypt(key, nonce, aad, plaintext)), result_nonce(nonce, Done{envelope}), Equal.cong(Result<&2, &2, AES.Error, AES.Envelope>, AES.Nonce, result => result_nonce(nonce, result), AES.encrypt(key, nonce, aad, plaintext), Done{envelope}, encrypted)), encrypt_nonce(key, nonce, aad, plaintext)) def successful_encrypt_envelope_tag_canonical(+key: AES.SecretKey, +nonce: AES.Nonce, +aad: List<&2, U32>, +plaintext: List<&2, U32>, +envelope: AES.Envelope, aad_ok: {AES.aad_valid(aad) == True{} : Bool}, plaintext_ok: {AES.plaintext_valid(plaintext) == True{} : Bool}, +encrypted: {AES.encrypt(key, nonce, aad, plaintext) == Done{envelope} : Result<&2, &2, AES.Error, AES.Envelope>}) -> {AES.tag_bytes(AES.envelope_tag(envelope)) == Core.gcm_tag_bytes( Core.gcm_tag_output(Core.aes256_expand(AES.secret_key_bytes(key)), AES.raw_nonce_bytes(AES.envelope_nonce(envelope)), aad, AES.ciphertext(envelope))) : List<&2, U32>}: canonical = successful_encrypt_tag_canonical(key, nonce, aad, plaintext, envelope, aad_ok, plaintext_ok, encrypted) nonce_matches = Equal.cong(AES.Nonce, List<&2, U32>, AES.raw_nonce_bytes, AES.envelope_nonce(envelope), nonce, preserves_nonce(key, nonce, aad, plaintext, envelope, encrypted)) nonce_rewrite = Equal.cong(List<&2, U32>, List<&2, U32>, value => Core.gcm_tag_bytes(Core.gcm_tag_output( Core.aes256_expand(AES.secret_key_bytes(key)), value, aad, AES.ciphertext(envelope))), AES.raw_nonce_bytes(nonce), AES.raw_nonce_bytes(AES.envelope_nonce(envelope)), Equal.sym(List<&2, U32>, AES.raw_nonce_bytes(AES.envelope_nonce(envelope)), AES.raw_nonce_bytes(nonce), nonce_matches)) Equal.trans(List<&2, U32>, AES.tag_bytes(AES.envelope_tag(envelope)), Core.gcm_tag_bytes(Core.gcm_tag_output( Core.aes256_expand(AES.secret_key_bytes(key)), AES.raw_nonce_bytes(nonce), aad, AES.ciphertext(envelope))), Core.gcm_tag_bytes(Core.gcm_tag_output( Core.aes256_expand(AES.secret_key_bytes(key)), AES.raw_nonce_bytes(AES.envelope_nonce(envelope)), aad, AES.ciphertext(envelope))), canonical, nonce_rewrite)def decrypt_auth_tag_canonical(+words: List<&2, U32>, +nonce: List<&2, U32>, +aad: List<&2, U32>, +ciphertext: List<&2, U32>, +envelope: AES.Envelope, +tag: AES.Tag, canonical: {AES.tag_bytes(tag) == Core.gcm_tag_bytes( Core.gcm_tag_output(words, nonce, aad, ciphertext)) : List<&2, U32>}) -> {AES.decrypt_authenticated_tag(words, nonce, aad, ciphertext, envelope, tag) == AES.decrypt_auth_result(words, envelope, True{}) : Result<&2, &2, AES.Error, List<&2, U32>>}: match tag: case AES.Tag{bytes, size, valid}: Equal.cong(Bool, Result<&2, &2, AES.Error, List<&2, U32>>, ok => AES.decrypt_auth_result(words, envelope, ok), AES.bytes_equal_full_scan(bytes, Core.gcm_tag_bytes( Core.gcm_tag_output(words, nonce, aad, ciphertext))), True{}, TagCompareProof.equal_of_equal(bytes, Core.gcm_tag_bytes(Core.gcm_tag_output(words, nonce, aad, ciphertext)), canonical))def successful_encrypt_decrypt_authenticated(+key: AES.SecretKey, +nonce: AES.Nonce, +aad: List<&2, U32>, +plaintext: List<&2, U32>, +envelope: AES.Envelope, +aad_ok: {AES.aad_valid(aad) == True{} : Bool}, +plaintext_ok: {AES.plaintext_valid(plaintext) == True{} : Bool}, +encrypted: {AES.encrypt(key, nonce, aad, plaintext) == Done{envelope} : Result<&2, &2, AES.Error, AES.Envelope>}) -> {AES.decrypt_authenticated(key, aad, envelope) == Done{plaintext} : Result<&2, &2, AES.Error, List<&2, U32>>}: match key envelope: case AES.SecretKey{+key_bytes, _, _} AES.Envelope{envelope_nonce, ciphertext, tag, _}: +words = Core.aes256_expand(key_bytes) +nonce_bytes = AES.raw_nonce_bytes(envelope_nonce) canonical = successful_encrypt_envelope_tag_canonical(key, nonce, aad, plaintext, envelope, aad_ok, plaintext_ok, encrypted) authenticated = decrypt_auth_tag_canonical(words, nonce_bytes, aad, ciphertext, envelope, tag, canonical) nonce_matches = Equal.cong(AES.Nonce, List<&2, U32>, AES.raw_nonce_bytes, envelope_nonce, nonce, preserves_nonce(key, nonce, aad, plaintext, envelope, encrypted)) ctr_roundtrip = successful_encrypt_ctr_decrypts(key, nonce, aad, plaintext, envelope, aad_ok, plaintext_ok, encrypted) expanded_nonce = Equal.cong(List<&2, U32>, List<&2, U32>, value => Core.gcm_decrypt_expanded(words, value, ciphertext), nonce_bytes, AES.raw_nonce_bytes(nonce), nonce_matches) expanded_to_raw = Equal.trans(List<&2, U32>, Core.gcm_decrypt_expanded(words, nonce_bytes, ciphertext), Core.gcm_decrypt_expanded(words, AES.raw_nonce_bytes(nonce), ciphertext), Core.gcm_decrypt_raw(AES.secret_key_bytes(key), AES.raw_nonce_bytes(nonce), ciphertext), expanded_nonce, {==}) expanded_roundtrip = Equal.trans(List<&2, U32>, Core.gcm_decrypt_expanded(words, nonce_bytes, ciphertext), Core.gcm_decrypt_raw(AES.secret_key_bytes(key), AES.raw_nonce_bytes(nonce), ciphertext), plaintext, expanded_to_raw, ctr_roundtrip) payload = Equal.cong(List<&2, U32>, Result<&2, &2, AES.Error, List<&2, U32>>, value => Done{value}, Core.gcm_decrypt_expanded(words, nonce_bytes, ciphertext), plaintext, expanded_roundtrip) Equal.trans(Result<&2, &2, AES.Error, List<&2, U32>>, AES.decrypt_authenticated(key, aad, envelope), AES.decrypt_auth_result(words, envelope, True{}), Done{plaintext}, authenticated, payload)def successful_encrypt_decrypt_roundtrip(+key: AES.SecretKey, +nonce: AES.Nonce, +aad: List<&2, U32>, +plaintext: List<&2, U32>, +envelope: AES.Envelope, +encrypted: {AES.encrypt(key, nonce, aad, plaintext) == Done{envelope} : Result<&2, &2, AES.Error, AES.Envelope>}) -> {AES.decrypt(key, aad, envelope) == Done{plaintext} : Result<&2, &2, AES.Error, List<&2, U32>>}: +aad_ok = successful_encrypt_aad_valid(key, nonce, aad, plaintext, AES.aad_valid(aad), AES.plaintext_valid(plaintext), {==}, {==}, envelope, encrypted) +plaintext_ok = successful_encrypt_plaintext_valid(key, nonce, aad, plaintext, AES.aad_valid(aad), AES.plaintext_valid(plaintext), {==}, {==}, envelope, encrypted) ciphertext_ok = successful_encrypt_ciphertext_valid(key, nonce, aad, plaintext, envelope, aad_ok, plaintext_ok, encrypted) authenticated = successful_encrypt_decrypt_authenticated(key, nonce, aad, plaintext, envelope, aad_ok, plaintext_ok, encrypted) aad_checked = Equal.cong(Bool, Result<&2, &2, AES.Error, List<&2, U32>>, flag => AES.decrypt_checked(key, aad, envelope, flag, AES.plaintext_valid(AES.ciphertext(envelope))), AES.aad_valid(aad), True{}, aad_ok) ciphertext_checked = Equal.cong(Bool, Result<&2, &2, AES.Error, List<&2, U32>>, flag => AES.decrypt_checked(key, aad, envelope, True{}, flag), AES.plaintext_valid(AES.ciphertext(envelope)), True{}, ciphertext_ok) Equal.trans(Result<&2, &2, AES.Error, List<&2, U32>>, AES.decrypt(key, aad, envelope), AES.decrypt_checked(key, aad, envelope, True{}, True{}), Done{plaintext}, Equal.trans(Result<&2, &2, AES.Error, List<&2, U32>>, AES.decrypt(key, aad, envelope), AES.decrypt_checked(key, aad, envelope, AES.aad_valid(aad), AES.plaintext_valid(AES.ciphertext(envelope))), AES.decrypt_checked(key, aad, envelope, True{}, True{}), {==}, Equal.trans(Result<&2, &2, AES.Error, List<&2, U32>>, AES.decrypt_checked(key, aad, envelope, AES.aad_valid(aad), AES.plaintext_valid(AES.ciphertext(envelope))), AES.decrypt_checked(key, aad, envelope, True{}, AES.plaintext_valid(AES.ciphertext(envelope))), AES.decrypt_checked(key, aad, envelope, True{}, True{}), aad_checked, ciphertext_checked)), authenticated)def output_is_done(+nonce: AES.Nonce, +output: Core.GcmOutput) -> {Result.is_done(&2, &2, AES.Error, AES.Envelope, AES.encrypt_output_from_gcm(nonce, output)) == True{} : Bool}: {==}def valid_is_done(key: AES.SecretKey, +nonce: AES.Nonce, aad: List<&2, U32>, plaintext: List<&2, U32>) -> {Result.is_done(&2, &2, AES.Error, AES.Envelope, AES.encrypt_valid(key, nonce, aad, plaintext)) == True{} : Bool}: output_is_done(nonce, AES.encrypt_valid_output(key, nonce, aad, plaintext))def valid_input_is_done(+key: AES.SecretKey, +nonce: AES.Nonce, +aad: List<&2, U32>, +plaintext: List<&2, U32>, aad_ok: {AES.aad_valid(aad) == True{} : Bool}, plaintext_ok: {AES.plaintext_valid(plaintext) == True{} : Bool}) -> {Result.is_done(&2, &2, AES.Error, AES.Envelope, AES.encrypt(key, nonce, aad, plaintext)) == True{} : Bool}: Equal.trans(Bool, Result.is_done(&2, &2, AES.Error, AES.Envelope, AES.encrypt(key, nonce, aad, plaintext)), Result.is_done(&2, &2, AES.Error, AES.Envelope, AES.encrypt_checked(key, nonce, aad, plaintext, True{}, AES.plaintext_valid(plaintext))), True{}, Equal.cong(Bool, Bool, b => Result.is_done(&2, &2, AES.Error, AES.Envelope, AES.encrypt_checked(key, nonce, aad, plaintext, b, AES.plaintext_valid(plaintext))), AES.aad_valid(aad), True{}, aad_ok), Equal.trans(Bool, Result.is_done(&2, &2, AES.Error, AES.Envelope, AES.encrypt_checked(key, nonce, aad, plaintext, True{}, AES.plaintext_valid(plaintext))), Result.is_done(&2, &2, AES.Error, AES.Envelope, AES.encrypt_valid(key, nonce, aad, plaintext)), True{}, Equal.cong(Bool, Bool, b => Result.is_done(&2, &2, AES.Error, AES.Envelope, AES.encrypt_checked(key, nonce, aad, plaintext, True{}, b)), AES.plaintext_valid(plaintext), True{}, plaintext_ok), valid_is_done(key, nonce, aad, plaintext)))