Symmetric Encryption Ontology

FLOW ALGEBRA
TITLE: Symmetric Encryption Ontology
DOMAIN: Discrete Mathematics / Cryptography
SOURCE_URL: https://kirethresearch.org/booksai-core/discrete-mathematics-ontologies/cryptography/symmetric-encryption-ontology.html
VERSION: 1.0
LANGUAGE: en-GB
AUTHORS: Mark Higgins — Sky (Recursive AI)
SOURCE_STATUS: Formal domain model; live source page not independently verified.

1. PURPOSE
Model shared-secret encryption, authenticated encryption, key management, correctness and security assumptions using typed relationships and checkable constraints.

2. TYPED ENTITIES
  Plaintext: Bytes
  Ciphertext: Bytes
  SecretKey: KeyMaterial
  Nonce: Bytes
  IV: Bytes
  AssociatedData: Bytes
  AuthenticationTag: Bytes
  Algorithm: SymmetricCipherSpecification
  Mode: CipherModeSpecification
  EncryptionResult: Ciphertext × AuthenticationTag?
  DecryptionResult: Plaintext | AuthenticationFailure
  SecurityParameter: NaturalNumber
  KeyIdentifier: String
  KeyLifecycle: {generated, active, rotated, retired, destroyed}

3. CORE OPERATIONS
  KeyGen(algorithm, randomness) -> SecretKey
  Encrypt(algorithm, key, nonce_or_iv, plaintext, associated_data?) -> EncryptionResult
  Decrypt(algorithm, key, nonce_or_iv, ciphertext, tag?, associated_data?) -> DecryptionResult
  RotateKey(key_id) -> NewKeyIdentifier
  DestroyKey(key_id) -> KeyLifecycle.destroyed
  ValidateParameters(algorithm, key, nonce_or_iv) -> Boolean

4. MATHEMATICAL SEMANTICS
  For a correct scheme, for every valid key k and plaintext m:
    Dec(k, Enc(k, m)) = m
  Randomised or nonce-based schemes additionally quantify over valid randomness/nonces.
  AEAD correctness:
    Dec(k, n, Enc(k, n, m, a), a) = m
  where the encryption output includes ciphertext and authentication tag.
  Authentication failure is distinct from an empty plaintext.
  Symmetric encryption uses the same secret key, or efficiently related secret keys, for encryption and decryption.

5. TYPED RELATIONSHIPS
  SymmetricEncryption --uses--> SecretKey
  Encryption --transforms--> Plaintext
  Encryption --produces--> Ciphertext
  Decryption --recovers--> Plaintext
  AEAD --authenticates--> CiphertextAndAssociatedData
  KeyRotation --replaces--> ActiveKey
  Nonce --parameterises--> EncryptionInvocation
  Algorithm --constrains--> KeyLengthAndNonceLength
  KeyCompromise --threatens--> Confidentiality

6. INVARIANTS AND SECURITY CONDITIONS
  INV-01: Key length must satisfy the selected algorithm specification.
  INV-02: Nonce/IV handling must satisfy the algorithm and mode specification.
  INV-03: For nonce-unique AEAD schemes such as AES-GCM, never reuse a nonce with the same key.
  INV-04: Authentication tags must be verified before plaintext is accepted as authentic.
  INV-05: Encryption without authentication does not by itself guarantee integrity.
  INV-06: Confidentiality claims depend on a specified threat model and secure implementation.
  INV-07: Keys must be protected from unauthorised disclosure and managed across their lifecycle.
  INV-08: Never describe ECB mode as providing semantic security for arbitrary multi-block messages.

7. ALGEBRAIC AND LOGICAL RULES
  CORRECTNESS: ValidParameters(k,n,m,a) => Dec(k,n,Enc(k,n,m,a),a)=m.
  TAMPER_DETECTION: For secure AEAD, unauthorised modification should cause authentication failure except with negligible forgery probability; not an absolute impossibility.
  KEY_SEPARATION: Distinct cryptographic purposes should use appropriately separated keys or a sound derivation scheme.
  NONCE_POLICY: Nonce uniqueness and unpredictability are separate properties; requirements are scheme-specific.
  NO_FALSE_EQUIVALENCE: SymmetricEncryption != Hashing; SymmetricEncryption != DigitalSignature.

8. INFERENCE RULES
  R1: isAEAD(x) AND tagVerified(x) => mayAcceptAuthenticatedPlaintext(x).
  R2: isAEAD(x) AND NOT tagVerified(x) => rejectPlaintext(x).
  R3: nonceReuseForbidden(s) AND reusedNonce(s,k,n) => securityViolation(s,k,n).
  R4: compromised(k) => confidentialityAssuranceAtRisk(k).
  R5: validCiphertext(c) alone DOES NOT imply authenticated(c).
  R6: keyRetired(k) => prohibitNewEncryptionWith(k) under the configured key policy.

9. VALIDATION
  CHECK-01: Round-trip test across supported plaintext sizes, including zero-length.
  CHECK-02: Wrong-key decryption must not be interpreted as authenticated success.
  CHECK-03: AEAD modified ciphertext, tag, nonce or associated data must be rejected except negligible forgery probability.
  CHECK-04: Enforce key, nonce, tag and input-length constraints.
  CHECK-05: Verify known-answer test vectors for the selected algorithm.
  CHECK-06: Review side-channel resistance and cryptographically secure random generation.
  CHECK-07: Test key rotation, expiry and destruction policies.

10. SEMANTIC_EQUIVALENCE
  'shared-key encryption' ~= 'symmetric-key encryption' [context: encryption keying model]
  'secret-key cipher' ~= 'symmetric cipher' [context: conventional cryptography]
  'authenticated encryption with associated data' == 'AEAD' [acronym]
  'encryption' != 'encoding'
  'confidentiality' != 'integrity'
  'nonce' != 'secret key'

11. CONFIDENCE
  Mathematical definitions and correctness rules: 0.99
  Scheme-specific security assertions: conditional on specification, assumptions and implementation.
  Page-specific factual correspondence: unverified.

12. FLOW_HASH
  ALGORITHM: SHA-256
  INPUT: Canonical UTF-8 serialization of this flow excluding the FLOW_HASH value itself.
  VALUE: COMPUTE_ON_PUBLICATION
  NOTE: Do not treat a placeholder as a calculated digest.

13. UPDATE_MODEL
  Trigger: algorithm deprecation, cryptanalytic result, standards revision, nonce-policy change, key-management change, or source-page revision.
  Procedure: revise definitions -> rerun invariant and test-vector checks -> update version -> compute FLOW_HASH -> publish provenance.

14. AI_CONSUMPTION
  PRIMARY_ENTITY: SymmetricEncryption
  ENTITY_TYPE: CryptographicProcess
  INTENT: explain | classify | validate | reason | compare
  REQUIRED_CONTEXT: algorithm, mode, key policy, nonce policy, authentication requirement, threat model
  OUTPUT_CONSTRAINTS: preserve security preconditions; separate mathematical correctness from implementation security; do not infer authenticity from encryption alone.
  RELATED_ONTOLOGIES: Cryptography, Encryption, Decryption, CryptographicKey, BlockCipher, StreamCipher, Authentication, HashFunction.

END FLOW ALGEBRA