Cryptography Topics

Objectives: Cryptography Topics

All Topics in Cryptography — Comprehensive Handbook

All Topics in Encryption Technology (Cryptography)

A broad, study-friendly handbook covering classical, modern, applied, and emerging cryptography.

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1) Foundations of Cryptography

  • History & evolution; cryptography vs. cryptology vs. cryptanalysis
  • Goals: confidentiality, integrity, authenticity, non-repudiation, forward secrecy, deniability
  • Primitives & constructions: ciphers, hashes, MACs, signatures, commitments, PRFs/PRPs
  • Mathematics: modular arithmetic, groups/fields, finite fields GF(2^n), lattices, elliptic curves
  • Hardness assumptions: factoring, discrete log (DLP/EDLP), DH, CDH/DDH, SIS/LWE, isogeny problems
  • Security notions: IND-CPA, IND-CCA, EUF-CMA, KDM, Malleability, Leakage resilience
  • Adversary models: chosen-plaintext/ciphertext, adaptive adversaries, quantum adversaries
  • Provable security: reductions, game-based proofs, simulation-based security
  • Composability: UC framework, computational vs. information-theoretic security

2) Classical Cryptography

  • Substitution & transposition ciphers; Caesar, Vigenère, Playfair, Hill
  • Rotor machines: Enigma, Lorenz; codebooks & one-time pads (OTP)
  • Telegraph/WW-era crypto; purple cipher; Navajo code talkers (operational security)
  • Frequency analysis; Kasiski, Friedman tests; crib-dragging
  • Information-theoretic security & OTP theory (Shannon)

3) Symmetric-Key Cryptography

  • Block ciphers: DES, 3DES, AES, Camellia, Serpent, Twofish, IDEA, ARIA, PRESENT, GOST
  • Designs: Feistel networks, SPN, Lai–Massey, ARX (add-rotate-xor)
  • Modes of operation: ECB, CBC, CFB, OFB, CTR, XTS, GCM, EAX, CCM, SIV, OCB
  • Authenticated encryption: AE, AEAD; misuse resistance; deterministic AE (DAE)
  • Stream ciphers: RC4, HC-128/256, Salsa20, ChaCha20, Grain, Trivium, SNOW
  • Message authentication: CBC-MAC, CMAC, GMAC, Poly1305
  • Pseudorandom functions/permutations (PRF/PRP); key schedules
  • Cryptanalysis: differential, linear, boomerang, impossible differential, integral, algebraic
  • Lightweight crypto & IoT ciphers; authenticated lightweight modes

4) Asymmetric/Public-Key Cryptography

  • RSA (encryption, signatures, OAEP, PSS); Rabin
  • Diffie–Hellman (finite fields); Elliptic-Curve Diffie–Hellman (ECDH)
  • ElGamal (finite-field & EC variants)
  • Elliptic Curve Cryptography: curves (P-256, Curve25519, Curve448, Koblitz), point arithmetic
  • Pairings: bilinear pairings (Weil/Tate), BLS signatures, pairing-friendly curves
  • Lattice-based: LWE, RLWE, SIS; encryption (Kyber), signatures (Dilithium, Falcon)
  • Code-based: McEliece/Niederreiter, BIKE, HQC
  • Multivariate-quadratic (MQ) schemes: Rainbow, GeMSS
  • Isogeny-based: SIDH/SIKE (history & cryptanalysis), CSIDH
  • Hash-based signatures: XMSS, LMS, SPHINCS+
  • Identity-based, certificateless, attribute-based encryption
  • Functional & predicate encryption; broadcast & proxy re-encryption

5) Hash Functions & Message Authentication

  • Hash families: MD5, SHA-1, SHA-2, SHA-3 (Keccak), BLAKE2/3, RIPEMD
  • Constructions: Merkle–Damgård, HAIFA, sponge, tree hashing (Merkle trees)
  • Security: collision/preimage/2nd-preimage resistance; length extension; multicollisions
  • MACs: HMAC, CMAC, GMAC, Poly1305; universal hashing (NH, UMAC, VMAC)
  • Random oracles & indifferentiability

6) Digital Signatures & Authentication

  • RSA-PSS, DSA, ECDSA, EdDSA (Ed25519/Ed448)
  • Deterministic signatures, Schnorr, MuSig/MuSig2 (multisignature)
  • Aggregate signatures, BLS
  • Blind signatures, group & ring signatures, linkable ring signatures
  • Designated verifier signatures, undeniable signatures
  • Threshold signatures (TSS), FROST

7) Key Management, PKI & Secret Sharing

  • Key generation, entropy sources, KDFs (HKDF, PBKDF2, scrypt, Argon2)
  • Key exchange: DH/ECDH, PAKE (SRP, SPAKE2, CPace, OPAQUE), KEMs
  • PKI: X.509 certificates, CA hierarchies, OCSP, CRLs, CT logs
  • Secret sharing: Shamir, Verifiable Secret Sharing, threshold cryptography
  • Hardware roots: TPM, HSM, secure enclaves (SGX/SEV/TEE)
  • Key rotation, escrow, recovery, backup, and destruction

8) Cryptographic Protocols & Constructions

  • Hybrid encryption; KEM/DEM paradigm
  • Authenticated key exchange (AKE), forward secrecy, 0-RTT considerations
  • Commitment schemes (Pedersen, hash-based); trapdoor permutations
  • Oblivious transfer (OT/ROT), private set intersection (PSI)
  • Secret ballots & e-voting protocols
  • Time-lock puzzles, verifiable delay functions (VDFs)
  • Secure channels: record protocols, key schedules, rekeying
  • Password hashing & storage (bcrypt, scrypt, Argon2id; peppering)

9) Advanced Cryptography & Privacy Technologies

  • Zero-knowledge proofs (Sigma protocols); zk-SNARKs, zk-STARKs, Bulletproofs
  • Homomorphic encryption (PHE/SHE/FHE): Paillier, BFV, BGV, CKKS
  • Secure multiparty computation (MPC/SMPC): Yao garbled circuits, GMW, SPDZ
  • Functional encryption, predicate encryption, IBE/ABE
  • Searchable encryption, property-preserving & order-revealing encryption (OPE/ORE)
  • Differential privacy (relation to crypto), PIR (single-server & multi-server)
  • Anon creds: Idemix, U-Prove; selective disclosure; verifiable credentials
  • Mix networks, onion routing (Tor), DC-nets; metadata privacy

10) Cryptanalysis & Attacks

  • Attack models: CPA, CCA/CCA2, KPA, adaptive attacks
  • Side-channel attacks: timing, cache, power (SPA/DPA), EM, fault injection, Rowhammer
  • Padding oracles, BEAST/CRIME/POODLE/Lucky13; downgrade & negotiation attacks
  • Meet-in-the-middle, related-key, slide, biclique, rebound
  • Collision attacks on hashes (MD5/SHA-1), length extension
  • Quantum attacks: Shor, Grover; post-quantum threat models
  • Protocol pitfalls: nonce reuse, IV collisions, key/nonce misuse in AEAD

11) Applied Cryptography & Systems

  • Transport security: TLS 1.2/1.3, QUIC, DTLS; certificate pinning, HPKP (history)
  • Network security: IPsec, WireGuard, SSH (OpenSSH), Kerberos
  • Data at rest: disk/volume encryption (BitLocker, LUKS, FileVault), database TDE
  • Messaging: Signal (Double Ratchet, X3DH), WhatsApp, Matrix/Olm/Megolm
  • Email: PGP/OpenPGP, S/MIME, DKIM, DMARC
  • Web: OAuth2/OIDC, JOSE (JWS/JWE/JWK), FIDO/WebAuthn (CTAP/U2F)
  • Mobile & app security: keystores, secure storage, keychain, attestation
  • Cloud KMS & envelope encryption; client-side vs. server-side encryption
  • Secure backups, secret management (Vault, KMS, age, minisign)

12) Post‑Quantum Cryptography (PQC)

  • NIST PQC standardization: KEMs (Kyber), signatures (Dilithium, Falcon, SPHINCS+)
  • Lattice-based: LWE/RLWE security, module lattices, decryption failure attacks
  • Code-based: Classic McEliece; decoding algorithms
  • Hash-based: stateful (XMSS/LMS) vs stateless (SPHINCS+)
  • Migration & hybrid handshakes (TLS 1.3 PQC hybrids)

13) Hardware, Implementation & Performance

  • Constant-time coding, masking, blinding; side-channel countermeasures
  • Accelerations: AES-NI, SHA extensions, ARM Cryptography Extensions, GPU/FPGA/ASIC
  • Smart cards, HSMs, TPMs, TEEs (SGX/SEV/TrustZone), secure elements
  • PRNG/TRNG hardware, noise sources, jitter entropy
  • Implementation verification, test vectors, fuzzing & differential testing

14) Randomness, Entropy & Key Derivation

  • Entropy estimation; Fortuna; Yarrow; /dev/random, CSPRNGs
  • DRBGs: Hash_DRBG, HMAC_DRBG, CTR_DRBG; NIST SP 800-90 series
  • KDFs: HKDF, scrypt, Argon2 (i/d/id); salts & peppers; memory-hard designs
  • Password-based cryptography, passphrases, PAKEs

15) Blockchain, DLT & Web3 Cryptography

  • Consensus & crypto: PoW/PoS, VRFs, VDFs
  • Wallets & key mgmt: HD wallets (BIP32/39/44), multisig, threshold wallets
  • Smart-contract security: reentrancy vs. crypto verification, precompiles
  • Privacy coins: zk-SNARKs (Zcash), ring signatures (Monero), Mimblewimble
  • Commit-reveal schemes, randomness beacons

16) Formal Methods, Proofs & Verification

  • Security definitions & games; ideal functionalities; UC framework
  • Proof assistants & tools: ProVerif, Tamarin, EasyCrypt, Cryptol/SAW
  • Modeling protocols: BAN logic, symbolic vs. computational models
  • Compositional security, robust combiners

17) Governance, Policy, Ethics & Law

  • Export controls (EAR/Wassenaar), key escrow debates, lawful intercept
  • Privacy law: GDPR, HIPAA, COPPA, eIDAS, data localization
  • Backdoors, exceptional access, policy controversies
  • Responsible disclosure; cryptographic agility & lifecycle management

18) Standards, Bodies & Compliance

  • NIST (FIPS 140-3, SP 800 series), ISO/IEC 19790/14888, IETF RFCs
  • CA/Browser Forum, CAB Baseline Requirements, Certificate Transparency
  • Common Criteria, FIPS validation, FedRAMP, PCI DSS
  • Open standards & reference libs: OpenSSL, BoringSSL, libsodium, NaCl, PQClean

19) Use‑Cases & Domain‑Specific Cryptography

  • Secure messaging, file sharing, storage at rest & in use
  • Payment systems, EMV, HCE, tokenization, HSM-backed processing
  • IoT & embedded: lightweight crypto, constrained environments
  • Vehicular & V2X, satellite & space communications
  • Healthcare, gov-ID/e-passports (BAC/EAC), e-voting
  • Privacy-preserving analytics & ML, federated learning with MPC/HE

20) Learning, Testing & Best Practices

  • Threat modeling, crypto misuse taxonomy, secure defaults
  • Key/nonce management, RNG health checks, incident response
  • Interoperability testing, conformance suites, vectors
  • Choosing algorithms & parameters; deprecation & migration planning
  • Reading specs/RFCs; safe library APIs; constant-time reviews
Note: This handbook aims to be comprehensive, but the field evolves rapidly (especially PQC and ZK). Treat this as a living checklist.
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Reference Book: Applied Cryptography – Bruce Schneier Cryptography and Network Security – William Stallings Understanding Cryptography – Christof Paar & Jan Pelzl Introduction to Modern Cryptography – Jonathan Katz & Yehuda Lindell Serious Cryptography – Jean-Philippe Aumasson

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