Cryptography.

Cryptography is the discipline that designs and analyses algorithms for protecting data and communications against eavesdropping, tampering, and impersonation. Modern cryptography combines number theory, algebra, probability, and complexity theory to build primitives such as block and stream ciphers, public-key systems, hash functions, message authentication codes, and digital signatures.

Security by assumption, not obscurity

A foundational rule is Kerckhoffs's principle: a system must stay secure even if everything except the key is public. Security is therefore evaluated under formal models — IND-CPA for confidentiality, EUF-CMA for signature unforgeability — and reduced to hard mathematical problems such as integer factorization (RSA), discrete logarithms (Diffie–Hellman, ECC), or learning-with-errors (lattice schemes). Standards bodies such as NIST, ISO, and IETF publish vetted algorithms; homegrown crypto is strongly discouraged because subtle flaws are catastrophic and rarely visible without expert review.

Why bad crypto keeps failing

Most real breaks target implementation, not the core mathematics: reused nonces, predictable IVs, padding oracles (as in the POODLE and Lucky-13 attacks on TLS), weak randomness, or timing side channels. This is why practitioners prefer authenticated encryption (AES-GCM, ChaCha20-Poly1305) and constant-time libraries.

The post-quantum transition

A sufficiently large quantum computer running Shor's algorithm would break RSA and elliptic-curve cryptography. In August 2024 NIST published its first post-quantum standards: FIPS 203 (ML-KEM, from CRYSTALS-Kyber) for key encapsulation, FIPS 204 (ML-DSA, from Dilithium) and FIPS 205 (SLH-DSA, from SPHINCS+) for signatures. Organisations are now pursuing "crypto-agility" and hybrid classical+PQC deployments to resist "harvest-now, decrypt-later" collection.

flowchart TD
  A[Cryptography] --> B[Symmetric<br/>shared key]
  A --> C[Asymmetric<br/>public / private key]
  A --> D[Keyless primitives]
  B --> B1[Block ciphers<br/>AES]
  B --> B2[Stream ciphers<br/>ChaCha20]
  B --> B3[AEAD + MAC<br/>GCM, Poly1305]
  C --> C1[Key exchange<br/>ECDH, ML-KEM]
  C --> C2[Signatures<br/>ECDSA, ML-DSA]
  D --> D1[Hash functions<br/>SHA-2, SHA-3]
  B1 --> E[Confidentiality]
  B3 --> F[Integrity + authenticity]
  C2 --> G[Authenticity + non-repudiation]