What's Next?

What's Next

You have built cryptographic primitives from scratch — from Caesar ciphers to zero-knowledge proofs. Here are natural next steps:

  • AES and ChaCha20 — The symmetric ciphers used in TLS today. AES uses a substitution-permutation network; ChaCha20 uses ARX (add-rotate-XOR) operations. Both are more sophisticated than the Feistel example here.
  • Elliptic Curve Cryptography (ECC) — Replace RSA's integer arithmetic with points on an elliptic curve. ECDH and ECDSA achieve the same security as RSA with much smaller key sizes.
  • TLS and PKI — The Transport Layer Security protocol combines Diffie-Hellman key exchange, digital signatures, and symmetric encryption. Certificate authorities form the Public Key Infrastructure that secures HTTPS.
  • Post-Quantum Cryptography — RSA and ECC are broken by Shor's algorithm on a quantum computer. NIST-standardized replacements (CRYSTALS-Kyber, CRYSTALS-Dilithium) use lattice-based hard problems.

Further Reading

  • Introduction to Modern Cryptography by Katz & Lindell — The standard academic text, rigorous and complete.
  • A Graduate Course in Applied Cryptography by Boneh & Shoup — Free online, covers everything from symmetric primitives to advanced protocols.
  • The Cryptopals Challenges (cryptopals.com) — Hands-on challenges that break real-world crypto, including CBC padding oracles and HMAC timing attacks. Essential practice.
  • Serious Cryptography by Jean-Philippe Aumasson — Practical focus, covers AES, RSA, ECC, TLS, and hash functions with clear explanations.
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