Cryptography & Secure Communication

The mathematics, algorithms, and historical practices that protect information in transit and at rest. From ancient scytalae to post-quantum lattice-based schemes, explore the foundations of digital trust.

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All Classical Modern Quantum Applied Math Foundations

RSA Algorithm

The foundational asymmetric cryptosystem relying on the practical difficulty of factoring large integers. Explains key generation, encryption, decryption, and security parameters.

Advanced Encryption Standard (AES)

The NIST-standardized block cipher operating on 128-bit blocks with 128, 192, or 256-bit keys. Covers SubBytes, ShiftRows, MixColumns, and AddRoundKey transformations.

Enigma Machine & Allied Codebreaking

The German rotor cipher system of WWII, its mechanical design, daily keying procedures, and the mathematical/political breakthroughs at Bletchley Park.

Zero-Knowledge Proofs

Interactive protocols allowing one party to prove knowledge of a value without revealing the value itself. Covers zk-SNARKs, zk-STARKs, and blockchain applications.

Elliptic Curve Cryptography (ECC)

Public-key cryptography based on the algebraic structure of elliptic curves over finite fields. Explores key size efficiency, ECDSA, and ECDH key exchange.

Post-Quantum Cryptography

Algorithms resistant to quantum computer attacks. Covers lattice-based, code-based, multivariate, and hash-based schemes standardized by NIST's PQC project.

Evolution of Secret Writing

c. 400 BCE
Scytale & Polybius Square
Early transposition ciphers used by ancient Greeks for military communications, laying groundwork for substitution and permutation principles.
1467
Alberti Cipher Disk
Leon Battista Alberti invents polyalphabetic substitution, marking the birth of modern cryptography and frequency-analysis resistance.
1917
One-Time Pad & Stream Ciphers
Gibson Vernam and Joseph Mauborgne formalize information-theoretic security, proving unconditional secrecy under strict key requirements.
1976
Diffie–Hellman Key Exchange
Whitfield Diffie and Martin Hellman introduce public-key cryptography, solving the key distribution problem and enabling secure open-channel communication.
2020s–Present
Post-Quantum Standardization
NIST finalizes lattice-based and hash-based algorithms to replace vulnerable RSA/ECC systems as quantum computing capabilities advance.

Recent Updates

Lattice-Based Key Encapsulation Mechanisms

Expanded with Kyber-1024 performance benchmarks & side-channel mitigations
+24 Sections

Homomorphic Encryption: Fully vs Somewhat

Added CKKS scheme examples & cloud computing use cases
+18 Sections

Cryptographic Hash Functions

Updated SHA-3/Keccak sponge construction diagrams & collision resistance proofs
+12 Sections

Secure Multi-Party Computation

Integrated garbled circuits & secret sharing protocols with interactive visualizations
+31 Sections