Cryptography · Cluster
Public-Key Cryptography
RSA, Diffie-Hellman, and elliptic curves.
- 01 Modular Exponentiation and the Cost of One Key Operation How square-and-multiply collapses a huge exponent into a few thousand multiplications, why private exponents cost far more than public ones, and where constant-time code changes the algorithm.
- 02 Discrete Logarithms and Why Group Order Decides Their Difficulty How Pohlig-Hellman reduces a discrete logarithm to its prime factors, why safe primes and Schnorr groups exist, and what small-subgroup confinement does to a protocol.
- 03 RSA Key Generation and the Prime Search Generating two large primes, testing them for primality, deriving the private exponent, and why the resulting key has structure that must be checked rather than assumed.
- 04 RSA Padding and Why Textbook RSA Fails Textbook RSA is multiplicative and deterministic, which makes it malleable and open to chosen-ciphertext attacks; how OAEP and PSS impose the structure that closes them.
- 05 Ephemeral Diffie-Hellman and What Forward Secrecy Actually Buys Why a fresh exponent per handshake protects past sessions after a key compromise, what the extra exponentiations cost, and how identity binding prevents the exchange from being hijacked.
- 06 Elliptic Curve Point Arithmetic and Validation The group law on a short Weierstrass curve, why scalar multiplication uses a ladder rather than double-and-add, and which malformed points a peer can send.
- 07 Key Size Equivalence Across RSA, Diffie-Hellman, and Curves Why 2048-bit RSA, 2048-bit finite-field Diffie-Hellman, and 256-bit elliptic curves are treated as comparable, and where the equivalence table comes from.
- 08 Hybrid Encryption and the Cost of Encrypting Long Messages Why a public-key operation wraps a symmetric key instead of the message, how RSA-KEM and ECIES derive that key, and what the encapsulation interface changes.
- 09 Signature Nonces: The Single Secret That Breaks ECDSA How the per-signature nonce turns a signature equation into a solvable linear system when it repeats or leaks, and how deterministic derivation removes the randomness requirement.
- 10 Why Larger Keys Do Not Answer the Quantum Threat Shor’s algorithm attacks the group structure rather than the key length, so every classical public-key family falls together; what a replacement primitive has to provide and where migration actually costs.