Cryptography · Cluster
Signatures and MACs
Authenticity and non-repudiation.
- 01 The Verification Split: Why a MAC Cannot Settle a Dispute Symmetric tags and public-key signatures differ in who is able to check them, and that single difference determines what each can be used as evidence for.
- 02 Why HMAC Hashes Twice and What Length Extension Has to Do With It The nested construction that turns a plain hash into a keyed MAC, the Merkle-Damgard weakness it neutralises, and why the two fixed inner and outer pads are load-bearing.
- 03 CBC-MAC Ends at the Last Block, and That Is the Problem Chaining a block cipher over a message authenticates only the final block, so variable-length messages invite splicing attacks; CMAC adds two derived subkeys to close the hole.
- 04 Poly1305 and the Arithmetic of a One-Time Key A 130-bit prime, a clamped scalar, and a carry structure that make a fast MAC provably secure only when each key is used exactly once.
- 05 Salt, Hash, and MGF1: What RSA-PSS Adds to the Verification Step Probabilistic signature padding turns a textbook RSA signature into one that resists chosen-message forgery, and moves work from the signer to the verifier.
- 06 ECDSA Nonce Reuse and the Private Key It Leaks A repeated signing nonce turns two signatures into a linear system that yields the private key, and biased nonces are nearly as bad because lattice reduction tolerates noise.
- 07 Ed25519 Cofactors, Canonical Encoding, and Strict Verification A twisted Edwards curve with a small cofactor and a single verification equation leaves several checks outside the signature standard, and different libraries have disagreed about them.
- 08 Encrypt-and-MAC, MAC-then-Encrypt, Encrypt-then-MAC Three orderings of a cipher and a MAC, only one of which authenticates the ciphertext itself, and the attacks that distinguish them under chosen-ciphertext access.
- 09 Merkle Trees as a Signature Scheme: One Key, Many One-Time Keys A hash-based signature is a one-time object, and a binary authentication tree is what turns a finite collection of them into a long-lived public key with logarithmic signatures.
- 10 BLS Aggregation and the Rogue-Key Attack It Invites A pairing lets many signatures collapse into one, but the straightforward multisignature construction lets the last signer choose a key that frames the others.