Signatures Summary

Cryptography · Axiom Academy

Key takeaways from the Digital Signatures unit Authentication: Proves who created the message Integrity: Detects any tampering or modification Non-repudiation: Signer cannot deny signing Key Insight: Sign with private key, verify with public key (opposite of encryption) RSA Signatures: Based on RSA problem, widely deployed in TLS and certificates DSA/ECDSA: Based on discrete log, used in Bitcoin and blockchain Schnorr: Elegant, linear structure, enables key aggregation EdDSA: Modern variant using Edwards curves for speed and security Blind Signatures: Signer doesn't see message content, enables privacy (e-cash, anonymous credentials) Multisignatures: n parties create one compact signature, efficient for group authentication Threshold Signatures: Requires t-of-n signers to collaborate, distributes trust Ring Signatures: One of group signed, but which one stays anonymous Aggregate Signatures: Combine multiple signatures into one for efficiency Group Signatures: Members sign on behalf of group with anonymity guarantees Security Goal (EUF-CMA): Existential Unforgeability under Chosen Message Attack—attacker can't forge signatures even after seeing many valid signatures Nonce Reuse Danger: Reusing randomness in DSA/ECDSA leaks private key (Sony PlayStation hack, Bitcoin wallet failures) Hash-then-Sign: Sign hash of message, not message itself, for efficiency and security Deterministic Nonces: Use RFC 6979 to derive nonces from message to prevent reuse

This is the written version of the interactive lesson above. See the full Cryptography course.