CyberGlossary

Cryptography

ECDSA

Definition

The elliptic-curve variant of the Digital Signature Algorithm, standardized in FIPS 186, producing compact signatures whose security relies on the elliptic-curve discrete logarithm problem.

The Elliptic Curve Digital Signature Algorithm (ECDSA) is the elliptic-curve analogue of DSA, standardized in ANSI X9.62 and FIPS 186. To sign, the signer computes a hash of the message, picks a random per-signature nonce k, and produces a pair (r, s) using the curve's base point and their private key. Verification uses the public key, the hash, and (r, s) without revealing the private key. ECDSA produces compact signatures — about 64 bytes for the popular P-256 curve — and is widely used in TLS, code signing, JWTs, and most cryptocurrencies (Bitcoin, Ethereum use secp256k1). Its critical pitfall is nonce reuse or poor randomness: a single repeated k leaks the private key, as Sony's PS3 firmware-signing breach famously demonstrated. EdDSA (Ed25519) is often preferred today because it is deterministic and side-channel-friendly.

Examples

  • TLS server certificates increasingly use ECDSA-P256 instead of RSA.
  • Bitcoin transactions are authorized by ECDSA signatures over secp256k1.

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