ECDSA

ECDSA (Elliptic Curve Digital Signature Algorithm) is the elliptic-curve form of the Digital Signature Algorithm, standardized in FIPS 186-5. A signer with a private scalar d and public key Q equal to d times the base point produces a signature from the message hash and a fresh per-signature nonce; verification uses only the public key. ECDSA over the secp256k1 curve signs every Bitcoin transaction, and over NIST P-256 it authenticates a large share of TLS connections. It is one instantiation of a digital signature built on elliptic-curve cryptography.

#Quantum vulnerability

ECDSA security rests on the elliptic-curve discrete logarithm problem, which Shor's algorithm solves in polynomial time, so a large quantum computer can forge signatures by recovering the private key from the public key. For Bitcoin this is the core of the quantum threat to ECDSA: any address whose public key is exposed on chain becomes forgeable. Implementation flaws add classical risk too, since a reused or biased nonce leaks the private key even without a quantum computer. The deterministic scheme Ed25519 mitigates that nonce risk, but remains equally quantum-vulnerable.