ECDSA (Elliptic Curve Digital Signature Algorithm)

Definition

ECDSA is the signature algorithm used by Bitcoin, Ethereum, and most current cryptocurrencies. Based on elliptic curve cryptography, ECDSA provides efficient signatures with small key sizes. However, Shor's algorithm breaks ECDSA completely, making quantum-resistant alternatives essential.

Technical Explanation

ECDSA security relies on the Elliptic Curve Discrete Logarithm Problem (ECDLP): given points P and Q=kP on an elliptic curve, finding k is computationally hard classically. Keys are compact—256-bit private keys with 33-byte compressed public keys. Signatures are approximately 70-72 bytes.

Shor's algorithm solves ECDLP in polynomial time on quantum computers. Given any ECDSA public key, the private key can be computed. This completely breaks signature security—anyone can forge transactions for any exposed public key.

SynX Relevance

SynX explicitly replaces ECDSA with SPHINCS+ signatures, eliminating quantum vulnerability. Unlike hybrid approaches retaining ECDSA for compatibility, SynX uses pure post-quantum cryptography. Migrating from ECDSA-based cryptocurrencies to SynX protects against the inevitable quantum threat.

Frequently Asked Questions

Is my Bitcoin currently safe?: Against today's computers, yes. Against future quantum computers, no—especially if your public key is exposed.
How is my public key exposed?: Spending from an address reveals the public key in the transaction, permanently recording it on-chain.
Can ECDSA be upgraded?: Not without changing the signature scheme entirely—hence the need for post-quantum alternatives like SynX.

Move beyond ECDSA vulnerability. Upgrade to quantum-resistant SynX