What Is Shor's Algorithm and Why Does It Threaten Crypto?

Shor's algorithm, published by mathematician Peter Shor in 1994, is a quantum algorithm that efficiently solves integer factorization and discrete logarithm problems. These mathematical problems form the security foundation of RSA, Diffie-Hellman, and ECDSA cryptography—including the signatures protecting virtually all current cryptocurrencies.

Classical computers require exponential time to factor large numbers or compute discrete logarithms. A 2048-bit RSA key would take classical computers longer than the age of the universe to break. Shor's algorithm reduces this to polynomial time, making these operations feasible on sufficiently powerful quantum computers.

For cryptocurrency, the threat is specific: Shor's algorithm can derive ECDSA private keys from public keys. Bitcoin, Ethereum, and most cryptocurrencies use ECDSA with the secp256k1 curve. Once public keys are exposed (which occurs when addresses are spent from), quantum computers running Shor's algorithm can compute the corresponding private keys.

Technical requirements for running Shor's algorithm against 256-bit ECDSA include approximately 4,000 logical qubits. Current quantum computers have achieved around 1,000 physical qubits, with logical qubits requiring roughly 1,000 physical qubits each for error correction. This places the requirement at millions of physical qubits—not yet achieved but within projected development timelines.

Post-quantum cryptography addresses this threat by using mathematical problems that Shor's algorithm cannot solve efficiently. Lattice-based cryptography (Kyber) and hash-based signatures (SPHINCS+) have no known efficient quantum attacks.

SynX implements Kyber-768 and SPHINCS+ algorithms specifically because Shor's algorithm provides no advantage against them. This future-proofs cryptocurrency holdings against the inevitable advancement of quantum computing technology.