Shor's algorithm is the primary reason quantum computers threaten cryptocurrency. Every major blockchain — Bitcoin, Ethereum, Solana — relies on the mathematical difficulty of factoring large numbers or solving elliptic curve discrete logarithms. Classical computers need billions of years to crack these problems. A sufficiently powerful quantum computer running Shor's algorithm could do it in hours.
The algorithm works by exploiting quantum superposition to test many possible factors simultaneously. When applied to the elliptic curve cryptography (ECDSA) used by most blockchains, it can derive private keys from public keys — giving an attacker full control of any wallet whose public key has been exposed on-chain.
Why it matters for crypto: Every Bitcoin transaction exposes the sender's public key. Once quantum computers reach approximately 4,000 error-corrected logical qubits, Shor's algorithm could crack Bitcoin's secp256k1 curve in under 24 hours. IBM targets 100,000 qubits by 2033.
How BMIC addresses this: BMIC uses CRYSTALS-Kyber lattice-based encryption, which is resistant to Shor's algorithm. The security of Kyber is based on the Learning With Errors (LWE) problem — a mathematical problem that remains hard for both classical and quantum computers.