What Is Shor's Algorithm?
Shor's algorithm, developed by mathematician Peter Shor in 1994, is a quantum algorithm that can factor large numbers and solve discrete logarithm problems exponentially faster than classical computers. In practical terms: running on a sufficiently powerful quantum computer, Shor's algorithm can derive an Elliptic Curve private key from its corresponding public key. This is the mathematical attack on ECDSA.
Why ECDSA Is Vulnerable
Bitcoin and Ethereum use ECDSA (Elliptic Curve Digital Signature Algorithm) for all transaction signing. The security of ECDSA rests on the computational difficulty of solving the Elliptic Curve Discrete Logarithm Problem (ECDLP). This is computationally hard for classical computers. Shor's algorithm solves ECDLP efficiently on a quantum computer — breaking the mathematical foundation of ECDSA security.
BMIC's ML-DSA: Quantum-Safe Signatures
BMIC uses ML-DSA (FIPS 204) — the NIST-approved quantum-safe replacement for ECDSA. ML-DSA is based on lattice mathematics that remains hard even for quantum computers running Shor's algorithm. When quantum computers advance to cryptographic relevance, BMIC signatures remain secure. ⚠️ DYOR. Not financial advice. Crypto investments carry significant risk including total loss of capital.