As Project Eleven notes, Bitcoin uses ECDSA for transaction signatures. Quantum computers, using Shor’s algorithm, could theoretically derive private keys from public keys
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Quantum computing research firm Project Eleven is offering 1 BTC to anyone who can break Bitcoin's cryptography
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Project Eleven’s Q-Day Prize directly challenges the Elliptic Curve Digital Signature Algorithm (ECDSA), which is central to Bitcoin’s transaction security and vulnerable to Shor’s algorithm.
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