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Google's recent 57-page whitepaper reveals that Shor's algorithm can potentially compromise the 256-bit elliptic curve cryptography used by Bitcoin and Ethereum. The paper indicates that with fewer than 500,000 physical qubits on a superconducting architecture, a quantum circuit can break this encryption in about nine minutes, coinciding with Bitcoin's average block time. Despite withholding the specific circuit details for responsible disclosure, the paper provides enough architectural information that skilled quantum algorithm teams could replicate similar circuits. Ben Goertzel, CEO of SingularityNET, believes that even his team, which doesn't focus primarily on quantum computing, could produce comparable circuit designs.
The paper outlines significant architectural details, including the use of kickmix architecture, modular inversion techniques, and specific gate counts for elliptic curve point addition. For instance, the paper mentions that the circuits involve around 2.7 million non-Clifford gates for each point addition subroutine. The optimizations discussed are not groundbreaking but demonstrate a notable improvement over previous work, achieving about an order of magnitude better efficiency than earlier designs. Goertzel estimates that a small team of experts could reproduce circuits within 2-3 times Google's efficiency in six to twelve months, given the readily available knowledge in the field.
While Google's specific implementation remains undisclosed, the optimizations mentioned are well-documented in existing literature. Goertzel points out that the last stages of optimization require sophisticated scheduling and decision-making, which is where Google’s resources provide a competitive advantage. However, even if a circuit requires double the gates, it still poses a significant threat to current cryptographic systems. The implications are clear: any well-funded research group, including national labs and defense contractors, could replicate these findings, raising serious concerns about the future of blockchain security.
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