How Does Shor’s Algorithm on a Quantum Computer Pose a Threat to This Assumption?

Shor's algorithm is a theoretical quantum algorithm that can efficiently solve the Discrete Logarithm Problem and, by extension, the Elliptic Curve Discrete Logarithm Problem (ECDLP). A sufficiently powerful, fault-tolerant quantum computer running Shor's algorithm could break 256-bit ECDSA keys in a matter of hours or minutes.

This represents an existential threat to all current public-key cryptography, including the security of most cryptocurrencies.

What Does “Post-Quantum Secure” Mean in the Context of Cryptography?
What Mathematical Problem Is the Security of ECDSA Based Upon?
Can a Quantum Computer Theoretically Break SHA-256 Encryption, and What Would Be the Impact on Options Pricing for Bitcoin?
Could a Quantum Computer Theoretically Execute a 51% Attack on Bitcoin?
What Mathematical Property of Elliptic Curves Provides Security for ECDSA?
How Does the Discrete Logarithm Problem Relate to ECDSA’s Security?
What Is the Current State of Quantum Computing’s Threat to ECDSA?
What Makes the ECDSA Process “One-Way” and Why Is This Critical for Security?

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