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Bitcoin primarily uses two cryptographic algorithms: ECDSA (Elliptic Curve Digital Signature Algorithm) for digital signatures and SHA-256 for hashing.
The security of ECDSA in Bitcoin is based on the difficulty of the elliptic curve discrete logarithm problem, while SHA-256's security is based on its preimage resistance.
Breaking ECDSA: A quantum computer would attack ECDSA using Shor's algorithm, which is efficient at solving problems like the discrete logarithm
problem on which ECDSA's security is based. It's estimated that a quantum computer would need roughly 1500 qubits to break ECDSA effectively.
However, this is a simplified estimate. The actual number of qubits required could be higher due to the need for error correction and other quantum computing complexities.
Breaking SHA-256: Grover's algorithm would be used to attack SHA-256. While Grover's algorithm can theoretically halve the number of steps
needed to break a hash function like SHA-256, this still represents a significant computational challenge. To effectively break SHA-256,
a quantum computer would need a large number of qubits, potentially in the range of several thousand or more, and even then,
the process would be slower than the common perception of "instant breaking" of cryptographic schemes.