Grover's Algorithm

Grover's algorithm is a quantum search procedure published by Lov Grover in 1996 that finds a target in an unsorted space of N possibilities in roughly the square root of N steps. Against symmetric cryptography this quadratic speedup effectively halves security, reducing a 256-bit hash such as SHA-256 to about 128 bits of quantum resistance.

How it works

The algorithm amplifies the probability of the correct answer through repeated quantum operations, so a search that would classically take on the order of 2 to the 256th power tries needs on the order of 2 to the 128th power quantum iterations. Crucially, 128 bits of security remains far beyond any plausible machine, and each Grover iteration is slow and must run coherently, so the practical threat to hashing is widely judged to be minimal compared with Shor's algorithm against public keys.

For bitcoin mining, Grover's algorithm could in principle accelerate the search for valid block hashes, but published analyses conclude the advantage would be modest against the massive parallelism of ASIC fleets and would arrive, if ever, long after signature vulnerabilities matter.

In the gold vs bitcoin debate

In the quantum discussion, Grover is the manageable half of the threat and Shor is the serious half. Bitcoin's hashes bend but do not break, while its signatures would eventually need replacement. Gold sits outside the discussion entirely, which is precisely the argument its advocates make.