Grover’s algorithm is one of the most well-known quantum algorithms, offering a quadratic speedup for solving unstructured search problems. In classical computing, searching an unsorted database of NNN elements requires O(N)O(N)O(N) queries in the worst case. Grover’s algorithm, by leveraging quantum superposition and amplitude amplification, reduces this to O(N)O(sqrt{N})O(N), a significant but not exponential improvement.
The algorithm was introduced by Lov Grover in 1996 and relies on the principles of quantum parallelism and constructive interference to amplify the probability of measuring the correct result. Unlike Shor’s algorithm, which breaks RSA and ECDSA by efficiently solving the integer factorization and discrete logarithm problems, Grover’s algorithm is mainly a brute-force accelerator. It does not completely break cryptographic hash functions or symmetric key cryptography, but it does weaken them by effectively halving their bit security.
For Bitcoin, where security depends heavily on cryptographic hash functions (SHA-256, RIPEMD-160) and elliptic curve cryptography (secp256k1), Grover’s algorithm has important but nuanced implications. While it does not pose an immediate existential threat, it does reduce the time…
