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In 1996, Lov Grover discovered a quantum algorithm that searches unsorted databases quadratically faster than classical computers. If you're searching through N items, classical computers need N/2 operations on average. Grover's algorithm needs roughly ?N operations. This matters for cryptography because brute-force key search is basically database searching. A 128-bit AES key has 2^128 possible values. Classically, you'd need to try 2^127 keys on average (half the space). Grover's algorithm finds it in roughly 2^64 tries - that's "only" 18 quintillion instead of 170 undecillion, which sounds like a big reduction. But here's the catch: 2^64 operations on a quantum computer still requires billions of physical qubits running for months. Most experts think Grover's algorithm is impractical for cryptanalysis. Still, to be safe, NIST recommends doubling symmetric key lengths - use AES-256 instead of AES-128, SHA-384 instead of SHA-256.
Unlike Shor's algorithm which breaks public-key crypto completely, Grover's algorithm only weakens symmetric crypto, and even then only theoretically. The practical threat is low, but the precaution is simple - use AES-256. Some experts debate whether we're being too conservative, but doubling key length is cheap insurance.
The real impact is psychological and policy. Grover's algorithm is why quantum computers are seen as a threat to all encryption, not just public-key crypto. In practice, AES-256 remains secure even against quantum computers, making symmetric encryption a safe anchor during the quantum transition.
Setting cryptographic policy for post-quantum security, determining symmetric key lengths for long-term security, designing protocols combining symmetric and asymmetric crypto, quantum threat modeling and risk assessment
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