In this note, we give a quantum algorithm that finds collisions in arbitrary τ-to-one functions after only O ( 3 √ N /τ) expected evaluations of the function. Assuming the function is given by a black box, this is more efficient than the best possible classical algorithm, even allowing probabilism. We also give a similar algorithm for finding claws in pairs of functions. Furthermore, we exhibit a space-time tradeoff for our technique. Our approach uses Grover's quantum searching algorithm in a novel way.
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Quantum cryptanalysis of hash and claw-free functions
Brassard, Gilles; Høyer, Peter; Tapp, Alain
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, Volume 28 (2)
Association for Computing Machinery – Jun 1, 1997
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