Improved Quantum Multicollision-Finding Algorithm
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The current paper improves the number of queries of the previous quantum multi-collision finding algorithms presented by Hosoyamada et al. at Asiacrypt 2017. Let an l-collision be a tuple of l distinct inputs that result in the same output of a target function. The previous algorithm finds l-collisions by recursively calling the algorithm for finding (l-1)-collisions, and it achieves the query complexity of O(N^(3^l-1-1) / (2 · 3^l-1)). The new algorithm removes the redundancy of the previous recursive algorithm so that different recursive calls can share a part of computations. The new algorithm achieves the query complexity of Õ(N^(2^l-1-1) / (2^l-1)). Moreover, it finds multiclaws for random functions, which are harder to find than multicollisions.
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