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- W2952629894 abstract "The current paper presents a new quantum algorithm for finding multicollisions, often denoted by l-collisions, where an l-collision for a function is a set of l distinct inputs having the same output value. Although it is fundamental in cryptography, the problem of finding multicollisions has not received much attention in a quantum setting. The tight bound of quantum query complexity for finding 2-collisions of random functions has been revealed to be (varTheta (N^{1/3})), where N is the size of a codomain. However, neither the lower nor upper bound is known for l-collisions. The paper first integrates the results from existing research to derive several new observations, e.g. l-collisions can be generated only with (O(N^{1/2})) quantum queries for a small constant l. Then a new quantum algorithm is proposed, which finds an l-collision of any function that has a domain size l times larger than the codomain size. A rigorous proof is given to guarantee that the expected number of quantum queries is (Oleft( N^{(3^{l-1}-1)/(2 cdot 3^{l-1})} right) ) for a small constant l, which matches the tight bound of (varTheta (N^{1/3})) for (l=2) and improves the known bounds, say, the above simple bound of (O(N^{1/2}))." @default.
- W2952629894 created "2019-06-27" @default.
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- W2952629894 date "2017-01-01" @default.
- W2952629894 modified "2023-10-16" @default.
- W2952629894 title "Quantum Multicollision-Finding Algorithm." @default.
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