Cryptology ePrint Archive: Report 2018/1122

Improved Quantum Multicollision-Finding Algorithm

Akinori Hosoyamada and Yu Sasaki and Seiichiro Tani and Keita Xagawa

Abstract: 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 $O(N^{(3^{l-1}-1) / (2 \cdot 3^{l-1})})$. 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 $O(N^{(2^{l-1}-1) / (2^{l}-1)})$. Moreover, it finds multiclaws for random functions, which are harder to find than multicollisions.

Category / Keywords: foundations / post-quantum cryptography, quantum algorithm, multiclaw, multicollision

Date: received 18 Nov 2018, last revised 30 Nov 2018

Contact author: hosoyamada akinori at lab ntt co jp

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Version: 20181130:115207 (All versions of this report)

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