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An Efficient Quantum Multi-Collision Search Algorithm
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DOI：10.1109/ACCESS.2020.3028736.png)
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Abstract
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In this article, we propose an efficient quantum k-collision search algorithm with low quantum memory O(n). The previous quantum k-collision algorithms can not be converted into a low quantum memory k-collision algorithm directly, because the time complexity of the converted algorithm is larger than the basic k-collision algorithm. To solve this problem, we shall not only divide our low memory quantum k-collision algorithm into several subroutines, but also need to achieve some balances between these subroutines. The time complexity of our k-collision search algorithm is (O) over tilde (2((2k-2)n/2k+1-3)), and the classical memory and quantum memory complexities are (O) over tilde (2((2k-1-1)n/2k+1-3)) and O(n) respectively. In addition, we propose an efficient k-claw search algorithm, which can output a k-claw with O(n) qubits. Given 2(s) quantum processors, we can construct our quantum k-collision and k-claw parallel algorithm with the time of (O) over tilde (2 ((2k-2)n-(2k+1-2k-1-3)s/2k+1-3)), while the classical memory and quantum memory complexities are (O) over tilde (2 ((2k-1-1)n+s.2k-2/2k+1-3)) and O(n), respectively.
Keywords:
Grover's algorithm
k-collision
post-quantum cryptography
symmetric cryptography
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