Improved quantum algorithm for the random subset sum problem
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We propose a quantum algorithm for solving random subset sum instances which play a crucial role in cryptographic constructions. In 2013, Bernstein, Jeffery, Lange and Meurer constructed a quantum subset sum algorithm with heuristic time complexity 2^0.241n, by enhancing the classical random subset sum algorithm of Howgrave-Graham and Joux with a quantum walk technique. In 2018, Helm and May improved heuristic running time and memory to 2^0.226n by quantizing the classical Becker, Coron and Joux algorithm. In our paper, we get a new quantum algorithm with running time down to O(2^0.209n) for all but a negligible fraction of random subset sum instances by combining the classical sampling and quantum walks.
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