  Hidden shift problems are relevant to assess the quantum security of various
cryptographic constructs. Multiple quantum subexponential time algorithms have
been proposed. In this paper, we propose some improvements on a polynomial
quantum memory algorithm proposed by Childs, Jao and Soukharev in 2010. We use
subset-sum algorithms to significantly reduce its complexity. We also propose
new tradeoffs between quantum queries, classical time and classical memory to
solve this problem.

Quantum Physics;Cryptography and Security