1207.4537 (Mirmojtaba Gharibi)

Reduction from non-injective hidden shift problem to injective hidden
shift problem    [PDF]

Mirmojtaba Gharibi

We introduce a simple tool that can be used to reduce non-injective instances of the hidden shift problem over arbitrary group to injective instances over the same group. In particular, we show that the average-case non-injective hidden shift problem admit this reduction. We show similar results for (non-injective) hidden shift problem for bent functions. In particular, these results can be used to simplify the main results by Gavinsky, Roetteler, and Roland about the hidden shift problem for the Boolean-valued functions and bent functions, and also to generalize their results to non-Boolean domains (thereby answering an open question that they pose).

View original: http://arxiv.org/abs/1207.4537