# Baby-step giant-step algorithms for the symmetric group

@article{Bach2018BabystepGA, title={Baby-step giant-step algorithms for the symmetric group}, author={E. Bach and Bryce Sandlund}, journal={J. Symb. Comput.}, year={2018}, volume={85}, pages={55-71} }

Abstract We study discrete logarithms in the setting of group actions. Suppose that G is a group that acts on a set S . When r , s ∈ S , a solution g ∈ G to r g = s can be thought of as a kind of logarithm. In this paper, we study the case where G = S n and develop analogs to Shanks' baby-step / giant-step procedure for ordinary discrete logarithms. Specifically, we compute two sets A , B ⊆ S n such that every permutation of S n can be written as a product ab of elements a ∈ A and b ∈ B . Our… Expand

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