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

References

SHOWING 1-10 OF 21 REFERENCES
Computational complexity and the classification of finite simple groups
  • L. Babai, W. Kantor, E. Luks
  • Mathematics, Computer Science
  • 24th Annual Symposium on Foundations of Computer Science (sfcs 1983)
  • 1983
Graph Isomorphism in Quasipolynomial Time
  • L. Babai
  • Computer Science, Mathematics
  • ArXiv
  • 2015
Lower Bounds for Discrete Logarithms and Related Problems
  • V. Shoup
  • Mathematics, Computer Science
  • EUROCRYPT
  • 1997
Combinatorial Tools for Computational Group Theory
Computation schemes for splitting fields of polynomials
...
1
2
3
...