2 research outputs found
Baby-Step Giant-Step Algorithms for the Symmetric Group
We study discrete logarithms in the setting of group actions. Suppose that
is a group that acts on a set . When , a solution
to can be thought of as a kind of logarithm. In this paper, we study
the case where , and develop analogs to the Shanks baby-step /
giant-step procedure for ordinary discrete logarithms. Specifically, we compute
two sets such that every permutation of can be
written as a product of elements and . Our
deterministic procedure is optimal up to constant factors, in the sense that
and can be computed in optimal asymptotic complexity, and and
are a small constant from in size. We also analyze randomized
"collision" algorithms for the same problem
Computation Schemes for Splitting Fields of Polynomials
International audienceIn this article, we present new results about the computation of a general shape of a triangular basis generating the splitting ideal of an irreducible polynomial given with the permutation representation of its Galois group G. We provide some theoretical results and a new general algorithm based on the study of the non redundant bases of permutation groups. These new results deeply increase the efficiency of the computation of the splitting field of a polynomial