Publication details

A short basis of the Stickelberger ideal of a cyclotomic field



Year of publication 2024
Type Article in Periodical
Magazine / Source Mathematics of Computation
MU Faculty or unit

Faculty of Science

Keywords Cyclotomic fields; Stickelberger ideal; short basis; relative class number
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Description We exhibit an explicit short basis of the Stickelberger ideal of cyclotomic fields of any conductor, i.e., a basis containing only short elements. An element of the group ring Z[G], where G is the Galois group of the field, is said to be short if all of its coefficients in basis G are 0 or 1. As a direct practical consequence, we deduce from this short basis an explicit upper bound on the relative class number that is valid for any conductor. This basis also has several concrete applications, in particular for the cryptanalysis of the Shortest Vector Problem on Ideal Lattices.

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