Roots of unity in orders
Commutative Algebra
2016-03-14 v4 Cryptography and Security
Number Theory
Abstract
We give deterministic polynomial-time algorithms that, given an order, compute the primitive idempotents and determine a set of generators for the group of roots of unity in the order. Also, we show that the discrete logarithm problem in the group of roots of unity can be solved in polynomial time. As an auxiliary result, we solve the discrete logarithm problem for certain unit groups in finite rings. Our techniques, which are taken from commutative algebra, may have further potential in the context of cryptology and computer algebra.
Cite
@article{arxiv.1509.02612,
title = {Roots of unity in orders},
author = {H. W. Lenstra and A. Silverberg},
journal= {arXiv preprint arXiv:1509.02612},
year = {2016}
}
Comments
The numbering of the results has been changed to agree with the published version