In this paper, we describe a new, generic algorithm to compute primary elements in cyclotomic fields; which we apply for $p=3,5,7,11,13$. A key insight is a careful selection of fundamental units as put forward by Dénes.
This solves an essential step in the Caranay--Scheidler algorithm. We give a unified view of the problem. Finally, we provide the first efficient deterministic algorithm for the computation of the 9-th and 16-th power residue symbols.
Category / Keywords: foundations / Primarity, Cyclotomic field, Power residue symbol, Cryptography Date: received 28 Aug 2021, last revised 28 Aug 2021 Contact author: david naccache at ens fr Available format(s): PDF | BibTeX Citation Version: 20210831:132445 (All versions of this report) Short URL: ia.cr/2021/1106