The Eleventh Power Residue Symbol

Journal of mathematical cryptology

article

Marc Joye¹  Oleksandra Lapiha²  Ky Nguyen²  David Naccache² 

[1] Zama;École normale supérieure

关键词: Power residue symbol;    Cyclotomic field;    Reciprocity law;    Cryptography;   

DOI  :  10.1515/jmc-2020-0077

学科分类：社会科学、人文和艺术（综合）

来源: De Gruyter

【 摘 要 】

This paper presents an efficient algorithm for computing 11 th -power residue symbols in the cyclo-tomic field ℚ(ζ11),$ \mathbb{Q}\left( {{\zeta }_{11}} \right), $where 11 is a primitive 11 th root of unity. It extends an earlier algorithm due to Caranay and Scheidler (Int. J. Number Theory, 2010) for the 7 th -power residue symbol. The new algorithm finds applications in the implementation of certain cryptographic schemes.

【 授权许可】

CC BY|CC BY-NC-ND