The Eleventh Power Residue Symbol

Journal of Mathematical Cryptology

Joye Marc¹  Lapiha Oleksandra²  Naccache David²  Nguyen Ky² 

[1] Zama, Paris, France;École normale supérieure, Paris, France;

关键词: power residue symbol;    cyclotomic field;    reciprocity law;    cryptography;    11a15;    11r18;    11a05;    11y40;    11t71;   

DOI  :  10.1515/jmc-2020-0077

来源: DOAJ

【 摘 要 】

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

【 授权许可】

Unknown