The Eleventh Power Residue Symbol

Abstract

Abstract 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.