Journal of Mathematical Cryptology (Nov 2020)

The Eleventh Power Residue Symbol

  • Joye Marc,
  • Lapiha Oleksandra,
  • Nguyen Ky,
  • Naccache David

DOI
https://doi.org/10.1515/jmc-2020-0077
Journal volume & issue
Vol. 15, no. 1
pp. 111 – 122

Abstract

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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.

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