LMS Journal of Computation and Mathematics

Table of Contents - Volume 15 - 2012  

Research Article

On modular inverses of cyclotomic polynomials and the magnitude of their coefficients

Clément Dunanda1

a1 Institut de recherche mathématique de Rennes, Université de Rennes 1, Campus de Beaulieu F-35042 Rennes Cedex, France (email: clement.dunand@wanadoo.fr)

Abstract

Let p and r be two primes, and let n and m be two distinct divisors of pr. Consider Φ n and Φ m , the nth and mth cyclotomic polynomials. In this paper, we present lower and upper bounds for the coefficients of the inverse of Φ n modulo Φ m and discuss an application to torus-based cryptography.

(Received November 10 2009)

(Revised July 06 2011)

(Online publication April 2012)

2010 Mathematics subject classification

  • 11S05 (primary)