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

Part of: Algebraic number theory: local and $p$-adic fields

Published online by Cambridge University Press:  01 April 2012

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

Abstract

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

MSC classification

Secondary: 11S05: Polynomials
Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 15 , May 2012 , pp. 44 - 58
Copyright
Copyright © London Mathematical Society 2012

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