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Arithmetics pp 35-73 | Cite as

Applications: Algorithms, Primality and Factorization, Codes

Part of the Universitext book series (UTX)

Abstract

This chapter describes some industrial applications of number theory, via computer science. We succinctly describe the main algorithms as well as their theoretical complexity or computation time. We use the notation O(f(n)) to denote a function ≤Cf(n); furthermore, the unimportant—at least from a theoretical point of view—constants which appear will be ignored. In the following sections, we introduce the basics of cryptography and of the “RSA” system, which motivates the study of primality tests and factorization methods. We finish the chapter with an introduction to error-correcting codes, which will lead us into the study of cyclotomic polynomials.

Keywords

Prime Number Linear Code Cyclic Code Minimal Polynomial Irreducible Factor 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag London Limited 2011

Authors and Affiliations

  1. 1.Institut de Mathématiques de JussieuUniversité Paris 7 Denis DiderotParisFrance

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