Applications: Algorithms, Primality and Factorization, Codes
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.
KeywordsPrime Number Linear Code Cyclic Code Minimal Polynomial Irreducible Factor
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