Abstract

Algorithmic (or computational) number theory is mainly concerned with computer algorithms (sometimes also including computer architectures), in particular efficient algorithms, for solving different sorts of problems in number theory. Primality testing, integer factorization and discrete logarithms are, amongst many others, the most interesting, difficult and useful problems in number theory. In this chapter, we shall study the algorithmic aspects of number theory, and more specifically, we shall introduce various algorithms for solving these three types of number-theoretic problems.

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