Computational introduction to number theory and algebra

Includes index

Includes bibliography (p. 566-571) and references

1.Basic properties of the integers 2.Congruences 3.Computing with large integers 4.Euclid's algorithm 5.The distribution of primes 6.Abelian groups 7.Rings 8.Finite and discrete probability distributions 9.Probabilistic algorithms 10.Probabilistic primality testing 11.Finding generators and discrete logarithms in Z[subscript p][superscript *] 12.Quadratic reciprocity and computing modular square roots 13.Modules and vector spaces 14.Matrices 15.Subexponential-time discrete logarithms and factoring 16.More rings 17.Polynomial arithmetic and applications 18.Linearly generated sequences and applications 19.Finite fields 20.Algorithms for finite fields 21.Deterministic primality testing

Number theory and algebra play an increasingly significant role in computing and communications, as evidenced by the striking applications of these subjects to such fields as cryptography and coding theory. This introductory book emphasizes algorithms and applications, such as cryptography and error correcting codes. The presentation alternates between theory and applications in order to motivate and illustrate the mathematics. The mathematical coverage includes the basics of number theory, abstract algebra and discrete probability theory.