Algorithmic Number Theory: Lattices, Number Fields, Curves and Cryptography (Mathematical Sciences Research Institute Publications)

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9780521808545: Algorithmic Number Theory: Lattices, Number Fields, Curves and Cryptography (Mathematical Sciences Research Institute Publications)
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Number theory is one of the oldest and most appealing areas of mathematics. Computation has always played a role in number theory, a role which has increased dramatically in the last 20 or 30 years, both because of the advent of modern computers, and because of the discovery of surprising and powerful algorithms. As a consequence, algorithmic number theory has gradually emerged as an important and distinct field with connections to computer science and cryptography as well as other areas of mathematics. This text provides a comprehensive introduction to algorithmic number theory for beginning graduate students, written by the leading experts in the field. It includes several articles that cover the essential topics in this area, and in addition, there are contributions pointing in broader directions, including cryptography, computational class field theory, zeta functions and L-series, discrete logarithm algorithms, and quantum computing.

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Book Description:

This comprehensive 2008 introduction for beginning graduate students contains articles by the leading experts in the field. It covers basic topics such as algorithmic aspects of number fields, elliptic curves, and lattice basis reduction and advanced topics including cryptography, computational class field theory, zeta functions and L-series, and quantum computing.

About the Author:

Peter Stevenhagen obtained his PhD from the University of California at Berkeley in 1988. He was charge de recherche in the CNRS in Besanšon, France before forming a small number theory group at the University of Amsterdam. Since 1993, he is the organizer of the biweekly Intercity Number Theory Seminar, the Dutch national platform for research in number theory. In 2000 he was appointed at Leiden University, the oldest university in the Netherlands, which was founded in 1575. Besides his research papers, his bibliography counts various papers in number theory of popularizing and historical nature. He is a member of the board of the Dutch Mathematical Society, the Wiskundig Genootschap.

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