Prime numbers and computer methods for factorization
著者
書誌事項
Prime numbers and computer methods for factorization
（Progress in mathematics, vol. 126）
Birkhäuser, c1994
2nd ed
- : us
- : sz
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注記
Includes list of textbooks for further reading (p. 457) and index
内容説明・目次
- 巻冊次
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: us ISBN 9780817637439
内容説明
In the modern age of almost universal computer usage, practically every individual in a technologically developed society has routine access to the most up-to-date cryptographic technology that exists, the so-called RSA public-key cryptosystem. A major component of this system is the factorization of large numbers into their primes. Thus an ancient number-theory concept now plays a crucial role in communication among millions of people who may have little or no knowledge of even elementary mathematics. The independent structure of each chapter of the book makes it highly readable for a wide variety of mathematicians, students of applied number theory, and others interested in both study and research in number theory and cryptography.
目次
Preface.-The Number of Primes Below a Given Limit.-The Primes Viewed at Large.-Subtleties in the Distribution of Primes.-The Recognition of Primes.-Classical Methods of Factorization.-Modern Factorization Methods.-Prime Numbers and Cryptography.-Appendix 1. Basic Concepts in Higher Algebra.-Appendix 2. Basic concepts in Higher Arithmetic.-Appendix 3. Quadratic Residues.-Appendix 4. The Arithmetic of Quadratic Fields.-Appendix 5. Higher Algebraic Number Fields.-Appendix 6. Algebraic Factors.-Appendix 7. Elliptic Curves.-Appendix 8. Continued Fractions.-Appendix 9. Multiple-Precision Arithmetic.-Appendix 10. Fast Multiplication of Large Integers.-Appendix 11. The Stieltjes Integral.-Tables.-List of Textbooks.-Index.
- 巻冊次
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: sz ISBN 9783764337438
内容説明
This edition has been updated to include advances in computational prime number theory and in factorization, as well as re-computed and enlarged tables, accompanied by new tables reflecting research by both the author and his co-workers, and by independent researchers. The book treats four fundamental problems: the number of primes below a given limit; the approximation of primes; the recognition of primes; and the factorization of large numbers. The author provides explicit algorithms and computer programs, which are written in PASCAL in order to allow the reader to translate the programs into the language of their own computers.
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