Prime Numbers and Computer Methods for Factorization
Springer Science & Business Media, 23 нояб. 2011 г. - Всего страниц: 464
From the original hard cover edition:
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.
Hans Riesel’s highly successful first edition of this book has now been enlarged and updated with the goal of satisfying the needs of researchers, students, practitioners of cryptography, and non-scientific readers with a mathematical inclination. It includes important advances in computational prime number theory and in factorization as well as re-computed and enlarged tables, accompanied by new tables reflecting current research by both the author and his coworkers and by independent researchers.
The book treats four fundamental problems: the number of primes below a given limit, the approximate number of primes, the recognition of primes and the factorization of large numbers. The author provides explicit algorithms and computer programs, and has attempted to discuss as many of the classically important results as possible, as well as the most recent discoveries. The programs include are written in PASCAL to allow readers to translate the programs into the language of their own computers.
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.
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CHAPTER 2 THE PRIMES VIEWED AT LARGE
CHAPTER 3 SUBTLETIES IN THE DISTRffiUTION OF PRIMES
CHAPTER 4 THE RECOGNITION OF PRIMES
CHAPTER 5 CLASSICAL METHODS OF FACTORIZATION
CHAPTER 6 MODERN FACTORIZATION METHODS
CHAPTER 7 PRIME NUMBERS AND CRYPTOGRAPHY
APPENDIX 1 BASIC CONCEPTS IN HIGHER ALGEBRA
APPENDIX 2 BASIC CONCEPTS IN HIGHER ARITHMETIC
APPENDIX 6 ALGEBRAIC FACTORS
APPENDIX 7 ELLIPTIC CURVES
APPENDIX 8 CONTINUED FRACTIONS
APPENDIX 9 MULTIPLEPRECISION ARITHMETIC
APPENDIX 10 FAST MULTIPLICATION OF LARGE INTEGERS
APPENDIX 11THE STIELTJES INTEGRAL