Pollards Number Field Sieve
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| Author | : Arjen K. Lenstra |
| Publisher | : Springer |
| Total Pages | : 138 |
| Release | : 2006-11-15 |
| Genre | : Mathematics |
| ISBN | : 3540478922 |
The number field sieve is an algorithm for finding the prime factors of large integers. It depends on algebraic number theory. Proposed by John Pollard in 1988, the method was used in 1990 to factor the ninth Fermat number, a 155-digit integer. The algorithm is most suited to numbers of a special form, but there is a promising variant that applies in general. This volume contains six research papers that describe the operation of the number field sieve, from both theoretical and practical perspectives. Pollard's original manuscript is included. In addition, there is an annotated bibliography of directly related literature.
| Author | : Alexander Shaumyan |
| Publisher | : |
| Total Pages | : 252 |
| Release | : 1998 |
| Genre | : Algebraic number theory |
| ISBN | : |
The Number Field Sieve has revolutionized the field of computational number theory and enabled researchers to factor very large integers--a task which seemed insurmountable with the best computers and the best factorization techniques that were available a few years earlier. We'll illustrate how the Number Field Sieve works, using various examples of factorizations in different number fields. We'll also see how the method can be extended to factor any integer m, not just a special m which can be written in the form m = r"--S for which the original algorithm was developed. We'll look at the modified version of the Number Field Sieve known as the General Number Field Sieve (GNFS) and look at an example of a number factored with GNFS. But in order to understand the process, we need to introduce the concepts of algebraic number fields and algebraic numbers.
| Author | : Arjen K. Lenstra |
| Publisher | : Springer |
| Total Pages | : 140 |
| Release | : 1993-08-30 |
| Genre | : Mathematics |
| ISBN | : 9783540570134 |
The number field sieve is an algorithm for finding the prime factors of large integers. It depends on algebraic number theory. Proposed by John Pollard in 1988, the method was used in 1990 to factor the ninth Fermat number, a 155-digit integer. The algorithm is most suited to numbers of a special form, but there is a promising variant that applies in general. This volume contains six research papers that describe the operation of the number field sieve, from both theoretical and practical perspectives. Pollard's original manuscript is included. In addition, there is an annotated bibliography of directly related literature.
| Author | : Carl Pomerance |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 188 |
| Release | : 1990 |
| Genre | : Computers |
| ISBN | : 9780821801550 |
In the past dozen or so years, cryptology and computational number theory have become increasingly intertwined. Because the primary cryptologic application of number theory is the apparent intractability of certain computations, these two fields could part in the future and again go their separate ways. But for now, their union is continuing to bring ferment and rapid change in both subjects. This book contains the proceedings of an AMS Short Course in Cryptology and Computational Number Theory, held in August 1989 during the Joint Mathematics Meetings in Boulder, Colorado. These eight papers by six of the top experts in the field will provide readers with a thorough introduction to some of the principal advances in cryptology and computational number theory over the past fifteen years. In addition to an extensive introductory article, the book contains articles on primality testing, discrete logarithms, integer factoring, knapsack cryptosystems, pseudorandom number generators, the theoretical underpinnings of cryptology, and other number theory-based cryptosystems. Requiring only background in elementary number theory, this book is aimed at nonexperts, including graduate students and advanced undergraduates in mathematics and computer science.
| Author | : Arthur T. Benjamin |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 311 |
| Release | : 2020-07-29 |
| Genre | : Mathematics |
| ISBN | : 1470458438 |
| Author | : Richard A. Mollin |
| Publisher | : CRC Press |
| Total Pages | : 424 |
| Release | : 2011-01-05 |
| Genre | : Computers |
| ISBN | : 1439845999 |
Bringing the material up to date to reflect modern applications, this second edition has been completely rewritten and reorganized to incorporate a new style, methodology, and presentation. It offers a more complete and involved treatment of Galois theory, a more comprehensive section on Pollard's cubic factoring algorithm, and more detailed explanations of proofs to provide a sound understanding of challenging material. This edition also studies binary quadratic forms and compares the ideal and form class groups. The text includes convenient cross-referencing, a comprehensive index, and numerous exercises and applications.
| Author | : Lejla Batina |
| Publisher | : Springer Nature |
| Total Pages | : 346 |
| Release | : 2022-12-06 |
| Genre | : Computers |
| ISBN | : 3031228294 |
This book constitutes the refereed proceedings of the 12th International Conference on Security, Privacy, and Applied Cryptography Engineering, SPACE 2022 held in Jaipur, India, during December 9–12, 2022. The 18 full papers included in this book were carefully reviewed and selected from 61 submissions. They were organized in topical sections as follows: symmetric cryptography; public-key cryptography, post-quantum cryptography, zero knowledge proofs; hardware security and AI; and network security, authentication, and privacy.
| Author | : Henri Cohen |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 422 |
| Release | : 1996-08-07 |
| Genre | : Computers |
| ISBN | : 9783540615811 |
This book constitutes the refereed post-conference proceedings of the Second International Algorithmic Number Theory Symposium, ANTS-II, held in Talence, France in May 1996. The 35 revised full papers included in the book were selected from a variety of submissions. They cover a broad spectrum of topics and report state-of-the-art research results in computational number theory and complexity theory. Among the issues addressed are number fields computation, Abelian varieties, factoring algorithms, finite fields, elliptic curves, algorithm complexity, lattice theory, and coding.
| Author | : David Wells |
| Publisher | : Turner Publishing Company |
| Total Pages | : 260 |
| Release | : 2011-01-13 |
| Genre | : Mathematics |
| ISBN | : 1118045718 |
A fascinating journey into the mind-bending world of prime numbers Cicadas of the genus Magicicada appear once every 7, 13, or 17 years. Is it just a coincidence that these are all prime numbers? How do twin primes differ from cousin primes, and what on earth (or in the mind of a mathematician) could be sexy about prime numbers? What did Albert Wilansky find so fascinating about his brother-in-law's phone number? Mathematicians have been asking questions about prime numbers for more than twenty-five centuries, and every answer seems to generate a new rash of questions. In Prime Numbers: The Most Mysterious Figures in Math, you'll meet the world's most gifted mathematicians, from Pythagoras and Euclid to Fermat, Gauss, and Erd?o?s, and you'll discover a host of unique insights and inventive conjectures that have both enlarged our understanding and deepened the mystique of prime numbers. This comprehensive, A-to-Z guide covers everything you ever wanted to know--and much more that you never suspected--about prime numbers, including: * The unproven Riemann hypothesis and the power of the zeta function * The "Primes is in P" algorithm * The sieve of Eratosthenes of Cyrene * Fermat and Fibonacci numbers * The Great Internet Mersenne Prime Search * And much, much more
| Author | : Julian Brown |
| Publisher | : Simon and Schuster |
| Total Pages | : 404 |
| Release | : 2001-08-14 |
| Genre | : Computers |
| ISBN | : 0684870045 |
A Science journalist reveals the existence of the world's first quantum computer--created by a team of Silicon Valley researchers and able to simultaneously compute all possible solutions to a problem, making it the most powerful computer in the world.
