Primality and Cryptography
Author:
Publisher: Springer-Verlag
Published: 2013-08-13
Total Pages: 250
ISBN-13: 332296647X
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Primality Testing and Integer Factorization in Public-Key Cryptography
Author: Song Y. Yan
Publisher: Springer Science & Business Media
Published: 2013-06-29
Total Pages: 249
ISBN-13: 1475738161
DOWNLOAD EBOOKPrimality Testing and Integer Factorization in Public-Key Cryptography introduces various algorithms for primality testing and integer factorization, with their applications in public-key cryptography and information security. More specifically, this book explores basic concepts and results in number theory in Chapter 1. Chapter 2 discusses various algorithms for primality testing and prime number generation, with an emphasis on the Miller-Rabin probabilistic test, the Goldwasser-Kilian and Atkin-Morain elliptic curve tests, and the Agrawal-Kayal-Saxena deterministic test for primality. Chapter 3 introduces various algorithms, particularly the Elliptic Curve Method (ECM), the Quadratic Sieve (QS) and the Number Field Sieve (NFS) for integer factorization. This chapter also discusses some other computational problems that are related to factoring, such as the square root problem, the discrete logarithm problem and the quadratic residuosity problem.
Primality and Cryptography
Author: Evangelos Kranakis
Publisher:
Published: 1985
Total Pages: 0
ISBN-13:
DOWNLOAD EBOOKPrimality Testing in Polynomial Time
Author: Martin Dietzfelbinger
Publisher: Springer Science & Business Media
Published: 2004-06-29
Total Pages: 153
ISBN-13: 3540403442
DOWNLOAD EBOOKA self-contained treatment of theoretically and practically important efficient algorithms for the primality problem. The text covers the randomized algorithms by Solovay-Strassen and Miller-Rabin from the late 1970s as well as the recent deterministic algorithm of Agrawal, Kayal and Saxena. The volume is written for students of computer science, in particular those with a special interest in cryptology, and students of mathematics, and it may be used as a supplement for courses or for self-study.
1992 Census of Wholesale Trade
Author:
Publisher:
Published: 1994
Total Pages: 104
ISBN-13:
DOWNLOAD EBOOKPrimality and Cryptography
Author: Evangelos Kranakis
Publisher: Wiley
Published: 1991-01-08
Total Pages: 278
ISBN-13: 9780471909347
DOWNLOAD EBOOKA comprehensive account of recent algorithms developed in computational number theory and primality testing. Provides a general framework for the theoretical study of public key cryptography and pseudorandom generators. Unique in its approach, the book will be a valuable addition to computer literature.
Prime Numbers and Computer Methods for Factorization
Author: Hans Riesel
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 481
ISBN-13: 1461202515
DOWNLOAD EBOOKIn 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.
Primality Testing in Polynomial Time: from Randomized Algorithms to Primes Is in P
Author: M. Dietzfelbinger
Publisher:
Published: 2004
Total Pages: 147
ISBN-13: 9781280307959
DOWNLOAD EBOOKThis book is devoted to algorithms for the venerable primality problem: Given a natural number n, decide whether it is prime or composite. The problem is basic in number theory, efficient algorithms that solve it, i.e., algorithms that run in a number of computational steps which is polynomial in the number of digits needed to write n, are important for theoretical computer science and for applications in algorithmics and cryptology. This book gives a self-contained account of theoretically and practically important efficient algorithms for the primality problem, covering the randomized algorithms by Solovay-Strassen and Miller-Rabin from the late 1970s as well as the recent deterministic algorithm of Agrawal, Kayal, and Saxena. The textbook is written for students of computer science, in particular for those with a special interest in cryptology, and students of mathematics, and it may be used as a supplement for courses or for self-study.
Prime Numbers
Author: Richard Crandall
Publisher: Springer Science & Business Media
Published: 2006-04-07
Total Pages: 597
ISBN-13: 0387289798
DOWNLOAD EBOOKBridges the gap between theoretical and computational aspects of prime numbers Exercise sections are a goldmine of interesting examples, pointers to the literature and potential research projects Authors are well-known and highly-regarded in the field
Primality Testing for Beginners
Author: Lasse Rempe-Gillen
Publisher: American Mathematical Soc.
Published: 2013-12-11
Total Pages: 258
ISBN-13: 0821898833
DOWNLOAD EBOOKHow can you tell whether a number is prime? What if the number has hundreds or thousands of digits? This question may seem abstract or irrelevant, but in fact, primality tests are performed every time we make a secure online transaction. In 2002, Agrawal, Kayal, and Saxena answered a long-standing open question in this context by presenting a deterministic test (the AKS algorithm) with polynomial running time that checks whether a number is prime or not. What is more, their methods are essentially elementary, providing us with a unique opportunity to give a complete explanation of a current mathematical breakthrough to a wide audience. Rempe-Gillen and Waldecker introduce the aspects of number theory, algorithm theory, and cryptography that are relevant for the AKS algorithm and explain in detail why and how this test works. This book is specifically designed to make the reader familiar with the background that is necessary to appreciate the AKS algorithm and begins at a level that is suitable for secondary school students, teachers, and interested amateurs. Throughout the book, the reader becomes involved in the topic by means of numerous exercises.
