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Number-Theoretic Algorithms in Cryptography

2007 Language Arts & Disciplines
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Release : 2007
Genre : Language Arts & Disciplines
Kind : eBook
Book Rating : 900/5 ( reviews)

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Book Synopsis Number-Theoretic Algorithms in Cryptography by : Oleg Nikolaevich Vasilenko

Download or read book Number-Theoretic Algorithms in Cryptography written by Oleg Nikolaevich Vasilenko. This book was released on 2007. Available in PDF, EPUB and Kindle. Book excerpt: Algorithmic number theory is a rapidly developing branch of number theory, which, in addition to its mathematical importance, has substantial applications in computer science and cryptography. Among the algorithms used in cryptography, the following are especially important: algorithms for primality testing; factorization algorithms for integers and for polynomials in one variable; applications of the theory of elliptic curves; algorithms for computation of discrete logarithms; algorithms for solving linear equations over finite fields; and, algorithms for performing arithmetic operations on large integers. The book describes the current state of these and some other algorithms. It also contains extensive bibliography. For this English translation, additional references were prepared and commented on by the author.

Cryptanalysis of Number Theoretic Ciphers

2019-08-22 Mathematics
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Release : 2019-08-22
Genre : Mathematics
Kind : eBook
Book Rating : 693/5 ( reviews)

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Book Synopsis Cryptanalysis of Number Theoretic Ciphers by : Samuel S. Wagstaff, Jr.

Download or read book Cryptanalysis of Number Theoretic Ciphers written by Samuel S. Wagstaff, Jr.. This book was released on 2019-08-22. Available in PDF, EPUB and Kindle. Book excerpt: At the heart of modern cryptographic algorithms lies computational number theory. Whether you're encrypting or decrypting ciphers, a solid background in number theory is essential for success. Written by a number theorist and practicing cryptographer, Cryptanalysis of Number Theoretic Ciphers takes you from basic number theory to the inner workings of ciphers and protocols. First, the book provides the mathematical background needed in cryptography as well as definitions and simple examples from cryptography. It includes summaries of elementary number theory and group theory, as well as common methods of finding or constructing large random primes, factoring large integers, and computing discrete logarithms. Next, it describes a selection of cryptographic algorithms, most of which use number theory. Finally, the book presents methods of attack on the cryptographic algorithms and assesses their effectiveness. For each attack method the author lists the systems it applies to and tells how they may be broken with it. Computational number theorists are some of the most successful cryptanalysts against public key systems. Cryptanalysis of Number Theoretic Ciphers builds a solid foundation in number theory and shows you how to apply it not only when breaking ciphers, but also when designing ones that are difficult to break.

A Handbook of Algorithms in Number Theory

Mathematics
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Genre : Mathematics
Kind : eBook
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Book Synopsis A Handbook of Algorithms in Number Theory by : N.B. Singh

Download or read book A Handbook of Algorithms in Number Theory written by N.B. Singh. This book was released on . Available in PDF, EPUB and Kindle. Book excerpt: "A Handbook of Algorithms in Number Theory" is designed for absolute beginners, providing a comprehensive introduction to the fundamental concepts of number theory and their applications in computer science. This book explores a range of topics, from cryptographic hash functions and primality testing to random number generation and error detection. Through clear, step-by-step descriptions, readers will gain a solid understanding of how number theory underpins modern algorithms and cryptographic protocols, making complex ideas accessible and engaging for those new to the subject.

Number-Theoretic Methods in Cryptology

2018-03-09 Computers
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Release : 2018-03-09
Genre : Computers
Kind : eBook
Book Rating : 201/5 ( reviews)

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Book Synopsis Number-Theoretic Methods in Cryptology by : Jerzy Kaczorowski

Download or read book Number-Theoretic Methods in Cryptology written by Jerzy Kaczorowski. This book was released on 2018-03-09. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed post-conference proceedings of the First International Conference on Number-Theoretic Methods in Cryptology, NuTMiC 2017, held in Warsaw, Poland, in September 2017.The 15 revised full papers presented in this book together with 3 invited talks were carefully reviewed and selected from 32 initial submissions. The papers are organized in topical sections on elliptic curves in cryptography; public-key cryptography; lattices in cryptography; number theory; pseudorandomness; and algebraic structures and analysis.

Cryptographic Applications of Analytic Number Theory

2003-02-12 Computers
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Release : 2003-02-12
Genre : Computers
Kind : eBook
Book Rating : 544/5 ( reviews)

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Book Synopsis Cryptographic Applications of Analytic Number Theory by : Igor Shparlinski

Download or read book Cryptographic Applications of Analytic Number Theory written by Igor Shparlinski. This book was released on 2003-02-12. Available in PDF, EPUB and Kindle. Book excerpt: The book introduces new ways of using analytic number theory in cryptography and related areas, such as complexity theory and pseudorandom number generation. Cryptographers and number theorists will find this book useful. The former can learn about new number theoretic techniques which have proved to be invaluable cryptographic tools, the latter about new challenging areas of applications of their skills.

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