computational number theory

Topics in Computational Number Theory Inspired by Peter L. Montgomery【電子書籍】Quantum Computational Number Theory【電子書籍】 Song Y. Yan洋書 Paperback, Notes from the International Autumn School on Computational Number Theory (Tutorials, Schools, and Workshops in the Mathematical Sciences)Computational Number Theory and Modern Cryptography【電子書籍】 Song Y. YanNotes from the International Autumn School on Computational Number Theory【電子書籍】
 

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  • <p>Peter L. Montgomery has made significant contributions to computational number theory, introducing many basic tools such as Montgomery multiplication, Montgomery simultaneous inversion, Montgomery curves, and the Montgomery ladder. This book features state-of-the-art research in computational number theory related to Montgomery's work and its impact on computational efficiency and cryptography. Topics cover a wide range of topics such as Montgomery multiplication for both hardware and software implementations; Montgomery curves and twisted Edwards curves as proposed in the latest standards for elliptic curve cryptography; and cryptographic pairings. This book provides a comprehensive overview of integer factorization techniques, including dedicated chapters on polynomial selection, the block Lanczos method, and the FFT extension for algebraic-group factorization algorithms. Graduate students and researchers in applied number theory and cryptography will benefit from this survey...
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    商品の説明

  • <p>This book provides a comprehensive introduction to advanced topics in the computational and algorithmic aspects of number theory, focusing on applications in cryptography. Readers will learn to develop fast algorithms, including quantum algorithms, to solve various classic and modern number theoretic problems. Key problems include prime number generation, primality testing, integer factorization, discrete logarithms, elliptic curve arithmetic, conjecture and numerical verification.</p> <p>The author discusses quantum algorithms for solving the Integer Factorization Problem (IFP), the Discrete Logarithm Problem (DLP), and the Elliptic Curve Discrete Logarithm Problem (ECDLP) and for attacking IFP, DLP and ECDLP based cryptographic systems. Chapters also cover various other quantum algorithms for Pell's equation, principal ideal, unit group, class group, Gauss sums, prime counting function, Riemann's hypothesis and the BSD conjecture.</p> <p><em>Quantum Computational Nu...
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  • *** We ship internationally, so do not use a package forwarding service. We cannot ship to a package forwarding company address because of the Japanese customs regulation. If it is shipped and customs office does not let the package go, we do not make a refund. 【注意事項】 *** 特に注意してください。 *** ・個人ではない法人・団体名義での購入はできません。この場合税関で滅却されてもお客様負担になりますので御了承願います。 ・お名前にカタカナが入っている場合法人である可能性が高いため当店システムから自動保留します。カタカナで記載が必要な場合はカタカナ変わりローマ字で記載してください。 ・お名前またはご住所が法人・団体名義(XX株式会社等)、商店名などを含めている場合、または電話番号が個人のものではない場合、税関から法人名義でみなされますのでご注意ください。 ・転送サービス会社への発送もできません。この場合税関で滅却されてもお客様負担になりますので御了承願います。 *** ・注文後品切れや価格変動でキャンセルされる場合がございますので予めご了承願います。 ・当店でご購入された商品は、原則として、「個...
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  • <p><strong>The only book to provide a unified view of the interplay between computational</strong> <strong>number theory and cryptography</strong></p> <p>Computational number theory and modern cryptography are two of the most important and fundamental research fields in information security. In this book, Song Y. Yang combines knowledge of these two critical fields, providing a unified view of the relationships between computational number theory and cryptography. The author takes an innovative approach, presenting mathematical ideas first, thereupon treating cryptography as an immediate application of the mathematical concepts. The book also presents topics from number theory, which are relevant for applications in public-key cryptography, as well as modern topics, such as coding and lattice based cryptography for post-quantum cryptography. The author further covers the current research and applications for common cryptographic algorithms, describing the mathematical ...
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    商品の説明

  • <p>This volume collects lecture notes and research articles from the International Autumn School on Computational Number Theory, which was held at the Izmir Institute of Technology from October 30th to November 3rd, 2017 in Izmir, Turkey. Written by experts in computational number theory, the chapters cover a variety of the most important aspects of the field. By including timely research and survey articles, the text also helps pave a path to future advancements. Topics include:</p> <ul> <li> <p>Modular forms</p> </li> <li> <p>L-functions</p> </li> <li> <p>The modular symbols algorithm</p> </li> <li> <p>Diophantine equations</p> </li> <li> <p>Nullstellensatz</p> </li> <li> <p>Eisenstein series</p> </li> </ul> <p><em>Notes from the International Autumn School on Computational Number Theory</em> will offer graduate students an invaluable introduction to computational number theory. In addition, it provides the state-of-the...
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