{"product_id":"computational-number-theory-and-modern-cryptography-isbn-9781118188583","title":"Computational Number Theory and Modern Cryptography","description":"\u003cb\u003eThe only book to provide a unified view of the interplay between computational\u003c\/b\u003e \u003cb\u003enumber theory and cryptography\u003c\/b\u003e  \u003cp\u003eComputational 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 problems behind these applications in a manner accessible to computer scientists and engineers. \u003c\/p\u003e \u003cul\u003e \u003cli\u003eMakes mathematical problems accessible to computer scientists and engineers by showing their immediate application\u003c\/li\u003e \u003cli\u003ePresents topics from number theory relevant for public-key cryptography applications\u003c\/li\u003e \u003cli\u003eCovers modern topics such as coding and lattice based cryptography for post-quantum cryptography\u003c\/li\u003e \u003cli\u003eStarts with the basics, then goes into applications and areas of active research\u003c\/li\u003e \u003cli\u003eGeared at a global audience; classroom tested in North America, Europe, and Asia\u003c\/li\u003e \u003cli\u003eIncudes exercises in every chapter\u003c\/li\u003e \u003cli\u003eInstructor resources available on the book’s Companion Website \u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003e\u003ci\u003eComputational Number Theory and Modern Cryptography\u003c\/i\u003e is ideal for  graduate and advanced undergraduate students in computer science, communications engineering, cryptography and mathematics. Computer scientists, practicing cryptographers, and other professionals involved in various security schemes will also find this book to be a helpful reference. \u003c\/p\u003e \u003cp\u003eAbout the Author ix\u003c\/p\u003e \u003cp\u003ePreface xi\u003c\/p\u003e \u003cp\u003eAcknowledgments xiii\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart I Preliminaries\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Introduction 3\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 What is Number Theory? 3\u003c\/p\u003e \u003cp\u003e1.2 What is Computation Theory? 9\u003c\/p\u003e \u003cp\u003e1.3 What is Computational Number Theory? 15\u003c\/p\u003e \u003cp\u003e1.4 What is Modern Cryptography? 29\u003c\/p\u003e \u003cp\u003e1.5 Bibliographic Notes and Further Reading 32\u003c\/p\u003e \u003cp\u003eReferences 32\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Fundamentals 35\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Basic Algebraic Structures 35\u003c\/p\u003e \u003cp\u003e2.2 Divisibility Theory 46\u003c\/p\u003e \u003cp\u003e2.3 Arithmetic Functions 75\u003c\/p\u003e \u003cp\u003e2.4 Congruence Theory 89\u003c\/p\u003e \u003cp\u003e2.5 Primitive Roots 131\u003c\/p\u003e \u003cp\u003e2.6 Elliptic Curves 141\u003c\/p\u003e \u003cp\u003e2.7 Bibliographic Notes and Further Reading 154\u003c\/p\u003e \u003cp\u003eReferences 155\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart II Computational Number Theory\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Primality Testing 159\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Basic Tests 159\u003c\/p\u003e \u003cp\u003e3.2 Miller–Rabin Test 168\u003c\/p\u003e \u003cp\u003e3.3 Elliptic Curve Tests 173\u003c\/p\u003e \u003cp\u003e3.4 AKS Test 178\u003c\/p\u003e \u003cp\u003e3.5 Bibliographic Notes and Further Reading 187\u003c\/p\u003e \u003cp\u003eReferences 188\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Integer Factorization 191\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Basic Concepts 191\u003c\/p\u003e \u003cp\u003e4.2 Trial Divisions Factoring 194\u003c\/p\u003e \u003cp\u003e4.3 \u003ci\u003eρ \u003c\/i\u003eand \u003ci\u003ep \u003c\/i\u003e− 1 Methods 198\u003c\/p\u003e \u003cp\u003e4.4 Elliptic Curve Method 205\u003c\/p\u003e \u003cp\u003e4.5 Continued Fraction Method 209\u003c\/p\u003e \u003cp\u003e4.6 Quadratic Sieve 214\u003c\/p\u003e \u003cp\u003e4.7 Number Field Sieve 219\u003c\/p\u003e \u003cp\u003e4.8 Bibliographic Notes and Further Reading 231\u003c\/p\u003e \u003cp\u003eReferences 232\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Discrete Logarithms 235\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Basic Concepts 235\u003c\/p\u003e \u003cp\u003e5.2 Baby-Step Giant-Step Method 237\u003c\/p\u003e \u003cp\u003e5.3 Pohlig–Hellman Method 240\u003c\/p\u003e \u003cp\u003e5.4 Index Calculus 246\u003c\/p\u003e \u003cp\u003e5.5 Elliptic Curve Discrete Logarithms 251\u003c\/p\u003e \u003cp\u003e5.6 Bibliographic Notes and Further Reading 260\u003c\/p\u003e \u003cp\u003eReferences 261\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart III Modern Cryptography\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Secret-Key Cryptography 265\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Cryptography and Cryptanalysis 265\u003c\/p\u003e \u003cp\u003e6.2 Classic Secret-Key Cryptography 277\u003c\/p\u003e \u003cp\u003e6.3 Modern Secret-Key Cryptography 285\u003c\/p\u003e \u003cp\u003e6.4 Bibliographic Notes and Further Reading 291\u003c\/p\u003e \u003cp\u003eReferences 291\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Integer Factorization Based Cryptography 293\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 RSA Cryptography 293\u003c\/p\u003e \u003cp\u003e7.2 Cryptanalysis of RSA 302\u003c\/p\u003e \u003cp\u003e7.3 Rabin Cryptography 319\u003c\/p\u003e \u003cp\u003e7.4 Residuosity Based Cryptography 326\u003c\/p\u003e \u003cp\u003e7.5 Zero-Knowledge Proof 331\u003c\/p\u003e \u003cp\u003e7.6 Bibliographic Notes and Further Reading 335\u003c\/p\u003e \u003cp\u003eReferences 335\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Discrete Logarithm Based Cryptography 337\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Diffie–Hellman–Merkle Key-Exchange Protocol 337\u003c\/p\u003e \u003cp\u003e8.2 ElGamal Cryptography 342\u003c\/p\u003e \u003cp\u003e8.3 Massey–Omura Cryptography 344\u003c\/p\u003e \u003cp\u003e8.4 DLP-Based Digital Signatures 348\u003c\/p\u003e \u003cp\u003e8.5 Bibliographic Notes and Further Reading 351\u003c\/p\u003e \u003cp\u003eReferences 351\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Elliptic Curve Discrete Logarithm Based Cryptography 353\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Basic Ideas 353\u003c\/p\u003e \u003cp\u003e9.2 Elliptic Curve Diffie–Hellman–Merkle Key Exchange Scheme 356\u003c\/p\u003e \u003cp\u003e9.3 Elliptic Curve Massey–Omura Cryptography 360\u003c\/p\u003e \u003cp\u003e9.4 Elliptic Curve ElGamal Cryptography 365\u003c\/p\u003e \u003cp\u003e9.5 Elliptic Curve RSA Cryptosystem 370\u003c\/p\u003e \u003cp\u003e9.6 Menezes–Vanstone Elliptic Curve Cryptography 371\u003c\/p\u003e \u003cp\u003e9.7 Elliptic Curve DSA 373\u003c\/p\u003e \u003cp\u003e9.8 Bibliographic Notes and Further Reading 374\u003c\/p\u003e \u003cp\u003eReferences 375\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart IV Quantum Resistant Cryptography\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Quantum Computational Number Theory 379\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Quantum Algorithms for Order Finding 379\u003c\/p\u003e \u003cp\u003e10.2 Quantum Algorithms for Integer Factorization 385\u003c\/p\u003e \u003cp\u003e10.3 Quantum Algorithms for Discrete Logarithms 390\u003c\/p\u003e \u003cp\u003e10.4 Quantum Algorithms for Elliptic Curve Discrete Logarithms 393\u003c\/p\u003e \u003cp\u003e10.5 Bibliographic Notes and Further Reading 397\u003c\/p\u003e \u003cp\u003eReferences 397\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Quantum Resistant Cryptography 401\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 Coding-Based Cryptography 401\u003c\/p\u003e \u003cp\u003e11.2 Lattice-Based Cryptography 403\u003c\/p\u003e \u003cp\u003e11.3 Quantum Cryptography 404\u003c\/p\u003e \u003cp\u003e11.4 DNA Biological Cryptography 406\u003c\/p\u003e \u003cp\u003e11.5 Bibliographic Notes and Further Reading 409\u003c\/p\u003e \u003cp\u003eReferences 410\u003c\/p\u003e \u003cp\u003eIndex 413\u003c\/p\u003e  \u003cp\u003e\u003cb\u003eSong Y. Yan\u003c\/b\u003e, \u003ci\u003eNorth China University of Technology, P.R. China and Harvard University, USA\u003c\/i\u003e   \u003c\/p\u003e\u003cp\u003e\u003cb\u003eComputational Number Theory and Modern Cryptography\u003c\/b\u003e \u003c\/p\u003e\u003cp\u003eComputational number theory and modern cryptography are two of the most important and fundamental research fields in information security. In this book, Song Y. Yan 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 problems behind these applications in a manner accessible to computer scientists and engineers. \u003c\/p\u003e\u003cul\u003e \u003cli\u003eMakes mathematical problems accessible to computer scientists and engineers by showing their immediate application\u003c\/li\u003e \u003cli\u003ePresents topics from number theory relevant for public-key cryptography applications\u003c\/li\u003e \u003cli\u003eCovers modern topics such as coding and lattice based cryptography for postquantum cryptography\u003c\/li\u003e \u003cli\u003eStarts with the basics, then goes into applications and areas of active research\u003c\/li\u003e \u003cli\u003eGeared at a global audience; classroom tested in North America, Europe, and Asia\u003c\/li\u003e \u003cli\u003eIncludes exercises in every chapter\u003c\/li\u003e \u003cli\u003eInstructor resources available on the book's Companion Website\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003e\u003ci\u003eComputational Number Theory and Modern Cryptography\u003c\/i\u003e is ideal for graduate and advanced undergraduate students in computer science, communications engineering, cryptography and mathematics. Computer scientists, practicing cryptographers, and other professionals involved in various security schemes will also find this book to be a helpful reference.\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47988967145701,"sku":"NP9781118188583","price":116.95,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9781118188583.jpg?v=1761782245","url":"https:\/\/k12savings.com\/products\/computational-number-theory-and-modern-cryptography-isbn-9781118188583","provider":"K12savings","version":"1.0","type":"link"}