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Mathematics of Public Key Cryptography - Steven D. Galbraith

Mathematics of Public Key Cryptography

Buch | Hardcover
630 Seiten
2012
Cambridge University Press (Verlag)
978-1-107-01392-6 (ISBN)
CHF 99,45 inkl. MwSt
Public key cryptography is a major interdisciplinary subject with many real-world applications. This book has been carefully written to communicate the major ideas and techniques in this subject to a wide readership. With numerous examples and exercises, it is suitable as a textbook for an advanced course or for self-study.
Public key cryptography is a major interdisciplinary subject with many real-world applications, such as digital signatures. A strong background in the mathematics underlying public key cryptography is essential for a deep understanding of the subject, and this book provides exactly that for students and researchers in mathematics, computer science and electrical engineering. Carefully written to communicate the major ideas and techniques of public key cryptography to a wide readership, this text is enlivened throughout with historical remarks and insightful perspectives on the development of the subject. Numerous examples, proofs and exercises make it suitable as a textbook for an advanced course, as well as for self-study. For more experienced researchers it serves as a convenient reference for many important topics: the Pollard algorithms, Maurer reduction, isogenies, algebraic tori, hyperelliptic curves and many more.

Steven D. Galbraith is a leading international authority on the mathematics of public key cryptography. He is an Associate Professor in the Department of Mathematics at the University of Auckland.

Preface; Acknowledgements; 1. Introduction; Part I. Background: 2. Basic algorithmic number theory; 3. Hash functions and MACs; Part II. Algebraic Groups: 4. Preliminary remarks on algebraic groups; 5. Varieties; 6. Tori, LUC and XTR; 7. Curves and divisor class groups; 8. Rational maps on curves and divisors; 9. Elliptic curves; 10. Hyperelliptic curves; Part III. Exponentiation, Factoring and Discrete Logarithms: 11. Basic algorithms for algebraic groups; 12. Primality testing and integer factorisation using algebraic groups; 13. Basic discrete logarithm algorithms; 14. Factoring and discrete logarithms using pseudorandom walks; 15. Factoring and discrete logarithms in subexponential time; Part IV. Lattices: 16. Lattices; 17. Lattice basis reduction; 18. Algorithms for the closest and shortest vector problems; 19. Coppersmith's method and related applications; Part V. Cryptography Related to Discrete Logarithms: 20. The Diffie–Hellman problem and cryptographic applications; 21. The Diffie–Hellman problem; 22. Digital signatures based on discrete logarithms; 23. Public key encryption based on discrete logarithms; Part VI. Cryptography Related to Integer Factorisation: 24. The RSA and Rabin cryptosystems; Part VII. Advanced Topics in Elliptic and Hyperelliptic Curves: 25. Isogenies of elliptic curves; 26. Pairings on elliptic curves; Appendix A. Background mathematics; References; Author index; Subject index.

Erscheint lt. Verlag 15.3.2012
Zusatzinfo Worked examples or Exercises; 11 Line drawings, unspecified
Verlagsort Cambridge
Sprache englisch
Maße 178 x 254 mm
Gewicht 1280 g
Themenwelt Informatik Theorie / Studium Algorithmen
Informatik Theorie / Studium Kryptologie
Mathematik / Informatik Mathematik Angewandte Mathematik
ISBN-10 1-107-01392-5 / 1107013925
ISBN-13 978-1-107-01392-6 / 9781107013926
Zustand Neuware
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