The mathematics of public key cryptography
By: Steven D. Galbraith
Publisher: Cambridge University Press
Published: 2012
Place of publication: Cambridge; New York
Language: eng
ISBN-13: 9781107013926
Subjects: Mathematics; MATHEMATICS / Discrete Mathematics; Coding theory; Cryptography
Description: "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"--
Notes: Includes bibliographical references and index.
Table of contents: title: Machine generated contents note: Preface; Acknowledgements; Notation; 1. Introduction; Part I. Background: 2. Background mathematics; 3. Basic algorithmic number theory; 4. Hash functions and MACs; Part II. Algebraic Groups: 5. Preliminary remarks on algebraic groups; 6. Varieties; 7. Tori, LUC and XTR; 8. Curves and divisor class groups; 9. Rational maps on curves and divisors; 10. Elliptic curves; 11. Hyperelliptic curves; Part III. Exponentiation, Factoring and Discrete Logarithms: 12. Basic algorithms for algebraic groups; 13. Primality and factoring using algebraic groups; 14. Basic discrete logarithm algorithms; 15. Pseudorandom walks; 16. Subexponential algorithms; Part IV. Lattices: 17. Lattices; 18. Lattice basis reduction; 19. Close and short vectors; 20. Coppersmith's method and related applications; Part V. Cryptography Related to Discrete Logarithms: 21. Diffie-Hellman cryptography; 22. The Diffie-Hellman problem; 23. Digital signatures based on discrete logarithms; 24. Encryption from discrete logarithms; Part VI. Cryptography Related to Integer Factorisation: 25. The RSA and Rabin cryptosystems; Part VII. Advanced Topics in Elliptic and Hyperelliptic Curves: 26. Isogenies of elliptic curves; 27. Pairings on elliptic curves; References; Author index; Subject index.