Mathematics of public key cryptography / Steven D. Galbraith.

Author/creator Galbraith, Steven D.
Format Book
Publication InfoCambridge ; New York : Cambridge University Press, 2012.
Descriptionxiv, 615 pages : illustrations ; 26 cm
Subjects
Coding theory.
Cryptography--Mathematics.

Contents 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.
Abstract "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"-- Provided by publisher.
Bibliography noteIncludes bibliographical references and index.
LCCN 2011042606
ISBN9781107013926 (hardback)
ISBN1107013925 (hardback)

Availability

Library Location Call Number Status Item Actions
Joyner General Stacks QA268 .G35 2012 ✔ Available Place Hold