Galbraith, Steven D.
Cambridge New York : Cambridge University Press, 2012.
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Notes:
- 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.
- Includes bibliographical references (p. 579-602) and indexes.
- 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 algorithms — Part IV. Lattices: 16. Lattices 17. Lattice basis reduction 18. Algorithms for the closet 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.
Subjects:
Requested by Haines, M