The mathematics of public key cryptography /
"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 st...
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| Format: | Book |
| Language: | English |
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Cambridge ; New York :
Cambridge University Press,
2012.
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| Online Access: | Cover image |
Table of 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.