Mathematics Of Public Key Cryptography Steven Galbraith Pdf To Word

Steven D Galbraith

Galbraith, Steven D. Mathematics of public key cryptography / Steven D. Includes bibliographical references and index. ISBN 978-1-107-01392-6 (hardback) 1. Coding theory. Cryptography – Mathematics. QA268.G35 2012 003.54 – dc606 ISBN 978-1-107-01392-6 Hardback Additional resources for this.

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Steven D Galbraith

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.
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