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Algebraic Aspects of Cryptography / Edition 1
     

Algebraic Aspects of Cryptography / Edition 1

by Neal Koblitz, Y.-H. Wu, R.J. Zuccherato
 

ISBN-10: 3540634460

ISBN-13: 9783540634461

Pub. Date: 06/24/2004

Publisher: Springer Berlin Heidelberg

From the reviews: "This is a textbook in cryptography with emphasis on algebraic methods. It is supported by many exercises (with answers) making it appropriate for a course in mathematics or computer science. [...] Overall, this is an excellent expository text, and will be very useful to both the student and researcher." Mathematical Reviews

Overview

From the reviews: "This is a textbook in cryptography with emphasis on algebraic methods. It is supported by many exercises (with answers) making it appropriate for a course in mathematics or computer science. [...] Overall, this is an excellent expository text, and will be very useful to both the student and researcher." Mathematical Reviews

Product Details

ISBN-13:
9783540634461
Publisher:
Springer Berlin Heidelberg
Publication date:
06/24/2004
Series:
Algorithms and Computation in Mathematics Series , #3
Edition description:
1st ed. 1998. Corr. 2nd printing 1999. 3rd printing 2004
Pages:
206
Product dimensions:
6.10(w) x 9.25(h) x 0.36(d)

Table of Contents

1. Cryptography.- §1. Early History.- §2. The Idea of Public Key Cryptography.- §3. The RSA Cryptosystem.- §4. Diffie-Hellman and the Digital Signature Algorithm.- §5. Secret Sharing, Coin Flipping, and Time Spent on Homework.- §6. Passwords, Signatures, and Ciphers.- §7. Practical Cryptosystems and Useful Impractical Ones.- Exercises.- 2. Complexity of Computations.- §1. The Big-O Notation.- Exercises.- §2. Length of Numbers.- Exercises.- §3. Time Estimates.- Exercises.- §4. P, NP, and NP-Completeness.- Exercises.- §5. Promise Problems.- §6. Randomized Algorithms and Complexity Classes.- Exercises.- §7. Some Other Complexity Classes.- Exercises.- 3. Algebra.- §1. Fields.- Exercises.- §2. Finite Fields.- Exercises.- §3. The Euclidean Algorithm for Polynomials.- Exercises.- §4. Polynomial Rings.- Exercises.- §5. Gröbner Bases.- Exercises.- 4. Hidden Monomial Cryptosystems.- § 1. The Imai-Matsumoto System.- Exercises.- §2. Patarin’s Little Dragon.- Exercises.- §3. Systems That Might Be More Secure.- Exercises.- 5. Combinatorial-Algebraic Cryptosystems.- §1. History.- §2. Irrelevance of Brassard’s Theorem.- Exercises.- §3. Concrete Combinatorial-Algebraic Systems.- Exercises.- §4. The Basic Computational Algebra Problem.- Exercises.- §5. Cryptographic Version of Ideal Membership.- §6. Linear Algebra Attacks.- §7. Designing a Secure System.- 6. Elliptic and Hyperelliptic Cryptosystems.- § 1. Elliptic Curves.- Exercises.- §2. Elliptic Curve Cryptosystems.- Exercises.- §3. Elliptic Curve Analogues of Classical Number Theory Problems.- Exercises.- §4. Cultural Background: Conjectures on Elliptic Curves and Surprising Relations with Other Problems.- §5. Hyperelliptic Curves.- Exercises.- §6. Hyperelliptic Cryptosystems.- Exercises.- §1. Basic Definitions and Properties.- §2. Polynomial and Rational Functions.- §3. Zeros and Poles.- §4. Divisors.- §5. Representing Semi-Reduced Divisors.- §6. Reduced Divisors.- §7. Adding Reduced Divisors.- Exercises.- Answers to Exercises.

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