Author | Koblitz, Neal. author |
---|---|
Title | Algebraic Aspects of Cryptography [electronic resource] / by Neal Koblitz |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1998 |
Connect to | http://dx.doi.org/10.1007/978-3-662-03642-6 |
Descript | IX, 206 p. online resource |
1. Cryptography -- ยง1. Early History -- ยง2. The Idea of Public Key Cryptography -- ยง3. The RSA Cryptosystem -- ยง4. Diffie-Hellman and the Digital Signature Algorithm -- ยง5. Secret Sharing, Coin Flipping, and Time Spent on Homework -- ยง6. Passwords, Signatures, and Ciphers -- ยง7. Practical Cryptosystems and Useful Impractical Ones -- 2. Complexity of Computations -- ยง1. The Big-O Notation -- ยง2. Length of Numbers -- ยง3. Time Estimates -- ยง4. P, NP, and NP-Completeness -- ยง5. Promise Problems -- ยง6. Randomized Algorithms and Complexity Classes -- ยง7. Some Other Complexity Classes -- 3. Algebra -- ยง1. Fields -- ยง2. Finite Fields -- ยง3. The Euclidean Algorithm for Polynomials -- ยง4. Polynomial Rings -- ยง5. Grรถbner Bases -- 4. Hidden Monomial Cryptosystems -- ยง 1. The Imai-Matsumoto System -- ยง2. Patarinโs Little Dragon -- ยง3. Systems That Might Be More Secure -- 5. Combinatorial-Algebraic Cryptosystems -- ยง1. History -- ยง2. Irrelevance of Brassardโs Theorem -- ยง3. Concrete Combinatorial-Algebraic Systems -- ยง4. The Basic Computational Algebra Problem -- ยง5. Cryptographic Version of Ideal Membership -- ยง6. Linear Algebra Attacks -- ยง7. Designing a Secure System -- 6. Elliptic and Hyperelliptic Cryptosystems -- ยง 1. Elliptic Curves -- ยง2. Elliptic Curve Cryptosystems -- ยง3. Elliptic Curve Analogues of Classical Number Theory Problems -- ยง4. Cultural Background: Conjectures on Elliptic Curves and Surprising Relations with Other Problems -- ยง5. Hyperelliptic Curves -- ยง6. Hyperelliptic Cryptosystems -- ยง1. Basic Definitions and Properties -- ยง2. Polynomial and Rational Functions -- ยง3. Zeros and Poles -- ยง4. Divisors -- ยง5. Representing Semi-Reduced Divisors -- ยง6. Reduced Divisors -- ยง7. Adding Reduced Divisors -- Exercises -- Answers to Exercises.ย