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Algebraic aspects of cryptography / Neal Koblitz.

By: Koblitz, Neal, 1948-.
Series: Algorithms and computation in mathematics, v. 3. Publisher: Berlin : Springer-Verlag, c1998Description: ix, 206 p. : ill. ; 24 cm.ISBN: 3540634460.Subject(s): Coding theory | Curves, EllipticDDC classification: 005.8201512
Contents:
Ch. 1 Cryptography. 1. Early History. 2. The Idea of Public Key Cryptography. 3. The RSA Cryptosystem. 4. Diffie_Hellman and he Digital Signature Algorithm. 5. Secret Sharing, Coin Flipping, and Time Spent on Homework. 6. Paswords, Signatures, and Ciphers. 7. Practical Cryptosystems and Useful Impractical Ones. - Ch. 2 Complexity of Computations. 1. The Big-O Notation. 2. Length of Numbers. 3. Time Estimates. 4. P, NP, and NP_Completeness. 5. Promise Problems. 6. Randomized Algorithms and Complexity Classes. 7. Some Other Complexity Classes. - Ch. 3 Algebra. 1. Fields. 2. Finite Fields. 3. The Euclidean Algorithm for Polynomials. 4. Polynomial Rings. 5. Grobner Bases. - Ch. 4 Hidden Monomial Cryptosystems. 1. The Imai-Matsumoto System. 2. Patarin's Little Dragan. 3. Systems That Might Be More Secure. - Ch. 5 Combinatorial-Algebraic Cryptosystems. 1. History. 2. Irrelevance of Brassard's Theorem. 3. Concrete Combinatorial- Algebra Systems. 4. The Basic Computational Algebra Problem. 5. Cryptographic Version of Ideal Membership. 6. Linear Algebra Attacks. 7. Designing a Secure System. - Ch. 6 Elliptic and Hyperelliptic Cryptosystems. 1. Elliptic Curves. 2. Elliptic Curve Cryptosystems. 3. Elliptic Curve Analogues of Classical Number Theory Problems. 4. Cultural Background : Conjectures on Elliptic Curves asnd Surprising Relations with Other Problems. 5. Hyperelliptic Curves. Hyperelliptic Cryptosystems. - Appendic. An Elementary Introduction to Hyperelliptic Curves / Alfred J. Menezes, Yi-Hong Wu, Robert J. Zuccherato. 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. - Answers to Exercises. - Bibliography. - Subject Index.
Summary: This is a textbook for a course (or self-instruction) in cryptography with emphasis on algebraic methods. The first half of the book is a self-contained informal introduction to areas of algebra, number theory, and computer science that are used in cryptography. Most of the material in the second half - "hidden monomial" systems, combinatorial-algebraic systems, and hyper-elliptic systems - has not previously appeared in monograph form. The Appendix by Menezes, Wu, and Zuccherato gives an elementary treatment of hyper-elliptic curves. This book is intended for graduate students, advanced undergraduates, and scientists working in various fields of data security. - Back cover.
Item type Current location Call number Copy number Status Notes Date due Barcode Remark
Main Collection TU External Storage-LCS
005.8201512 KOB (Browse shelf) 1 Available SOCIT, SOCIT, 560490 1000109362 Please fill up online form at https://taylorslibrary.taylors.edu.my/services/external_storage1

"With 7 Figures"

"With an Appendix on Hyperelliptic Curves by Alfred J. Menezes, Yi-Hong Wu, and Robert J. Zuccherato"

Ch. 1 Cryptography. 1. Early History. 2. The Idea of Public Key Cryptography. 3. The RSA Cryptosystem. 4. Diffie_Hellman and he Digital Signature Algorithm. 5. Secret Sharing, Coin Flipping, and Time Spent on Homework. 6. Paswords, Signatures, and Ciphers. 7. Practical Cryptosystems and Useful Impractical Ones. - Ch. 2 Complexity of Computations. 1. The Big-O Notation. 2. Length of Numbers. 3. Time Estimates. 4. P, NP, and NP_Completeness. 5. Promise Problems. 6. Randomized Algorithms and Complexity Classes. 7. Some Other Complexity Classes. - Ch. 3 Algebra. 1. Fields. 2. Finite Fields. 3. The Euclidean Algorithm for Polynomials. 4. Polynomial Rings. 5. Grobner Bases. - Ch. 4 Hidden Monomial Cryptosystems. 1. The Imai-Matsumoto System. 2. Patarin's Little Dragan. 3. Systems That Might Be More Secure. - Ch. 5 Combinatorial-Algebraic Cryptosystems. 1. History. 2. Irrelevance of Brassard's Theorem. 3. Concrete Combinatorial- Algebra Systems. 4. The Basic Computational Algebra Problem. 5. Cryptographic Version of Ideal Membership. 6. Linear Algebra Attacks. 7. Designing a Secure System. - Ch. 6 Elliptic and Hyperelliptic Cryptosystems. 1. Elliptic Curves. 2. Elliptic Curve Cryptosystems. 3. Elliptic Curve Analogues of Classical Number Theory Problems. 4. Cultural Background : Conjectures on Elliptic Curves asnd Surprising Relations with Other Problems. 5. Hyperelliptic Curves. Hyperelliptic Cryptosystems. - Appendic. An Elementary Introduction to Hyperelliptic Curves / Alfred J. Menezes, Yi-Hong Wu, Robert J. Zuccherato. 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. - Answers to Exercises. - Bibliography. - Subject Index.

This is a textbook for a course (or self-instruction) in cryptography with emphasis on algebraic methods. The first half of the book is a self-contained informal introduction to areas of algebra, number theory, and computer science that are used in cryptography. Most of the material in the second half - "hidden monomial" systems, combinatorial-algebraic systems, and hyper-elliptic systems - has not previously appeared in monograph form. The Appendix by Menezes, Wu, and Zuccherato gives an elementary treatment of hyper-elliptic curves. This book is intended for graduate students, advanced undergraduates, and scientists working in various fields of data security. - Back cover.