Algebraic Aspects of Cryptography - neues Buch

EAN (ISBN-13): 9783662036426
Erscheinungsjahr: 2012
Herausgeber: Springer Berlin Heidelberg

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ISBN/EAN: 9783662036426

ISBN - alternative Schreibweisen:
978-3-662-03642-6
Alternative Schreibweisen und verwandte Suchbegriffe:
Autor des Buches: neal koblitz
Titel des Buches: algebraic aspects cryptography

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Daten vom Verlag:

Autor/in: Neal Koblitz
Titel: Algorithms and Computation in Mathematics; Algebraic Aspects of Cryptography
Verlag: Springer; Springer Berlin
206 Seiten
Erscheinungsjahr: 2012-12-06
Berlin; Heidelberg; DE
Sprache: Englisch
187,00 € (DE)

EA; E107; eBook; Nonbooks, PBS / Informatik, EDV/Informatik; Theoretische Informatik; Verstehen; Algebra; DES; Digital Signature Algorithm; algebraic methods; algorithms; complexity; computational number theory; cryptography; data security; elliptic and hyperelliptic curves; finite field; linear algebra; number theory; combinatorics; B; Theory of Computation; Number Theory; Data Structures and Information Theory; Discrete Mathematics; Cryptology; Mathematics and Statistics; Zahlentheorie; Algorithmen und Datenstrukturen; Informationstheorie; Diskrete Mathematik; Kodierungstheorie und Verschlüsselung (Kryptologie); Kryptografie, Verschlüsselungstechnologie; BB

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.- 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.- 3. Algebra.- §1. Fields.- §2. Finite Fields.- §3. The Euclidean Algorithm for Polynomials.- §4. Polynomial Rings.- §5. Gröbner Bases.- 4. Hidden Monomial Cryptosystems.- § 1. The Imai-Matsumoto System.- §2. Patarin’s Little Dragon.- §3. Systems That Might Be More Secure.- 5. Combinatorial-Algebraic Cryptosystems.- §1. History.- §2. Irrelevance of Brassard’s Theorem.- §3. Concrete Combinatorial-Algebraic Systems.- §4. The Basic Computational Algebra Problem.- §5. Cryptographic Version of Ideal Membership.- §6. Linear Algebra Attacks.- §7. Designing a Secure System.- 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 and Surprising Relations with Other Problems.- §5. Hyperelliptic Curves.- §6. Hyperelliptic Cryptosystems.- §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.