Algebraic Aspects of Cryptography

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Description

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



Contenu

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

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Détails sur le produit

Titre
Algebraic Aspects of Cryptography
Auteur
EAN
9783662036426
Format
eBook (pdf)
Producteur
Springer Berlin Heidelberg
Genre
Informatique et Internet
Parution
06.12.2012
Protection contre la copie numérique
filigrane numérique
Nombre de pages
206
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