Introduction to cryptography对密码学的介绍

2004-7  

Springer Verlag  

Johannes Buchmann  

335  

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Cryptography is a key technology in electronic key systems. It is used to keep data secret, digitally sign documents, access control, and so forth. Users therefore should not only know how its techniques work, but they must also be able to estimate their efficiency and security. Based on courses taught by the author, this book explains the basic methods of modern cryptography. It is written for readers with only basic mathematical knowledge who are interested in modern cryptographic algorithms and their mathematical foundation. Several exercises are included following each chapter. This revised and extended edition includes new material on the AES encryption algorithm, the SHA-1 Hash algorithm, on secret sharing, as well as updates in the chapters on factoring and discrete logarithms. Johannes A. Buchmann is Professor of Computer Science and Mathematics at the Technical University of Darmstadt, and an Associate Editor of the Journal of Cryptology. In 1985, he received a Feodor Lynen Fellowship of the Alexander von Humboldt Foundation. He has also received the most prestigious award in science in Germany, the Leibniz Award of the German Science Foundation (Deutsche Forschungsgemeinschaft).

Preface for the Second EditionPreface1 Integers 1.1 Basics 1.2 Divisibility 1.3 Representation of Integers 1.4 O-and Ω-Notation 1.5 Cost of Addition, Multiplication, and Division with Remainder 1.6 Polynomial Time 1.7 Greatest Common Divisor 1.8 Euclidean Algorithm 1.9 Extended Euclidean Algorithm 1.10 Analysis of the Extended Euclidean Algorithm 1.11 Factoring into Primes 1.12 Exercises2 Congruences and Residue Class Rings 2.1 Congruences 2.2 Semigroups 2.3 Groups 2.4 Residue Class Ring 2.5 Fields 2.6 Division in the Residue Class Ring 2.7 Analysis of the Operations in the Residue Class Ring 2.8 Multiplicative Group of Residues mod rn 2.9 Order of Group Elements 2.10 Subgroups 2.11 Fermat's Little Theorem 2.12 Fast Exponentiation 2.13 Fast Evaluation of Power Products 2.14 Computation of Element Orders 2.15 The Chinese Remainder Theorem 2.16 Decomposition of the Residue Class Ring 2.17 A Formula for the Euler фo-Function 2.18 Polynomials 2.19 Polynomials over Fields 2.20 Construction of Finite Fields 2.21 The Structure of the Unit Group of Finite Fields 2.22 Structure of the Multiplicative Group of Residues Modulo a Prime Number 2.23 Exercises3 Encryption 3.1 Encryption Schemes 3.2 Symmetric and Asymmetric Cryptosystems 3.3 Cryptanalysis 3.4 Alphabets and Words 3.5 Permutations 3.6 Block Ciphers 3.7 Multiple Encryption 3.8 The Use of Block Ciphers 3.9 Stream Ciphers 3.10 The Affine Cipher 3.11 Matrices and Linear Maps 3.12 Affine Linear Block Ciphers 3.13 Vigenere, Hill, and Permutation Ciphers ……4 Probability and Perfect Secrecy5 DES6 AES7 Prime Number Generation8 Public-key Encryption9 Factoring10 Discrete Logarithms11 Cryptographic Hash Functions12 Digital Signatures13 Other Systems14 Identification15 Secret Sharing16 Public-key InfrastructuresSolutions of the exercisesReferencesIndex

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