Introduction to Cryptography / by Johannes A. Buchmann
(Undergraduate Texts in Mathematics)
データ種別 | 電子ブック |
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出版者 | New York, NY : Springer US |
出版年 | 2001 |
本文言語 | 英語 |
大きさ | XI, 281p. 7 illus : online resource |
書誌詳細を非表示
内容注記 | 1 Integers 1.1 Basics 1.2 Divisibility 1.3 Representation of Integers 1.4 O- and ?-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 Exercises 2 Congruences and Residue Class Rings 2.1 Congruences 2.2 Semigroups 2.3 Groups 2.4 Residue Class Rings 2.5 Fields 2.6 Division in the Residue Class Ring 2.7 Analysis of Operations in the Residue Class Ring 2.8 Multiplicative Group of Residues 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 ?-Function 2.18 Polynomials 2.19 Polynomials over Fields 2.20 Structure of the Unit Group of Finite Fields 2.21 Structure of the Multiplicative Group of Residues mod a Prime Number 2.22 Exercises 3 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 Use of Block Ciphers 3.9 Stream Ciphers 3.10 Affine Cipher 3.11 Matrices and Linear Maps 3.12 Affine Linear Block Ciphers 3.13 Vigenère, Hill, and Permutation Ciphers 3.14 Cryptanalysis of Affine Linear Block Ciphers 3.15 Exercises 4 Probability and Perfect Secrecy 4.1 Probability 4.2 Conditional Probability 4.3 Birthday Paradox 4.4 Perfect Secrecy 4.5 Vernam One-Time Pad 4.6 Random Numbers 4.7 Pseudorandom Numbers 4.8 Exercises 5 DES 5.1 Feistel Ciphers 5.2 DES Algorithm 5.3 An Example 5.4 Security of DES 5.5 Exercises 6 Prime Number Generation 6.1 Trial Division 6.2 Fermat Test 6.3 Carmichael Numbers 6.4 Miller-Rabin Test 6.5 Random Primes 6.6 Exercises 7 Public-Key Encryption 7.1 Idea 7.2 RSA Cryptosystem 7.3 Rabin Encryption 7.4 Diffie-Hellman Key Exchange 7.5 ElGamal Encryption 7.6 Exercises 8 Factoring 8.1 Trial Division 8.2 p — 1 Method 8.3 Quadratic Sieve 8.4 Analysis of the Quadratic Sieve 8.5 Efficiency of Other Factoring Algorithms 8.6 Exercises 9 Discrete Logarithms 9.1 DL Problem 9.2 Enumeration 9.3 Shanks Baby-Step Giant-Step Algorithm 9.4 Pollard ?-Algorithm 9.5 Pohlig-Hellman Algorithm 9.6 Index Calculus 9.7 Other Algorithms 9.8 Generalization of the Index Calculus Algorithm 9.9 Exercises 10 Cryptographic Hash Functions 10.1 Hash Functions and Compression Functions 10.2 Birthday Attack 10.3 Compression Functions from Encryption Functions 10.4 Hash Functions from Compression Functions 10.5 Efficient Hash Functions 10.6 An Arithmetic Compression Function 10.7 Message Authentication Codes 10.8 Exercises 11 Digital Signatures 11.1 Idea 11.2 RSA Signatures 11.3 Signatures from Public-Key Systems 11.4 ElGamal Signature 11.5 Digital Signature Algorithm (DSA) 11.6 Exercises 12 Other Groups 12.1 Finite Fields 12.2 Elliptic Curves 12.3 Quadratic Forms 12.4 Exercises 13 Identification 13.1 Passwords 13.2 One-Time Passwords 13.3 Challenge-Response Identification 13.4 Exercises 14 Public-Key Infrastructures 14.1 Personal Security Environments 14.2 Certification Authorities 14.3 Certificate Chains -- References -- Solutions to the Exercises |
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一般注記 | Cryptography is a key technology in electronic key systems. It is used to keep data secret, digitally sign documents, access control, etc. Therefore, users should not only know how its techniques work, but they must also be able to estimate their efficiency and security. For this new edition, the author has updated the discussion of the security of encryption and signature schemes and recent advances in factoring and computing discrete logarithms. He has also added descriptions of time-memory trade of attacks and algebraic attacks on block ciphers, the Advanced Encryption Standard, the Secure Hash Algorithm, secret sharing schemes, and undeniable and blind signatures. Johannes A. Buchmann is a Professor of Computer Science and Mathematics at the Technical University of Darmstadt, and the Associate Editor of the Journal of Cryptology. In 1985, he received the Feodor Lynen Fellowship of the Alexander von Humboldt Foundation. Furthermore, he has received the most prestigious award in science in Germany, the Leibniz Award of the German Science Foundation. About the first edition: It is amazing how much Buchmann is able to do in under 300 pages: self-contained explanations of the relevant mathematics (with proofs); a systematic introduction to symmetric cryptosystems, including a detailed description and discussion of DES; a good treatment of primality testing, integer factorization, and algorithms for discrete logarithms; clearly written sections describing most of the major types of cryptosystems....This book is an excellent reference, and I believe it would also be a good textbook for a course for mathematics or computer science majors..." -Neal Koblitz, The American Mathematical Monthly |
著者標目 | *Buchmann, Johannes A. author SpringerLink (Online service) |
件 名 | LCSH:Mathematics LCSH:Data structures (Computer science) LCSH:Number theory FREE:Mathematics FREE:Number Theory FREE:Data Structures, Cryptology and Information Theory |
分 類 | DC23:512.7 |
巻冊次 | ISBN:9781468404968 |
ISBN | 9781468404968 |
URL | http://dx.doi.org/10.1007/978-1-4684-0496-8 |
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