Introduction to Cryptography
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
1 online resource (xi, 281 pages 7 illustrations)
9781468404968, 1468404962
851800802
Print version:
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
Electronic reproduction, [Place of publication not identified], HathiTrust Digital Library, 2010
English