Introduction to cryptography, Second Edition

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 Due to the rapid growth of digital communication and electronic data exchange, information security has become a crucial issue in industry, business, and administration. Modern cryptography provides essential techniques for securing information and protecting data. In the first part, this book covers the key concepts of cryptography on an undergraduate level, from encryption and digital signatures to cryptographic protocols. Essential techniques are demonstrated in protocols for key exchange, user identification, electronic elections and digital cash. In the second part, more advanced topics are addressed, such as the bit security of one-way functions and computationally perfect pseudorandom bit generators. The security of cryptographic schemes is a central topic. Typical examples of provably secure encryption and signature schemes and their security proofs are given. Though particular attention is given to the mathematical foundations, no special background in mathematics is presumed. The necessary algebra, number theory and probability theory are included in the appendix. Each chapter closes with a collection of exercises. The second edition contains corrections, revisions and new material, including a complete description of the AES, an extended section on cryptographic hash functions, a new section on random oracle proofs, and a new section on public-key encryption schemes that are provably secure against adaptively-chosen-ciphertext attacks

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).

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. TOC:* Integers * Congruences and Residue Class Rings * Encryption * Probability and Perfect Secrecy * DES * AES * Prime Number Generation *Public-Key Encryption* Factoring.* Discrete Logarithms * Cryptographic Hash Functions *Digital Signatures *Other Systems * Identification * Public-Key Infrastructures * Solutions of the Odd Exercises * Subject Index * Bibliography Introduction to Cryptography......Page 4 Contents......Page 8 Preface for the Second Edition......Page 14 Preface......Page 16 1 Integers......Page 18 2 Congruences and Residue Class Rings......Page 46 3 Encryption......Page 88 4 Probability and Perfect Secrecy......Page 132 5 DES......Page 144 6 AES......Page 156 7 Prime Number Generation......Page 168 8 Public-Key Encryption......Page 180 9 Factoring......Page 216 10 Discrete Logarithms......Page 230 11 Cryptographic Hash Functions ......Page 252 12 Digital Signatures......Page 266 13 Other Systems......Page 294 14 Identification......Page 302 15 Secret Sharing......Page 310 16 Public-Key Infrastructures......Page 316 Solutions of the Exercises......Page 324 References......Page 342 Index......Page 348 "Cryptography is a key technology in electronic security 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 fought 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."--BOOK JACKET. 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. From the reviews: "Gives a clear and systematic introduction into the subject whose popularity is ever increasing, and can be recommended to all who would like to learn about cryptography." --ZENTRALBLATT MATH As usual, N = {1, 2, 3, 4, 5, . . .} is the set of positive integers and Z = {0, 1, 2, 3, . . .} is the set of integers.