Includes bibliographical references and index.

Introduction to Cryptography Hiding information: confidentiality Some basic definitions Attacks on a cryptosystem Some cryptographic problems Cryptographic protocols Some simple ciphers Cryptography and computer security Basic Number Theory Introduction Some basic definitions Some number theoretic calculations Primality testing Classical Cryptosystems Introduction The Caesar cipher Translation ciphers Transposition ciphers The Vigenere cipher The one-time pad Permutation ciphers Matrix ciphers Introduction to Information Theory Entropy and uncertainty Perfect secrecy Estimating the entropy of English Unicity distance Public-Key Cryptosystems Based on Factoring Introduction The RSA cryptosystem Attacks against RSA RSA in Sage Rabin's cryptosystem Rabin's cryptosystem in Sage Some notes on security Factoring Public-Key Cryptosystems Based on Logarithms and Knapsacks El Gamal's cryptosystem El Gamal in Sage Computing discrete logarithms Diffie-Hellman key exchange Knapsack cryptosystems Breaking the knapsack Digital Signatures Introduction RSA signature scheme Rabin digital signatures The El Gamal digital signature scheme The Digital Signature Standard Block Ciphers and the Data Encryption Standard Block ciphers Some definitions Substitution/permutation ciphers Modes of encryption Exploring modes of encryption The Data Encryption Standard (DES) Feistel ciphers Simplified DES: sDES The DES algorithm Security of S-boxes Security of DES Using DES Experimenting with DES Lightweight ciphers Finite Fields Groups and rings Introduction to fields Fundamental algebra of finite fields Polynomials mod 2 A field of order 8 Other fields GF(2n) Multiplication and inversion Multiplication without power tables The Advanced Encryption Standard Introduction and some history Basic structure The layers in detail Decryption Experimenting with AES A simplified Rijndael Security of the AES Hash Functions Uses of hash functions Security of hash functions Constructing a hash function Provably secure hash functions New hash functions Message authentication codes Using a MAC Elliptic Curves and Cryptosystems Basic definitions The group on an elliptic curve Background and history Multiplication Elliptic curve cryptosystems Elliptic curve signature schemes Elliptic curves over binary fields Pairing based cryptography Exploring pairings in Sage Random Numbers and Stream Ciphers Introduction Pseudo-random number generators Some cryptographically strong generators The shrinking generator ISAAC and Fortuna Stream ciphers RC4 The Blum-Goldwasser cryptosystem Advanced Applications and Protocols Secure multi-party computation Zero knowledge proofs Oblivious transfer Digital cash Voting protocols Appendix A: Introduction to Sage Appendix B: Advanced Computational Number Theory Bibliography Index Exercises appear at the end of each chapter.

"This very well-written book is recommended to graduate or final-year undergraduate students intended to start research work on both theoretical and experimental cryptography. Most of the cryptographic protocols are illustrated by various examples and implemented using the open-source algebra software Sage. The book provides a rigorous introduction to the mathematics used in cryptography and covers almost all modern practical cryptosystems. Also, the book is certainly a valuable resource for practitioners looking for experimental cryptography with a computer algebra system." ―Abderrahmane Nitaj (LMNO, Université de Caen Basse Normandie), IACR book reviews, February 2014 "It would make a great first course in cryptography but it is also easy enough to read to make it suitable for solitary study. … Overall this is an excellent book. It is far from the theorem-proof format and it does try to explain the ideas and motivate the reader. The pattern of mixing some theory followed by some practice is good at keeping the less theory-minded reader rolling along as the need for the theory becomes all too apparent. … this is a really good book. If you want to master cryptography, this is a great place to start."

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