A pseudorandom generator is an easy-to-compute function that stretches a short random string into a much longer string that "looks" just like a random string to any efficient adversary. One immediate application of a pseudorandom generator is the construction of a private key cryptosystem that is secure against chosen plaintext attack. There do not seem to be natural examples of functions that are pseudorandom generators. On the other hand, there do seem to be a variety of natural examples of another basic primitive: the one-way function. A function is one-way if it is easy to compute but hard for any efficient adversary to invert on average. The first half of the book shows how to construct a pseudorandom generator from any one-way function. Building on this, the second half of the book shows how to construct other useful cryptographic primitives, such as private key cryptosystems, pseudorandom function generators, pseudorandom permutation generators, digital signature schemes, bit commitment protocols, and zero-knowledge interactive proof systems. The book stresses rigorous definitions and proofs.

The book introduces new ways of using analytic number theory in cryptography and related areas, such as complexity theory and pseudorandom number generation. Cryptographers and number theorists will find this book useful. The former can learn about new number theoretic techniques which have proved to be invaluable cryptographic tools, the latter about new challenging areas of applications of their skills.

Cryptography is one of the most active areas in current mathematics research and applications. This book focuses on cryptography along with two related areas: the study of probabilistic proof systems, and the theory of computational pseudorandomness. Following a common theme that explores the interplay between randomness and computation, the important notions in each field are covered, as well as novel ideas and insights.

A survey of pseudorandomness, the theory of efficiently generating objects that look random despite being constructed using little or no randomness. This theory has significance for areas in computer science and mathematics, including computational complexity, algorithms, cryptography, combinatorics, communications, and additive number theory.

This book constitutes the refereed proceedings of the 31st Annual International Conference on the Theory and Applications of Cryptographic Techniques, EUROCRYPT 2012, held in Cambgridge, UK, in April 2012. The 41 papers, presented together with 2 invited talks, were carefully reviewed and selected from 195 submissions. The papers are organized in topical sections on index calculus, symmetric constructions, secure computation, protocols, lossy trapdoor functions, tools, symmetric cryptanalysis, fully homomorphic encryption, asymmetric cryptanalysis, efficient reductions, public-key schemes, security models, and lattices.

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, in particular public-key cryptography, has emerged in the last 20 years as an important discipline that is not only the subject of an enormous amount of research, but provides the foundation for information security in many applications. Standards are emerging to meet the demands for cryptographic protection in most areas of data communications. Public-key cryptographic techniques are now in widespread use, especially in the financial services industry, in the public sector, and by individuals for their personal privacy, such as in electronic mail. This Handbook will serve as a valuable reference for the novice as well as for the expert who needs a wider scope of coverage within the area of cryptography. It is a necessary and timely guide for professionals who practice the art of cryptography. The Handbook of Applied Cryptography provides a treatment that is multifunctional: It serves as an introduction to the more practical aspects of both conventional and public-key cryptography It is a valuable source of the latest techniques and algorithms for the serious practitioner It provides an integrated treatment of the field, while still presenting each major topic as a self-contained unit It provides a mathematical treatment to accompany practical discussions It contains enough abstraction to be a valuable reference for theoreticians while containing enough detail to actually allow implementation of the algorithms discussed Now in its third printing, this is the definitive cryptography reference that the novice as well as experienced developers, designers, researchers, engineers, computer scientists, and mathematicians alike will use.