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.

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.

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.

The primer assumes basic familiarity with the notion of efficient algorithms and with elementary probability theory, but provides a basic introduction to all notions that are actually used. as a result, the primer is essentially self-contained, although the interested reader is at times referred to other sources for more detail. --Book Jacket.

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.

A fresh look at the question of randomness was taken in the theory of computing: A distribution is pseudorandom if it cannot be distinguished from the uniform distribution by any efficient procedure. This paradigm, originally associating efficient procedures with polynomial-time algorithms, has been applied with respect to a variety of natural classes of distinguishing procedures. The resulting theory of pseudorandomness is relevant to science at large and is closely related to central areas of computer science, such as algorithmic design, complexity theory, and cryptography. This primer surveys the theory of pseudorandomness, starting with the general paradigm, and discussing various incarnations while emphasizing the case of general-purpose pseudorandom generators (withstanding any polynomial-time distinguisher). Additional topics include the "derandomization" of arbitrary probabilistic polynomial-time algorithms, pseudorandom generators withstanding space-bounded distinguishers, and serveral natural notions of special-purpose pseudorandom generators. The primer assumes basic familiarity with the notion of efficient algorithms and with elementary probability theory, but provides a basic introduction to all notions that are actually used. as a result, the primer is essentially self-contained, although the interested reader is at times referred to other sources for more detail.

This book covers pseudorandom number generation algorithms, evaluation techniques, and offers practical advice and code examples. Random Numbers and Computers is an essential introduction or refresher on pseudorandom numbers in computer science. The first comprehensive book on the topic, readers are provided with a practical introduction to the techniques of pseudorandom number generation, including how the algorithms work and how to test the output to decide if it is suitable for a particular purpose. Practical applications are demonstrated with hands-on presentation and descriptions that readers can apply directly to their own work. Examples are in C and Python and given with an emphasis on understanding the algorithms to the point of practical application. The examples are meant to be implemented, experimented with and improved/adapted by the reader.