A Primer on Pseudorandom Generators
About this Title
Oded Goldreich, Weizmann Institute of Science, Rehovot, Israel
Publication: University Lecture Series
Publication Year 2010: Volume 55
ISBNs: 978-0-8218-5192-0 (print); 978-1-4704-1650-8 (online)
MathSciNet review: MR2677397
MSC: Primary 68-02; Secondary 68Q15, 68Q17, 68Q87, 68W20
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 several 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.
Advanced undergraduates and computer science majors, graduate students, and research mathematicians interested in complexity theory; cryptography; and pseudorandom generators.
Table of Contents
- Chapter 1. Introduction
- Chapter 2. General-purpose pseudorandom generators
- Chapter 3. Derandomization of time-complexity classes
- Chapter 4. Space-bounded distinguishers
- Chapter 5. Special purpose generators
- Concluding remarks
- Appendix A. Hashing functions
- Appendix B. On randomness extractors
- Appendix C. A generic hard-core predicate
- Appendix D. Using randomness in computation
- Appendix E. Cryptographic applications of pseudorandom functions
- Appendix F. Some basic complexity classes