© 2014

Cryptography in Constant Parallel Time


  • The author's related thesis was honorably mentioned (runner-up) for the ACM Dissertation Award in 2007

  • Assumes only a minimal background in computational complexity and cryptography

  • Introduces general techniques and tools of interest to experts in the area


Part of the Information Security and Cryptography book series (ISC)

Table of contents

  1. Front Matter
    Pages I-XVI
  2. Benny Applebaum
    Pages 1-9
  3. Benny Applebaum
    Pages 11-18
  4. Benny Applebaum
    Pages 19-31
  5. Benny Applebaum
    Pages 33-78
  6. Benny Applebaum
    Pages 107-121
  7. Benny Applebaum
    Pages 147-185
  8. Back Matter
    Pages 187-193

About this book


Locally computable (NC0) functions are "simple" functions for which every bit of the output can be computed by reading a small number of bits of their input. The study of locally computable cryptography attempts to construct cryptographic functions that achieve this strong notion of simplicity and simultaneously provide a high level of security. Such constructions are highly parallelizable and they can be realized by Boolean circuits of constant depth. 

This book establishes, for the first time, the possibility of local implementations for many basic cryptographic primitives such as one-way functions, pseudorandom generators, encryption schemes and digital signatures. It also extends these results to other stronger notions of locality, and addresses a wide variety of fundamental questions about local cryptography. The author's related thesis was honorably mentioned (runner-up) for the ACM Dissertation Award in 2007, and this book includes some expanded sections and proofs, and notes on recent developments. 

The book assumes only a minimal background in computational complexity and cryptography and is therefore suitable for graduate students or researchers in related areas who are interested in parallel cryptography. It also introduces general techniques and tools which are likely to interest experts in the area.


Computational Complexity Cryptanalysis Cryptography Cryptology NC0 One-Way Functions (OWF) Pseudorandom generators

Authors and affiliations

  1. 1.Tel Aviv UniversitySchool of Electrical EngineeringTel AvivIsrael

About the authors

The author is an assistant professor in the School of Electrical Engineering of Tel Aviv University. He had postdoctoral positions in the Faculty of Mathematics and Computer Science of the Weizmann Institute of Science, and the Department of Computer Science of Princeton University. He received his PhD in 2007 from the Computer Science Department of the Technion for the dissertation "Cryptography in Constant Parallel Time"; this was honorably mentioned (runner-up) for the ACM Dissertation Award in 2007. His research interests include cryptography, computational complexity, and coding theory.

Bibliographic information

  • Book Title Cryptography in Constant Parallel Time
  • Authors Benny Applebaum
  • Series Title Information Security and Cryptography
  • Series Abbreviated Title Information Security, Cryptography
  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 2014
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Computer Science Computer Science (R0)
  • Hardcover ISBN 978-3-642-17366-0
  • Softcover ISBN 978-3-662-50713-1
  • eBook ISBN 978-3-642-17367-7
  • Series ISSN 1619-7100
  • Edition Number 1
  • Number of Pages XVI, 193
  • Number of Illustrations 3 b/w illustrations, 0 illustrations in colour
  • Topics Mathematics of Computing
    Data Structures and Information Theory
  • Buy this book on publisher's site


From the book reviews:

“The book explores the minimal computational complexity of these cryptographic primitives necessary to keep them secure. … This is an important book with groundbreaking results that will continue to influence research in this area for years to come. … The ideal audience for this book comprises advanced graduate students or other researchers in the same field.” (Burkhard Englert, Computing Reviews, August, 2014)