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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.
List of contents
Introduction.- Preliminaries and Definitions.- Randomized Encoding of Functions.- Cryptography in NC 0 .- Computationally Private Randomizing Polynomials and Their Applications.- On Pseudorandom Generators with Linear Stretch in NC 0 .- Cryptography with Constant Input Locality.- One-Way Functions with Optimal Output Locality.- App. A, On Collections of Cryptographic Primitives.
About the author
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.
Summary
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.
Additional text
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)
Report
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)
