Cryptography in Constant Parallel Time

NCOfunctions 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 cryptography in NCO 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 NCO implementations for many basic cryptographic primitives such as one-way functions, pseudorandom generators, encryption schemes and digital signatures. It also addresses a wide variety of fundamental questions about cryptography in NCO, and, in addition, explores the cryptographic strength of several interesting subclasses of NCO. This includes simple forms of natural computation that can be performed by real-world dynamical systems in a constant number of steps. 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.

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.

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 Includes supplementary material: sn.pub/extras

Autorentext

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.

Inhalt

Introduction.- Preliminaries and Definitions.- Randomized Encoding of Functions.- Cryptography in NC0.- Computationally Private Randomizing Polynomials and Their Applications.- On Pseudorandom Generators with Linear Stretch in NC0.- Cryptography with Constant Input Locality.- One-Way Functions with Optimal Output Locality.- App. A, On Collections of Cryptographic Primitives.