Candidate Multilinear Maps / Edition 1

by Sanjam Garg

Overview

The aim of cryptography is to design primitives and protocols that withstand adversarial behavior. Information theoretic cryptography, how-so-ever desirable, is extremely restrictive and most non-trivial cryptographic tasks are known to be information theoretically impossible. In order to realize sophisticated cryptographic primitives, we forgo information theoretic security and assume limitations on what can be efficiently computed. In other words we attempt to build secure systems conditioned on some computational intractability assumption such as factoring, discrete log, decisional Diffie-Hellman, learning with errors, and many more. In this work, based on the 2013 ACM Doctoral Dissertation Award-winning thesis, we put forth new plausible lattice-based constructions with properties that approximate the sought after multilinear maps. The multilinear analog of the decision Diffie-Hellman problem appears to be hard in our construction, and this allows for their use in cryptography. These constructions open doors to providing solutions to a number of important open problems.

Product Details

ISBN-13:	9781627055376
Publisher:	Association for Computing Machinery and Morgan & C
Publication date:	03/01/2015
Series:	ACM Books
Pages:	122
Product dimensions:	7.50(w) x 9.30(h) x 0.00(d)

About the Author

Sanjam Garg grew up in royal Patiala, a beautiful city in southeastern Punjab, India. Growing up, even though he wasn’t good at it, he enjoyed playing cricket with his friends. He was also remarkably curious about everything and this curiosity led him to the Indian Institute of Technology Delhi where he started studying cryptography by mistake. One mistake led to another and ultimately leading to a disaster—he ended up getting a doctoral degree from University of California, Los Angeles. During his graduate study he pondered over the lesser important questions in cryptography and the more important questions about life, making some progress on the former but none whatsoever on the latter. Unfettered, he marches on!

Table of Contents

Table of Contents: Introduction / Survey of Applications / Multilinear Maps and Graded Encoding Systems / Preliminaries I: Lattices / Preliminaries II: Algebraic Number Theory Background / The New Encoding Schemes / Security of Our Constructions / Preliminaries III: Computation in a Number Field / Survey of Lattice Cryptanalysis / One-Round Key Exchange / Generalizing Graded Encoding Systems / Bibliography / Author's Biography