Candidate multilinear maps / Sanjam Garg.

Format:

Book

Author/Creator:

Garg, Sanjam, author.

Series:

ACM books ; #5.

ACM books ; #5

Language:

English

Subjects (All):

Data encryption (Computer science).

Cryptography.

Physical Description:

1 online resource (xi, 108 pages) : illustrations.

Edition:

First edition.

Place of Publication:

[New York] : Association for Computing Machinery ; [San Rafael, California] : Morgan & Claypool, 2015.

System Details:

Mode of access: World Wide Web.

System requirements: Adobe Acrobat Reader.

Summary:

Cryptography to me is "black magic," enabling tasks that often seem paradoxical or simply just impossible. Like the space explorers, we cryptographers often wonder, "What are the boundaries of this world of 'black magic'?" This book lays one of the founding stones in furthering our understanding of these edges.

Contents:

1. Introduction

1.1 Our results

1.2 Brief overview

1.3 Organization

2. Survey of applications

2.1 How flexible can we make access to encrypted data?

2.2 Program obfuscation

2.3 Other applications

3. Multilinear maps and graded encoding systems

3.1 Cryptographic multilinear maps

3.1.1 Efficient procedures

3.1.2 Hardness assumptions

3.2 Graded encoding schemes

3.2.1 Efficient procedures, the dream version

3.2.2 Efficient procedures, the real-life version

3.2.3 Hardness assumptions

4. Preliminaries I: lattices

4.1 Lattices

4.2 Gaussians on lattices

4.3 Sampling from discrete Gaussian

5. Preliminaries II: algebraic number theory background

5.1 Number fields and rings of integers

5.2 Embeddings and geometry

5.3 Ideals in the ring of integers

5.4 Prime ideals, unique factorization and distributions

5.5 Ideal lattices

6. The new encoding schemes

6.1 The basic graded encoding scheme

6.2 Setting the parameters

6.3 Extensions and variants

7. Security of our constructions

7.1 Our hardness assumption

7.2 Simplistic models of attacks

7.2.1 Hardness of GCDH in the arithmetic straight-line program model

7.3 Cryptanalysis beyond the generic models

7.3.1 Easily computable quantities

7.3.2 Using averaging attacks

7.3.3 Cryptanalysis with extra help

7.4 Some countermeasures

7.5 Easiness of other problems

8. Preliminaries III: computation in a number field

8.1 Some computational aspects of number fields and ideal lattices

8.2 Computational hardness assumptions over number fields

9. Survey of lattice cryptanalysis

9.1 Averaging attacks

9.2 Gentry-Szydlo: recovering v from v.v and (v)

9.3 Nguyen-Regev: a gradient descent attack

9.4 Ducas-Nguyen: gradient descent over zonotopes and deformed parallelepipeds

9.5 A new algorithm for the closest principal ideal generator problem

9.6 Coppersmith attacks

9.7 Dimension halving in principal ideal lattices

10. One-round key exchange

10.1 Definitions

10.2 Our construction

Appendix A. Generalizing graded encoding systems

Efficient procedures, the dream version

Efficient procedures, the real-life version

Hardness assumptions

Bibliography

Author's biography.

Notes:

Includes bibliographical references (pages 95-108).

Title from PDF title page (viewed on April 28, 2015).

Other Format:

Print version:

ISBN:

9781627055383

OCLC:

908155895

Access Restriction:

Restricted for use by site license.