Building an efficient lattice gadget toolkit: Subgaussian sampling and more

Document Type

Conference Proceeding

Publication Date

1-1-2019

Abstract

Many advanced lattice cryptography applications require efficient algorithms for inverting the so-called “gadget” matrices, which are used to formally describe a digit decomposition problem that produces an output with specific (statistical) properties. The common gadget inversion problems are the classical (often binary) digit decomposition, subgaussian decomposition, Learning with Errors (LWE) decoding, and discrete Gaussian sampling. In this work, we build and implement an efficient lattice gadget toolkit that provides a general treatment of gadget matrices and algorithms for their inversion/sampling. The main contribution of our work is a set of new gadget matrices and algorithms for efficient subgaussian sampling that have a number of major theoretical and practical advantages over previously known algorithms. Another contribution deals with efficient algorithms for LWE decoding and discrete Gaussian sampling in the Residue Number System (RNS) representation. We implement the gadget toolkit in PALISADE and evaluate the performance of our algorithms both in terms of runtime and noise growth. We illustrate the improvements due to our algorithms by implementing a concrete complex application, key-policy attribute-based encryption (KP-ABE), which was previously considered impractical for CPU systems (except for a very small number of attributes). Our runtime improvements for the main bottleneck operation based on subgaussian sampling range from 18x (for 2 attributes) to 289x (for 16 attributes; the maximum number supported by a previous implementation). Our results are applicable to a wide range of other advanced applications in lattice cryptography, such as GSW-based homomorphic encryption schemes, leveled fully homomorphic signatures, other forms of ABE, some program obfuscation constructions, and more.

Identifier

85065873540 (Scopus)

ISBN

[9783030176556]

Publication Title

Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics

External Full Text Location

https://doi.org/10.1007/978-3-030-17656-3_23

e-ISSN

16113349

ISSN

03029743

First Page

655

Last Page

684

Volume

11477 LNCS

Grant

W911NF-15-C-0226

Fund Ref

Defense Advanced Research Projects Agency

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