Cryptology ePrint Archive: Report 2014/645

Graph-Induced Multilinear Maps from Lattices

Craig Gentry and Sergey Gorbunov and Shai Halevi

Abstract: Graded multilinear encodings have found extensive applications in cryptography ranging from non-interactive key exchange protocols, to broadcast and attribute-based encryption, and even to software obfuscation. Despite seemingly unlimited applicability, essentially only two candidate constructions are known (GGH and CLT). In this work, we describe a new graph-induced multilinear encoding scheme from lattices. In a graph-induced multilinear encoding scheme the arithmetic operations that are allowed are restricted through an explicitly defined directed graph (somewhat similar to the "asymmetric variant" of previous schemes). Our construction encodes Learning With Errors (LWE) samples in short square matrices of higher dimensions. Addition and multiplication of the encodings corresponds naturally to addition and multiplication of the LWE secrets.

Category / Keywords: Lattices, LWE, Multilinear Maps

Date: received 20 Aug 2014, last revised 11 Nov 2014

Contact author: sergeyg at mit edu

Available format(s): PDF | BibTeX Citation

Version: 20141112:011502 (All versions of this report)

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