Cryptology ePrint Archive: Report 2018/1129

On Kilian's Randomization of Multilinear Map Encodings

Jean-Sebastien Coron and Hilder V. L. Pereira

Abstract: Indistinguishability obfuscation constructions based on matrix branching programs generally proceed in two steps: first apply Kilian's randomization of the matrix product computation, and then encode the matrices using a multilinear map scheme. In this paper we observe that by applying Kilian's randomization after encoding, the complexity of the best attacks is significantly increased for CLT13 multilinear maps. This implies that much smaller parameters can be used, which improves the efficiency of the constructions by several orders of magnitude.

As an application, we describe the first concrete implementation of non-interactive Diffie-Hellman key exchange secure against existing attacks. Key exchange was originally the most straightforward application of multilinear maps; however it was quickly broken for the three known families of multilinear maps (GGH13, CLT13 and GGH15). Here we describe the first implementation of key exchange based on CLT13 that is resistant against the Cheon et al. attack. For N=4 users and a medium level of security, our implementation requires 18 GB of public parameters, and a few minutes for the derivation of a shared key.

Category / Keywords: public-key cryptography / Multilinear maps, key-exchange, Approximate-GCD problem, GCD attacks, lattice attacks

Original Publication (with minor differences): IACR-ASIACRYPT-2019

Date: received 20 Nov 2018, last revised 24 Jun 2021

Contact author: jscoron at gmail com

Available format(s): PDF | BibTeX Citation

Version: 20210624:062508 (All versions of this report)

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