Welcome to the resource topic for 2021/046
Title:
Efficient Lattice-Based Inner-Product Functional Encryption
Authors: Jose Maria Bermudo Mera, Angshuman Karmakar, Tilen Marc, Azam Soleimanian
Abstract:In the recent years, many research lines on Functional Encryption (FE) have been suggested and studied regarding the functionality, security, or efficiency. Nevertheless, an open problem on a basic functionality, the single-input inner-product (IPFE), remains: can IPFE be instantiated based on the Ring Learning With Errors (RLWE) assumption? The RLWE assumption provides quantum-resistance security while in comparison with LWE assumption gives significant performance and compactness gains. In this paper we present the first RLWE-based IPFE scheme. We carefully choose strategies in the security proofs to optimize the size of parameters. More precisely, we develop two new results on ideal lattices. The first result is a variant of Ring-LWE, that we call multi-hint extended Ring-LWE, where some hints on the secret and the noise are given. We present a reduction from RLWE problem to this variant. The second tool is a special form of Leftover Hash Lemma (LHL) over rings, known as Ring-LHL. To demonstrate the efficiency of our scheme we provide an optimized implementation of RLWE-based IPFE scheme and show its performance on a practical use case. We further present new compilers that, combined with some existing ones, can transfer a single-input FE to its (identity-based, decentralized) multi-client variant with linear size of the ciphertext (w.r.t the number of clients).
ePrint: https://eprint.iacr.org/2021/046
Talk: https://www.youtube.com/watch?v=WAYwk3Pxzgs
Slides: https://iacr.org/submit/files/slides/2022/pkc/pkc2022/47/slides.pdf
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