Efficient Lattice-Based Inner-Product Functional Encryption

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).

cuFE: High Performance Privacy Preserving Support Vector Machine With Inner-Product Functional Encryption

“…Our fundamental motivation behind this work was to investigate efficient alternatives to mainstream privacy-preserving COED techniques such as FE and HE. We found that the RLWE-IPFE [MKMS22] scheme suits for the greatest part of our purpose. In this paper, we present cuFE, the first parallel implementation of the above mentioned RLWE-IPFE scheme on a graphics processing unit (GPU).…”

“…Similar to the MPC and HE techniques, FE or IPFE techniques are also computationally demanding and improving the efficiency of IPFE schemes is still an open problem to be solved. A recent work [MKMS22] has tried to address this issue by designing an IPFE scheme based on Ring-Learning with Errors (RLWE) [LPR10]. The main advantage here is the relatively shorter keys and possibility of using faster number theoretic transform (NTT) [Pol71] based polynomial multiplications.…”

“…We analyze the performance bottlenecks and identify the opportunities in parallelizing various computational components. We explore different parallelization techniques (coarse-grain and fine-grain) to speed up the RLWE-IPFE scheme [MKMS22]. We are the first to show how these computational components can be efficiently mapped to different independent computing units in a parallel computing platform, which in our case is a GPU.…”

Efficient Lattice-Based Ring Signature Scheme without Trapdoors for Machine Learning

“…In the postquantum era, the new cryptosystem based on lattice has become a focus of research due to its merits of high asymptotic efficiency, simple operation, parallelizability, resistance to quantum attacks, and enjoying the average-to-worst reduction. e development of latticebased provably secure encryption has developed rapidly and has made great progress [14][15][16][17][18], while lattice-based digital signature has experienced a tortuous and bumpy process in the earlier years. First, Goldreich et al [19] made an attempt at a lattice-based signature, then NTRU signature was proposed by Hoffstein et al [20], and it was repaired and enhanced in [21,22].…”

Flexible and Parallel Architectures for Optimal Ate pairing on FPGA

“…The widespread use of pairing functions in cryptography emerged in the early 2000s after Joux introduced the tripartite key exchange scheme for Diffie-Hellman [15]. Since then, pairing functions have been implemented in a variety of advanced cryptosystems including identity-based signatures [16], searchable encryption [17], and functional encryption [18]. One of the most prominent applications of pairing functions is the Identity-Based Encryption (IBE) [19] proposed by Boneh and Franklin. Pairing functions, which are used in cryptography, are typically constructed using a combination of the Miller Loop and Final Exponentiation.…”