Duhyeong Kim

We present a new and efficient method to obtain circuit privacy for lattice-based linearly homomorphic encryptions (LHE). In particular, our method does not involve noise-flooding with superpolynomially large errors or iterative bootstrapping. As a direct result, we obtain a semi-honest oblivious linear evaluation (OLE) protocol with the same efficiency, reducing the communication cost of the prior state of the art by 50%. Consequently, the amortized time of our protocol improves upon the prior work by 33% under a 100Mbps network setting. Our semi-honest OLE is the first to achieve both concrete efficiency and asymptotic quasi-optimality.

Fully Homomorphic Encryption (FHE) is a cryptographic primitive that allows performing arbitrary operations on encrypted data. Since the conception of the idea in [RAD78], it has been considered a holy grail of cryptography. After the first construction in 2009 [Gen09], it has evolved to become a practical primitive with strong security guarantees. Most modern constructions are based on well-known lattice problems such as Learning With Errors (LWE). Besides its academic appeal, in recent years FHE has also attracted significant attention from industry, thanks to its applicability to a considerable number of real-world use-cases. An upcoming standardization effort by ISO/IEC aims to support the wider adoption of these techniques. However, one of the main challenges that standards bodies, developers, and end users usually encounter is establishing parameters. This is particularly hard in the case of FHE because the parameters are not only related to the security level of the system, but also to the type of operations that the system is able to handle. In this paper we provide examples of parameter sets for LWE targeting particular security levels, that can be used in the context of FHE constructions. We also give examples of complete FHE parameter sets, including the parameters relevant for correctness and performance, alongside those relevant for security. As an additional contribution, we survey the parameter selection support offered in open-source FHE libraries.

A prevalent issue in the residue number system (RNS) variant of the Cheon-Kim-Kim-Song (CKKS) homomorphic encryption (HE) scheme is the challenge of efficiently achieving high precision on hardware architectures with a fixed, yet smaller, word-size of bit length W , especially when the scaling factor satisfies log Δ > W In this work, we introduce an efficient solution termed composite scaling. In this approach, we group multiple RNS primes as ql :=Π t-1 j=0 ql,j such that logql,j< W for 0 ≤ j < t, and use each composite ql in the rescaling procedure as ct →→ [ct/ql]. This strategy contrasts the traditional rescaling method in RNS-CKKS, where each ql is chosen as a single log Δ-bit prime, a method we designate as single scaling To achieve higher precision in single scaling, where log Δ > W , one would either need a novel hardware architecture with word size W' > log Δ or would have to resort to relatively inefficient solutions rooted in multi-precision arithmetic. This problem, however, doesn't arise in composite scaling. In the composite scaling approach, the larger the composition degree t, the greater the precision attainable with RNS-CKKS across an extensive range of secure parameters tailored for workload deployment. We have integrated composite scaling RNS-CKKS into both OpenFHE and Lattigo libraries. This integration was achieved via a concrete implementation of the method and its application to the most up-to-date workloads, specifically, logistic regression training and convolutional neural network inference. Our experiments demonstrate that single and composite scaling approaches are functionally equivalent, both theoretically and practically