International Association for Cryptologic Research

International Association
for Cryptologic Research

CryptoDB

Andrey Kim

ORCID: 0000-0002-0974-6787

Publications

Year
Venue
Title
2024
CRYPTO
Exploring the Advantages and Challenges of Fermat NTT in FHE Acceleration
Recognizing the importance of a fast and resource-efficient polynomial multiplication in homomorphic encryption, in this paper, we design a \emph{multiplier-less} number theoretic transform using a Fermat number as an auxiliary modulus. To make this algorithm scalable with the degree of polynomial, we apply a univariate to multivariate polynomial ring transformation. We develop an accelerator architecture for fully homomorphic encryption using these algorithmic techniques for efficient multivariate polynomial multiplication. For practical homomorphic encryption application benchmarks, the hardware accelerator achieves a 1,200$\times$ speed-up compared to software implementations. Finally, we conclude the paper by discussing the advantages and limitations of the proposed polynomial multiplication method.
2023
EUROCRYPT
Efficient FHEW Bootstrapping with Small Evaluation Keys, and Applications to Threshold Homomorphic Encryption
There are two competing approaches to bootstrap the FHEW fully homomorphic encryption scheme (Ducas and Micciancio, Eurocrypt 2015) and its variants: the original AP/FHEW method, which supports arbitrary secret key distributions, and the improved GINX/TFHE method, which uses much smaller evaluation keys, but is directly applicable only to binary secret keys, restricting the scheme's applicability. In this paper, we present a new bootstrapping procedure for FHEW-like encryption schemes that achieves the best features of both methods: support for arbitrary secret key distributions at no additional runtime costs, while using small evaluation keys. (Support for arbitrary secret keys is critical in a number of important applications, like threshold and some multi-key homomorphic encryption schemes.) As an added benefit, our new bootstrapping procedure results in smaller noise growth than both AP and GINX, regardless of the key distribution. Our improvements are both theoretically significant (offering asymptotic savings, up to a $O(log n)$ multiplicative factor, either on the running time or public evaluation key size), and practically relevant. For example, for a concrete 128-bit target security level, we show how to decrease the evaluation key size of the best previously known scheme by more than 30\%, while also slightly reducing the running time. We demonstrate the practicality of the proposed methods by building a prototype implementation within the PALISADE/OpenFHE open-source homomorphic encryption library. We provide optimized parameter sets and implementation results showing that the proposed algorithm has the best performance among all known FHEW bootstrapping methods in terms of runtime and key size. We illustrate the benefits of our method by sketching a simple construction of threshold homomorphic encryption based on FHEW.
2022
CRYPTO
A New Approach to Efficient Non-Malleable Zero-Knowledge 📺
Non-malleable zero-knowledge, originally introduced in the context of man-in-the-middle attacks, serves as an important building block to protect against concurrent attacks where different protocols may coexist and interleave. While this primitive admits almost optimal constructions in the plain model, they are several orders of magnitude slower in practice than standalone zero-knowledge. This is in sharp contrast to non-malleable commitments where practical constructions (under the DDH assumption) have been known for a while. We present a new approach for constructing efficient non-malleable zero-knowledge for all languages in NP, based on a new primitive called instance-based non-malleable commitment (IBNMC). We show how to construct practical IBNMC by leveraging the fact that simulators of sub-linear zero-knowledge protocols can be much faster than the honest prover algorithm. With an efficient implementation of IBNMC, our approach yields the first general-purpose non-malleable zero-knowledge protocol that achieves practical efficiency in the plain model. All of our protocols can be instantiated from symmetric primitives such as block-ciphers and hash functions, have reasonable efficiency in practice, and are general-purpose. Our techniques also yield the first efficient non-malleable commitment scheme without public-key assumptions.
2021
ASIACRYPT
Revisiting Homomorphic Encryption Schemes for Finite Fields 📺
The Brakerski-Gentry-Vaikuntanathan (BGV) and Brakerski/ Fan-Vercauteren (BFV) schemes are the two main homomorphic encryption (HE) schemes to perform exact computations over finite fields and integers. Although the schemes work with the same plaintext space, there are significant differences in their noise management, algorithms for the core homomorphic multiplication operation, message encoding, and practical usability. The main goal of our work is to revisit both schemes, focusing on closing the gap between the schemes by improving their noise growth, computational complexity of the core algorithms, and usability. The other goal of our work is to provide both theoretical and experimental performance comparison of BGV and BFV. More precisely, we propose an improved variant of BFV where the encryption operation is modified to significantly reduce the noise growth, which makes the BFV noise growth somewhat better than for BGV (in contrast to prior results showing that BGV has smaller noise growth for larger plaintext moduli). We also modify the homomorphic multiplication procedure, which is the main bottleneck in BFV, to reduce its algorithmic complexity. Our work introduces several other novel optimizations, including lazy scaling in BFV homomorphic multiplication and an improved BFV decryption procedure in the Residue Number System (RNS) representation. We also develop a usable variant of BGV as a more efficient alternative to BFV for common practical scenarios. We implement our improved variants of BFV and BGV in PALISADE and evaluate their experimental performance for several benchmark computations. The experimental results suggest that our BGV implementation is faster for intermediate and large plaintext moduli, which are often used in practical scenarios with ciphertext packing, while our BFV implementation is faster for small plaintext moduli. More precisely, we propose an improved variant of BFV where the encryption operation is modified to significantly reduce the noise growth, which makes the BFV noise growth somewhat better than for BGV (in contrast to prior results showing that BGV has smaller noise growth for larger plaintext moduli). We also modify the homomorphic multiplication procedure, which is the main bottleneck in BFV, to reduce its algorithmic complexity. Our work introduces several other novel optimizations, including lazy scaling in BFV homomorphic multiplication and an improved BFV decryption procedure in the Residue Number System (RNS) representation. We also develop a usable variant of BGV as a more efficient alternative to BFV for common practical scenarios. We implement our improved variants of BFV and BGV in PALISADE and evaluate their experimental performance for several benchmark computations. Our results suggest that BGV is faster for intermediate and large plaintext moduli, which are often used in practical scenarios with ciphertext packing, while BFV is faster for small plaintext moduli.
2018
EUROCRYPT
2017
ASIACRYPT