Homomorphic encryption (HE) is a foundational technology in privacy-enhancing cryptography, enabling computation over encrypted data. Recently, generalized HE primitives designed for multi-party applications, such as multi-party HE (MPHE), have garnered significant research interest. While constructing secure multi-party protocols from MPHE in the semi-honest model is straightforward, achieving malicious security remains challenging as it requires zero-knowledge arguments of knowledge (ZKAoKs) for MPHE ciphertexts and public keys.

Homomorphic encryption (FHE) enables the computation of arbitrary circuits over encrypted data. A widespread application of HE is oblivious circuit evaluation, where a sender evaluates its private circuit over a receiver's encrypted data, covering scenarios such as oblivious inference and oblivious PRF protocols. However, while the security of HE guarantees the receiver's privacy against the sender, the privacy of the sender's circuit is not solely derived from the security of HE.

The SPDZ protocol family is a popular choice for secure multi-party computation (MPC) in a dishonest majority setting with active adversaries. Over the past decade, a series of studies have focused on improving its offline phase, where special additive shares called authenticated triples are gener-ated. However, to accommodate recent demands for matrix operations in secure machine learning and big integer arith-metic in distributed RSA key generation, updates to the offline phase are required. In this work, we propose a new protocol for the SPDZ offline phase, MatriGear, which improves upon the previous state-of-the-art construction, TopGear (Baum et al., SAC '19), and its variant for matrix triples (Chen et al., Asiacrypt '20). Our protocol aims to achieve a speedup in matrix triple generation and support for larger prime fields up to 4096 bits in size. To achieve this, we devise a variant of the BFV scheme and a new homomorphic matrix multiplication algorithm optimized for our purpose. As a result, our protocol achieves about 3.6x speedup for generating scalar triples in a 1024-bit prime field and about 34x speedup for generating 128x128 matrix triples. In addition, we reduce the size of evaluation keys from 27.4 GB to 0.22 GB and the communication cost for MAC key generation from 816 MB to 16.6 MB.

Bootstrapping is currently the only known method for constructing fully homomorphic encryptions. In the BFV scheme specifically, bootstrapping aims to reduce the error of a ciphertext while preserving the encrypted plaintext. The existing BFV bootstrapping methods follow the same pipeline, relying on the evaluation of a digit extraction polynomial to annihilate the error located in the least significant digits. However, due to its strong dependence on performance, bootstrapping could only utilize a limited form of plaintext modulus, such as a power of a small prime number.

Statistical analysis of largescale data is useful as it enables the extraction of a large amount of information, despite its simplicity. Therefore, fusing and analyzing data from different security domains is an attractive and promising approach, unless it jeopardizes the privacy of the data in any security domain. In this study, we proposed the HEaaN-STAT toolkit that can efficiently fuse data from different domains to enable largescale statistical analysis while protecting data privacy. Moreover, we proposed an efficient inverse operation and a table lookup function for Cheon-Kim-Kim-Song (CKKS) encrypted data, as well as a data encoding method for counting encrypted data. Based on this, we proposed a method for generating a contingency table with a large number of cases and k-percentile for largescale data that is hundreds to thousands of times faster than the method proposed by Lu et al. in NDSS’17. The validity of the proposed toolkit was verified through practical use for business applications using real-world data.

Fully Homomorphic Encryption over the Torus (TFHE) is a homomorphic encryption scheme which supports efficient Boolean operations over encrypted bits. TFHE has a unique feature in that the evaluation of each binary gate is followed by a bootstrapping procedure to refresh the noise of a ciphertext. In particular, this gate bootstrapping involves two algorithms called the blind rotation and key-switching.

Homomorphic Encryption (HE) is a cryptosytem that allows us to perform an arbitrary computation on encrypted data. The standard HE, however, has a disadvantage in that the authority is concentrated in the secret key owner since computations can only be performed on ciphertexts encrypted under the same secret key. To resolve this issue, research is underway on Multi-Key Homomorphic Encryption (MKHE), which is a variant of HE supporting computations on ciphertexts possibly encrypted under different keys. Despite its ability to provide privacy for multiple parties, existing MKHE schemes suffer from poor performance due to the cost of multiplication which grows at least quadratically with the number of keys involved.