Homomorphic encryption (HE) ensures data security and privacy in cloud computing by permitting operations on encrypted information without revealing the original data. Reliable high-speed polynomial multiplication is an important operation to build HE and other lattice-based cryptography. There are two approaches in realizing polynomial multiplication:first school book multiplication and NTT-based polynomial multiplication. This paper proposed efficient NTT-based polynomial multiplication using improved folding Barrett modular multiplication (BMM) for Brakerski/Fan-Vercauteren (BFV) HE. We also implemented three types of BMM and integrated them into the polynomial multiplication to see and compare the performance. The result shows our architecture can reach 1.6× faster TPS compared to previous works.

We explore how homomorphic encryption (HE) can be used for secure medical image processing. While the CKKS scheme is the obvious choice because it supports floating-point numbers, it has drawbacks like larger ciphertexts and slower performance compared to the BFV and BGV schemes. BFV and BGV are faster and more efficient, but they can only handle integers, which limits their ability to perform more advanced image processing tasks. To overcome this, we modify the BFV scheme to work with fixed-point arithmetic, allowing it to handle basic real-number calculations. We tested this approach on simple image processing tasks like brightness enhancement, greyscaling, and sharpening filter, showing it can securely process images in the encrypted domain.

Homomorphic encryption (HE) ensures data security and privacy in cloud computing by permitting operations on encrypted information without revealing the original data. However, many of these advances only achieve Partial or Some-what Homomorphic Encryption. Fully Homomorphic Encryption (FHE), which overcomes the number of operation limitations, is being actively researched, with notable schemes like BGV, GSW, and CKKS. Particularly, the CKKS scheme focuses on real and complex number computations but has big parameters requiring many hardware resources. This paper presents an efficient hardware architecture for the number theoretical transform (NTT) 217and an optimized Barrett-based integer modular multiplier to address these challenges. The designs improve the efficiency of polynomial multiplication and modular multiplication processes.