Enhancing FHE Over the Integers: Beyond Binary Numbers and Batch Processing

Fully Homomorphic Encryption (FHE) schemes enable secure computations on encrypted data. Following Gentry’s groundbreaking result, the AGCD problem-based FHE scheme, also known as Fully Homomorphic Encryption over the Integers (FHE-OI), was introduced by Dijk et al. Over the time, several improvements have been made to FHE-OI, including the CS scheme proposed by Cheon and Stehlé. This paper presents two significant enhancements to CS scheme. The first contribution involves extending their FHE scheme to support message space \(\mathbb {Z}_g\) , removing the previous constraint limited to binary numbers as described in Cheon and Stehlé’s work. Building upon this advancement, the second enhancement further extends the scheme to encompass batch fully homomorphic encryption. This extension empowers the scheme to efficiently encrypt and perform homomorphic operations on entire vectors of plaintext bits using a single ciphertext, thereby enhancing its applicability and utility in various practical scenarios.