An Efficient Method for Comparing Numbers and Determining the Sign of a Number in RNS for Even Ranges

Fully Homomorphic Encryption (FHE) permits processing information in the form of ciphertexts without decryption. It can ensure security common technologies used today, such as cloud computing, Internet Things, and machine learning, among others. A primary disadvantage for its practical application is low efficiency sign comparison operations. Several FHE schemes use Residue Number System (RNS) to decrease time complexity these Converting from RNS positional number system calculating characteristic a are standard approaches both operations domain. In this paper, we propose new method comparing numbers determining RNS. We focus on even ranges that computationally simple due their peculiarities. compare performance several state-of-art algorithms based an implementation C++ relatively moduli with bit depth 24 64 bits. The experimental analysis shows better our approach all test cases; it improves detection between 1.93 15.3 times within 1.55–11.35 respect methods configurations.