Tasel, Faris SerdarSaran, Ayse Nurdan2026-01-052026-01-0520250920-85421573-0484https://doi.org/10.1007/s11227-025-08107-8https://hdl.handle.net/20.500.12416/15791Fully homomorphic encryption (FHE) enables computations to be performed directly on encrypted data without decryption, offering a promising solution for privacy-preserving applications, such as secure cloud computing, confidential machine learning, and encrypted analytics. However, one major drawback of FHE is the high computational cost of homomorphic operations, which slows down real-world implementations, making them impractical. This paper explores the implementation of arithmetic operations within the framework of Torus FHE (TFHE) and demonstrates the construction of gate-level optimization for fundamental operations such as addition, subtraction, negation, comparison, and multiplication on fixed-point numbers. Our work emphasizes optimizing arithmetic logic to reduce the number of bootstrapping operations, a critical factor in improving computational efficiency. Furthermore, we investigate the error rates associated with the proposed operations, providing valuable insight into their accuracy and practical applicability. This study contributes to developing more efficient and reliable arithmetic logic for privacy-preserving computations in FHE systems. The experimental results indicate that the proposed optimizations yield speedups of up to 2.27x for addition/subtraction, 3.55x for comparison, and 1.80x for multiplication operations.eninfo:eu-repo/semantics/closedAccessHomomorphic EncryptionProgrammable BootstrappingBoolean CircuitFixed-Point ArithmeticArticle10.1007/s11227-025-08107-82-s2.0-105024189364