Fully Homomorphic Encryption (FHE) is one of the most promising technologies for privacy protection as it allows an arbitrary number of function computations over encrypted data. However, the computational cost of these FHE systems limits their widespread applications. In this thesis, our objective is to improve the performance of FHE schemes by designing efficient parallel frameworks. In particular, we choose Torus Fully Homomorphic Encryption (TFHE) [1] as it offers exact results for an

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... te number of boolean gate (e.g., AND, XOR) evaluations. We first extend the gate operations to algebraic circuits such as addition, multiplication, and their vector and matrix equivalents. Secondly, we consider the multi-core CPUs to improve the efficiency of both the gate and the arithmetic operations. Finally, we port the TFHE to the Graphics Processing Units (GPU) and device novel optimizations for boolean and arithmetic circuits employing the multitude of cores. We also experimentally analyze both the CPU and GPU parallel frameworks for different numeric representations (16 to 32-bit). Our GPU implementation outperforms the existing technique [1], and it achieves a speedup of 20× for any 32-bit boolean operation and 14.5× for multiplications. ii