Design and Analysis of RSA and Paillier Homomorphic Cryptosystems Using PSO-Based Evolutionary Computation

Non-lattice based homomorphic encryption schemes usually involve huge modular exponentiation operations. Thus, improving the efficiency of modular exponentiation for large exponents is a real-world issue. Modular exponentiation can be computed by a series of modular multiplications. However, performing a series of modular multiplications is computationally expensive. This paper proposes hardware /software co-design for efficient modular exponentiation. This article first explores the use of particle swarm optimization (PSO) for the modular exponentiation in software, and present an efficient hardware co-design utilizing FPGA. Our findings reveal that the suggested PSO approach surpasses all other deterministic and non-deterministic approaches already in use. Further, we also demonstrate a comprehensive analysis for the optimal performance and parameter selection of our proposed PSO approach. Finally, we implement homomorphic encryption schemes, such as RSA and Paillier, using our PSO-based hardware /software co-design. Our approach gains resource savings for 1024-bit as follows: RSA encryption/decryption - 60.7% (area) and 65.3% (DSP); Paillier encryption - 46.3% (area) and 40% (DSP) and Paillier decryption - 73.7% (area) and 66.6% (DSP). We have obtained area-time improvements of 1024-bit as follows: RSA encryption/decryption - 2.7x; Paillier encryption - 2x and Paillier decryption - 4.6x using Xilinx Virtex-7 FPGAs.