Biblio

With the increasing awareness of privacy protection and data security, people’s concerns over the confidentiality of sensitive data still limit the application of distributed artificial intelligence. In fact, a new encryption form, called homomorphic encryption(HE), has achieved a balance between security and operability. In particular, one of the HE schemes named Paillier has been adopted to protect data privacy in distributed artificial intelligence. However, the massive computation of modular multiplication in Paillier greatly affects the speed of encryption and decryption. In this paper, we propose a fast CRT-Paillier scheme to accelerate its decryption process. We first introduce the Montgomery algorithm to the CRT-Paillier to improve the process of the modular exponentiation, and then compute the modular exponentiation in parallel by using OpenMP. The experimental results show that our proposed scheme has greatly heightened its decryption speed while preserving the same security level. Especially, when the key length is 4096-bit, its speed of decryption is about 148 times faster than CRT-Paillier.

Modular exponentiation of large number is widely applied in public-key cryptosystem, also the bottleneck in the computation of public-key algorithm. Modular multiplication is the key calculation in modular exponentiation. An improved Montgomery algorithm is utilized to achieve modular multiplication and converted into systolic array to increase the running frequency. A high efficiency fast modular exponentiation structure is developed to bring the best out of the modular multiplication module and enhance the ability of defending timing attacks and power attacks. For 1024-bit key operands, the design can be run at 170MHz and finish a modular exponentiation in 4,402,374 clock cycles.