Parallel implementations of somewhat homomorphic encryption based on Open-MP and CUDA

By using Homomorphic Encryption scheme, the Cloud can compute on encrypted data without any need of decryption and compromising privacy. However, this cryptography system requires a high delay due to lots of computations. In this paper, we present the first parallel implementations of somewhat homomorphic encryption scheme over integers using Open-MP and CUDA programming to reduce the time duration. The experimental results showed that software implementation using Open-MP can achieve speed improvement of 1.67, 1.87 and 8.63 in key generation algorithm, encryption and evaluation, respectively, in comparison to serial implementation on the processor. On other side, we used residue number system to achieve an efficient parallel implementation of somewhat homomorphic cryptography on GPU using CUDA. The results showed a significant speed improvement of 1.72 and 77.78 in encryption and evaluation algorithms, respectively.