An Improved Implementation of Elliptic Curve Cryptography Algorithm Based on Residue Number System and GPU

Elliptic curve cryptography with reliable security uses a small key length in comparing with other asymmetric cryptosystems. Despite the heavy load of encryption and decryption operations, finding a suitable implementation for it has been an important research challenge in this field. In this way using of Residue Number System (RNS) as a tool for converting sequential computations of Elliptic Curve Cryptography (ECC) algorithm to a large number of parallel processes to run on graphics processing unit (GPU) can be useful. In this paper, we focus on efficient implementation of point multiplication algorithm that is main operation in ECC process. In this direction, the RNS-based Montgomery Ladder algorithm is implemented using compute unified device architecture (CUDA) programming language which provides the possibility of sending and executing instructions on the GPU. Besides, efficient implementation of point multiplication algorithm used in Elliptic curve cryptography based on RNS and GPU parallelization techniques is presented. The proposed implementation on average achieved speedup of 1.78 compared with previous implementation

Keywords:

Elliptic Curve Cryptography , Residue Number System , Montgomery Ladder , GPU