Research Of The Curve And Base Point Choosing Of Elliptic Curve

With the rapid development and wide application of computer networks and communication technology, especially since1993, when the Internet began to commercialize, the type and quantity of e-business developed by the Internet is gradually increasing, so well as the information communication, as the result the process of the society information has been improved deeper and deeper, all these have brought great convenience to people’s daily lives and work, but the issues of security in the network information becomes increasingly prominent when people are enjoying these benefits and convenient brought by the information technology. In fact, the network information security is not only related with the processing of personal information, but has a important influence of national political stability, social stability, the global nature of the orderly operation of the economy, state secrets, military programs etc.The most basic and original function of cryptography is to guarantee security of information. Of all the cryptographic techniques, the elliptic curve had draw much attention of domestic and foreign scholars because of its short in the length of the key, high security strength of per-bit, well performance in flexibility, etc.In this paper, the author mainly discussed the curve and the point choosing algorithm of the elliptic curve on binary field, firstly he gave the analyses of the present curve and point choosing algorithms, and then proposed improved algorithms with the parallelize method, lastly gave the algorithm analysis, the main work is as follows:(1) On the curve choosing, firstly the author gave the computing performance and safety analysis of the two curve selection algorithms, which are the complex multiplication and random selection method, and perorated that though the curve complex multiplication has some certain potential security problem, but this would has been able to meet the general safety requirements, and besides, it has a greater advantage in computational complexity compare to the random choosing method. To the binary fields, the hardware implementation is much easier, therefore, the author finds out the fixed-order choosing algorithm of the curve using the idea of complex multiplication method of selecting and improved this method with parallel method. This method is based on the operations of the binary field, and finally gives the performance and safety analysis of the improved algorithm.(2) On the choosing of base point, the author firstly improves the existing algorithm of the algorithm of base point choosing on the binary field, and then together with the idea of parallelization, proposes a parallel algorithm of point choosing of elliptic curve, The present algorithm has not only reduced the time complexity, but also simplify the computational complexity of the original algorithm.These algorithms on the binary field, not only have a lower complexity, but have a easier hardware implementation compared to the algorithm on the prime field, so the improvements of elliptic curve algorithm on binary field have an important significant in the implement of fast ECC encryption and decryption algorithm, especially has a great advantages for those systems or applications environment with limited computing performance or safety performance, such as wireless sensor networks and RFID, IoT system.