Hardware Design Issues in Elliptic Curve Cryptography for Wireless Systems
Nicolas Sklavos, Xinmiao Zhang · 2017
Coordinates ............................................................................. 122 4.9.1.1 Point Addition-Doubling in Elliptic Curves over GF( p) Fields Using Projective Coordinates ........... 123 4.9.1.2 Point Addition-Doubling in Elliptic Curves over GF(2k) Fields Using Projective Coordinates .............................................................. 125 4.9.1.3 Comparison of EC Point Operations in Affine and Projective Coordinates...................................... 127 4.9.1.4 Design Issues for Elliptic Curve Point Addition and Point Squaring .................................................. 128 4.9.2 Point Multiplication Design Issues ........................................ 129 4.9.2.1 Point Multiplication Design .................................... 132 4.9.2.2 Designing Point Multiplication for SCA Resistant Elliptic Curve Cryptosystems.................. 134 4.10 Elliptic Curve Cryptographic Algorithms for Secure Wireless Systems ............................................................................................. 135 Algorithms ................................................................................................... 137 References.................................................................................................... 145 The immense growth of wireless system applications in today’s communica- tion environment cannot be ignored. Wireless systems are gradually replacing many traditional communication systems because of the increasing need for mobility in high-end technology applications. However, wireless systems remain a relatively new trend in the communication world. A great deal of improvement can still be made to better the functionality of those systems. One still open issue in wireless mobile systems is security. Wireless security is an essential factor for every wireless system. However, the very constrained resource technological environment of a wireless system poses strict limits on the security that such a system can support. Because of this, wireless security in many cases is not considered adequate for enterprise needs. Attempts have already been made to construct a more secure wireless environment by using more recent and efficient cryptographic algorithms. Moreover, this requires an increase in computational performance, power, and memory, factors that are restrictive in wireless systems.