ABSTRACT

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.