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.