Abstract
This paper presents a configuration of parallel multipliers for GF (2 m ) based on canonical bases. The possible parallel multipliers by the proposed configuration are limited to a class of fields GF (2 m ). However they can be constructed by O(m 2 ) AND-gates and O(m 2 ) EOR-gates with the structural modularity (this is a desirable feature for the hardware implementation), and their operation time is about (log m ) T , where m is the dimension of GF (2 m ) and T is the delay time of an EOR-gate. In order to construct such parallel multipliers, we define two types of polynomials of special form over GF (2), one is called all one polynomial (denoted by AOP) and the other is called equally spaced polynomial (denoted by ESP). Furthermore, we show a necessary and sufficient condition for ESPs to be irreducible over GF (2) and the uniqueness of the irreducible ESPs over GF (2). Finally, we propose the configuration of parallel multipliers for a class of fields GF (2 m ) based on irreducible AOPs and ESPs over GF (2).
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
