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GfXpress: A Technique for Synthesis and Optimization of \hbox {GF}(2^{m}) Polynomials

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3 Author(s)
Abusaleh M. Jabir ; Oxford Brookes Univ., Oxford ; Dhiraj K. Pradhan ; Jimson Mathew

This paper presents an efficient technique for synthesis and optimization of the polynomials over GF(2m), where to is a nonzero positive integer. The technique is based on a graph-based decomposition and factorization of the polynomials, followed by efficient network factorization and optimization. A technique for efficiently computing the coefficients of the polynomials over GF(pm), where p is a prime number, is first presented. The coefficients are stored as polynomial graphs over GF(pm). The synthesis and optimization is initiated from this graph-based representation. The technique has been applied to minimize multipliers over the fields GF(2k), where k = 2,...,8, generated with all the 51 primitive polynomials in the 0.18-mum CMOS technology with the help of the Synopsys design compiler. It has also been applied to minimize combinational exponentiation circuits, parallel integer adders and multipliers, and other multivariate bit- as well as word-level polynomials. The experimental results suggest that the proposed technique can reduce area, delay, and power by significant amounts. We also observed that the technique is capable of producing 100% testable circuits for stuck-at faults.

Published in:

IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems  (Volume:27 ,  Issue: 4 )