A Graph-Based Unified Technique for Computing and Representing Coefficients over Finite Fields
A Graph-Based Unified Technique for Computing and Representing Coefficients over Finite Fields
复制标题
一种基于图的有限域系数计算和表示统一技术
DOI：
10.1109/tc.2007.1060
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发表时间：
2007
影响因子：
3.7
通讯作者：
D. Pradhan
中科院分区：
文献类型：
--
作者：
A. Jabir;D. Pradhan
本文给出了任意极性有限域上多元正则多项式系数的计算和表示的一般理论和一种有效的基于图的方法。提出的计算系数的技术是不同的多项式插值或基于矩阵的技术，并考虑到有效的图形为基础的形式，可以作为现有的资源，在合成，验证，或模拟的数字系统。还提出了用于优化用于表示系数的基于图的形式的技术。对于较大的字段，算法的效率增加。作为一个测试案例，所提出的技术已被应用到GF（2m）上的基准电路。实验结果表明，该技术可以显着加快执行时间。
This paper presents the generalized theory and an efficient graph-based technique for the calculation and representation of coefficients of multivariate canonic polynomials over arbitrary finite fields in any polarity. The technique presented for computing coefficients is unlike polynomial interpolation or matrix-based techniques and takes into consideration efficient graph-based forms which can be available as an existing resource during synthesis, verification, or simulation of digital systems. Techniques for optimization of the graph-based forms for representing the coefficients are also presented. The efficiency of the algorithm increases for larger fields. As a test case, the proposed technique has been applied to benchmark circuits over GF(2m). The experimental results show that the proposed technique can significantly speed up execution time.