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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.
cryptography, functions, Galois fields, graph theory, interpolation, polynomials,graph-based unified technique, generalized theory, multivariate canonic polynomials, arbitrary finite fields, polarity, computing coefficients, polynomial interpolation, matrix-based techniques, digital systems,Galois fields, Polynomials, Error correction, Finite element methods, Cryptography, Elliptic curve cryptography, Digital systems,Finite or Galois fields, decision diagrams, coefficients, polynomials
"A Graph-Based Unified Technique for Computing and Representing Coefficients over Finite Fields", IEEE Transactions on Computers, vol. 56, no. , pp. 1119-1132, August 2007, doi:10.1109/TC.2007.1060
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