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This paper proposes an implementation model for finite fields GF[mq], m prime, based on a hybrid architecture that integrates symbolic programming developed in Mathematica with an imperative C language module. Its aim is to enable the user to write algorithms to perform calculations in GF's by using Mathematica's programming language and built-in math functions. First, the system's architecture is presented and it is shown that the proposed model has linear time complexity (O(q)) for all algebraic operations. Finally, we show the developed modules for the computation of exponential sums and the solution of equations over finite fields.
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