| Given a set of data over a finite field Fq, we are interested in finding a function that interpolates this data. This function can be obtained using reverse engineering. Such a function is of the form: f = (f1, f2, ..., fn) : Fqn→Fq n , where Fqn is the n-fold Cartesian product of a finite field with q elements, and fi ∈ Fq[x1,...,xn]. In applying these methods, a key question arises: Can we write fi in terms of xj?;Using a version of Sasao's Algorithm developed by D. Bollman and E. Orozco we can produce a minimal basis X with no redundant variables. Using X and The Chinese Remainder Algorithm, an alternative to the interpolation formula presented in [11], we find a particular solution f0 that interpolates the data in terms of xj and the variables of X . Later, we compute the ideal I of all solutions that vanish on the data, and, using elimination theory, we obtain the reduction f of f0 with respect to I∩FqX, xj . |
