Abstract
Multivariate Public key cryptosystems are widely spread and ever evolving domain. This study aims to find new techniques to characterize and detect permutation polynomials over finite fields, which enable us to find trapdoor, one way, functions that are essential to build robust cryptosystems. Let \(f\) be a polynomial over \(F_{q}\), a finite field of order \(q\), where \(q = p^{m}\), \(p\) is a prime number. If \(f\) induces a bijective mapping, one-to-one mapping, of \(F_{q}\), we call \(f\) a permutation polynomial over \(F_{q}\). In order to detect these polynomials, we constructed a program implementing multiple algorithms based on Galois field arithmetic. As a result, we have the number of all possible permutation polynomials in the fields \( F_{4}\), \(F_{8}\) and \(F_{16}\).
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Gharibah, M. (2014). On the Detection of Permutation Polynomials . In: Makhlouf, A., Paal, E., Silvestrov, S., Stolin, A. (eds) Algebra, Geometry and Mathematical Physics. Springer Proceedings in Mathematics & Statistics, vol 85. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-55361-5_39
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DOI: https://doi.org/10.1007/978-3-642-55361-5_39
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