Abstract
It is known that a bent function corresponds to a perfect nonlinear function, which makes it difficult to do the differential cryptanalysis in DES and in many other block ciphers. In this paper, for an odd prime p, quadratic p-ary bent functions defined on finite fields are given from the families of p-ary sequences with optimal correlation property. And quadratic p-ary bent functions, that is, perfect nonlinear functions from the finite field Fp m to its prime field F p are constructed by using the trace functions.
This work was supported in part by BK21 and ITRC program of the Korean Ministry of Information and Communications and the Norwegian Research Council.
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Kim, YS., Jang, JW., No, JS., Helleseth, T. (2003). On P-Ary Bent Functions Defined on Finite Fields. In: No, JS., Song, HY., Helleseth, T., Kumar, P.V. (eds) Mathematical Properties of Sequences and Other Combinatorial Structures. The Springer International Series in Engineering and Computer Science, vol 726. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-0304-0_8
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