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- W6553417 abstract "We introduce two infinite families of perfect nonlinear Dembowski-Ostrom multinomials over $textbf{F}_{p^{2k}}$ where p is any odd prime. We prove that in general these functions are CCZ-inequivalent to previously known PN mappings. One of these families has been constructed by extension of a known family of APN functions over $textbf{F}_{2^{2k}}$ . This shows that known classes of APN functions over fields of even characteristic can serve as a source for further constructions of PN mappings over fields of odd characteristics. Besides, we supply results indicating that these PN functions define new commutative semifields. After the works of Dickson (1906) and Albert (1952), these are the firstly found infinite families of commutative semifields which are defined for all odd primes p." @default.
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- W6553417 date "2008-09-11" @default.
- W6553417 modified "2023-10-14" @default.
- W6553417 title "New Perfect Nonlinear Multinomials over F $_{p^{2k}}$ for Any Odd Prime p" @default.
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- W6553417 doi "https://doi.org/10.1007/978-3-540-85912-3_35" @default.
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