an:06008446
Zbl 1291.12006
Budaghyan, Lilya; Helleseth, Tor
New commutative semifields defined by new PN multinomials
EN
Cryptogr. Commun. 3, No. 1, 1-16 (2011).
00295730
2011
j
12K10 11T71 94A60 51E99
commutative semifield; equivalence of functions; perfect nonlinear; planar function
Summary: We introduce two infinite classes of quadratic PN multinomials over \(\mathbb F_{p^{2k}}\) where \(p\) is any odd prime. We prove that for \(k\) odd one of these classes defines a new family of commutative semifields (in part by studying the nuclei of these semifields). After the works of \textit{L. E. Dickson} [Trans. Am. Math. Soc. 7, 514--522 (1906; JFM 37.0112.01)] and \textit{A. A. Albert} [Trans. Am. Math. Soc. 72, 296--309 (1952; Zbl 0046.03601)], this is the firstly found infinite family of commutative semifields which is defined for all odd primes \(p\). These results also imply that these PN functions are CCZ-inequivalent to all previously known PN mappings.
Reviewer (Berlin)
JFM 37.0112.01; Zbl 0046.03601