TY - JOUR UR - http://lib.ugent.be/catalog/pug01:535261 ID - pug01:535261 LA - eng TI - A new almost perfect nonlinear function which is not quadratic PY - 2009 JO - (2009) Advances in Mathematics of Communications SN - 1930-5346 PB - 2009 AU - Edel, Daniel UGent 802000229705 AU - Pott, Alexander AB - Following an example in [12], we show how to change one coordinate function of an almost perfect nonlinear (APN) function in order to obtain new examples. It turns out that this is a very powerful method to construct new APN functions. In particular, we show that our approach can be used to construct a "non-quadratic" APN function. This new example is in remarkable contrast to all recently constructed functions which have all been quadratic. An equivalent function has been found independently by Brinkmann and Leander [8]. However, they claimed that their function is CCZ equivalent to a quadratic one. In this paper we give several reasons why this new function is not equivalent to a quadratic one. ER -Download RIS file
00000nam^a2200301^i^4500 | |||
001 | 535261 | ||
005 | 20180813143430.0 | ||
008 | 090331s2009------------------------eng-- | ||
022 | a 1930-5346 | ||
024 | a 000263354000006 2 wos | ||
024 | a 1854/LU-535261 2 handle | ||
024 | a 10.3934/amc.2009.3.59 2 doi | ||
040 | a UGent | ||
245 | a A new almost perfect nonlinear function which is not quadratic | ||
260 | c 2009 | ||
520 | a Following an example in [12], we show how to change one coordinate function of an almost perfect nonlinear (APN) function in order to obtain new examples. It turns out that this is a very powerful method to construct new APN functions. In particular, we show that our approach can be used to construct a "non-quadratic" APN function. This new example is in remarkable contrast to all recently constructed functions which have all been quadratic. An equivalent function has been found independently by Brinkmann and Leander [8]. However, they claimed that their function is CCZ equivalent to a quadratic one. In this paper we give several reasons why this new function is not equivalent to a quadratic one. | ||
598 | a A1 | ||
100 | a Edel, Daniel u UGent 0 802000229705 0 822000229770 | ||
700 | a Pott, Alexander | ||
650 | a Mathematics and Statistics | ||
773 | t Advances in Mathematics of Communications g Adv. Math. Commun. 2009. 3 (1) p.59-81 q 3:1<59 | ||
856 | 3 Full Text u https://biblio.ugent.be/publication/535261/file/536262 z [ugent] y Edel.pdf | ||
920 | a article | ||
852 | x WE b WE01 | ||
922 | a UGENT-WE |
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