dc.contributor.author | Budaghyan, Lilya | |
dc.contributor.author | Carlet, Claude | |
dc.contributor.author | Helleseth, Tor | |
dc.contributor.author | Kaleyski, Nikolay Stoyanov | |
dc.date.accessioned | 2021-05-27T13:07:55Z | |
dc.date.available | 2021-05-27T13:07:55Z | |
dc.date.created | 2021-01-19T11:19:50Z | |
dc.date.issued | 2020 | |
dc.Published | IEEE Transactions on Information Theory. 2020, 66 (9), 5742-5753. | |
dc.identifier.issn | 0018-9448 | |
dc.identifier.uri | https://hdl.handle.net/11250/2756701 | |
dc.description.abstract | We investigate the differential properties of a vectorial Boolean function G obtained by modifying an APN function F . This generalizes previous constructions where a function is modified at a few points. We characterize the APN-ness of G via the derivatives of F, and deduce an algorithm for searching for APN functions whose values differ from those of F only on a given set U ⊆ F 2n . We introduce a value Π F associated with any F, which is invariant under CCZ-equivalence. We express a lower bound on the distance between a given APN function F and the closest APN function in terms of Π F . We show how Π F can be computed efficiently for F quadratic. We compute Π F for all known APN functions over F 2n . up to n ≤ 8. his is the first new CCZ-invariant for APN functions to be introduced within the last ten years. We derive a mathematical formula for this lower bound for the Gold function F (x) = x 3 , and observe that it tends to infinity with n. Finally, we describe how to efficiently find all sets U such that, taking G(x) = F (x) + v for x ∈ U and G(x) = F (x) for x ∉ U,G(x) is APN. | en_US |
dc.language.iso | eng | en_US |
dc.publisher | IEEE | en_US |
dc.title | On the Distance Between APN Functions | en_US |
dc.type | Journal article | en_US |
dc.type | Peer reviewed | en_US |
dc.description.version | acceptedVersion | en_US |
dc.rights.holder | Copyright 2020 IEEE | en_US |
cristin.ispublished | true | |
cristin.fulltext | postprint | |
cristin.qualitycode | 2 | |
dc.identifier.doi | https://doi.org/10.1109/TIT.2020.2983684 | |
dc.identifier.cristin | 1874120 | |
dc.source.journal | IEEE Transactions on Information Theory | en_US |
dc.source.40 | 66 | |
dc.source.14 | 9 | |
dc.source.pagenumber | 5742-5753 | en_US |
dc.identifier.citation | IEEE Transactions on Information Theory. 2020, 66(9), 5742-5753 | en_US |
dc.source.volume | 66 | en_US |
dc.source.issue | 9 | en_US |