Bundles, presemifields and nonlinear functions |
| |
Authors: | K J Horadam D G Farmer |
| |
Institution: | 1. RMIT University, Melbourne, VIC, 3001, Australia
|
| |
Abstract: | Bundles are equivalence classes of functions derived from equivalence classes of transversals. They preserve measures of resistance to differential and linear cryptanalysis. For functions over GF(2 n ), affine bundles coincide with EA-equivalence classes. From equivalence classes (“bundles”) of presemifields of order p n , we derive bundles of functions over GF(p n ) of the form λ(x)*ρ(x), where λ, ρ are linearised permutation polynomials and * is a presemifield multiplication. We prove there are exactly p bundles of presemifields of order p 2 and give a representative of each. We compute all bundles of presemifields of orders p n ≤ 27 and in the isotopism class of GF(32) and we measure the differential uniformity of the derived λ(x)*ρ(x). This technique produces functions with low differential uniformity, including PN functions (p odd), and quadratic APN and differentially 4-uniform functions (p = 2). |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|