Name
Title | ||
|---|---|---|
Highly nonlinear balanced S-boxes with improved bound on unrestricted and generalized nonlinearity |
Abstract | ||
|---|---|---|
We construct two classes of balanced S-boxes with high nonlinearity 2 n-1−2(n-1)/2 for n odd. From known results, it can be deduced that for any S-box which has nonlinearity 2 n-1−2(n-1)/2, the unrestricted nonlinearity is lower bounded by 2 n-1−2(m+n-1)/2 while the generalized nonlinearity is lower bounded by 2 n-1−(2 m −1)2(n-1)/2. We prove that the lower bound on the unrestricted nonlinearity of both our S-box constructions can be increased to 2 n-1−2(m+n)/2-1. For the first class of S-box, the lower bound on generalized nonlinearity can be increased to 2 n-1−2(n-1)/2+m-1. For the second class, the generalized nonlinearity is proven to be exactly 2 n-1−2(m+n)/2-1, which is much higher than the lower bound for our first construction. The first class of S-boxes have low maximum differential while the second class corresponds to GMW sequences, whose algebraic structure allows us to construct a larger family of S-boxes. Moreover, both classes of S-boxes can attain high algebraic degree. We also compare our constructions with some known functions with high unrestricted and/or generalized nonlinearity. |
Year | DOI | Venue |
|---|---|---|
2008 | 10.1007/s00200-008-0067-z | Appl. Algebra Eng. Commun. Comput. |
Keywords | DocType | Volume |
Generalized nonlinearity,Unrestricted nonlinearity,Vectorial Boolean functions,Power functions | Journal | 19 |
Issue | ISSN | Citations |
4 | 0938-1279 | 1 |
PageRank | References | Authors |
0.42 | 20 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Khoongming Khoo | 1 | 250 | 23.29 |
| Chu-Wee Lim | 2 | 73 | 4.76 |
| Guang Gong | 3 | 1717 | 160.71 |