Name
Title | ||
|---|---|---|
New Construction for Balanced Boolean Functions with Very High Nonlinearity*Parts of this paper was presented at the Australasian Conference on Information Security and Privacy 2003. |
Abstract | ||
|---|---|---|
In the past twenty years, there were only a few constructions for Boolean functions with nonlinearity exceeding the quadratic bound 2n-1 - 2(n-1)/2 when n is odd (we shall call them Boolean functions with very high nonlinearity). The first basic construction was by Patterson and Wiedemann in 1983, which produced unbalanced function with very high nonlinearity. But for cryptographic applications, we need balanced Boolean functions. Therefore in 1993, Seberry, Zhang and Zheng proposed a secondary construction for balanced functions with very high nonlinearity by taking the direct sum of a modified bent function with the Patterson-Wiedemann function. Later in 2000, Sarkar and Maitra constructed such functions by taking the direct sum of a bent function with a modified Patterson-Wiedemann function. In this paper, we propose a new secondary construction for balanced Boolean functions with very high nonlinearity by recursively composing balanced functions with very high nonlinearity with quadratic functions. This is the first construction for balanced function with very high nonlinearity not based on the direct sum approach. Our construction also have other desirable properties like high algebraic degree and large linear span. |
Year | DOI | Venue |
|---|---|---|
2007 | 10.1093/ietfec/e90-a.1.29 | IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences |
Keywords | DocType | Volume |
boolean function,bent function,balanced boolean functions,direct sum,australasian conference,information security,patterson-wiedemann function,modified patterson-wiedemann function,modified bent function,high nonlinearity,balanced boolean function,new construction,balanced function,high algebraic degree | Journal | E90-A |
Issue | ISSN | Citations |
1 | 0916-8508 | 0 |
PageRank | References | Authors |
0.34 | 0 | 2 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Khoongming Khoo | 1 | 250 | 23.29 |
| Guang Gong | 2 | 1717 | 160.71 |