Name
Abstract | ||
|---|---|---|
We explore three applications of geometric sequences in constructing cryptographic Boolean functions. First, we construct 1-resilient functions of n Boolean variables with nonlinearity 2n-1-2(n-1)/2, n odd. The Hadamard transform of these functions is 3-valued, which limits the efficiency of certain stream cipher attacks. From the case for n odd, we construct highly nonlinear 1-resilient functions which disprove a conjecture of Pasalic and Johansson for n even. Our constructions do not have a potential weakness shared by resilient functions which are formed from concatenation of linear functions. Second, we give a new construction for balanced Boolean functions with high nonlinearity, exceeding 2n-1-2(n-1)/2, which is not based on the direct sum construction. Moreover, these functions have high algebraic degree and large linear span. Third, we construct balanced vectorial Boolean functions with nonlinearity 2n-1-2(n-1)/2 and low maximum correlation. They can be used as nonlinear combiners for stream cipher systems with high throughput. |
Year | DOI | Venue |
|---|---|---|
2003 | 10.1007/3-540-45067-X_43 | ACISP |
Keywords | Field | DocType |
nonlinear boolean function,direct sum construction,n boolean variable,balanced boolean function,high throughput,1-resilient function,certain stream cipher attack,balanced vectorial boolean function,new construction,high algebraic degree,cryptographic boolean function,high nonlinearity,stream cipher,boolean function | Boolean function,Boolean network,Discrete mathematics,Combinatorics,Linear span,Bent function,Stream cipher,Boolean data type,Hadamard transform,Boolean expression,Mathematics | Conference |
Volume | ISSN | ISBN |
2727 | 0302-9743 | 3-540-40515-1 |
Citations | PageRank | References |
8 | 0.66 | 20 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Khoongming Khoo | 1 | 250 | 23.29 |
| Guang Gong | 2 | 1717 | 160.71 |