Construction of resilient S-boxes with higher-dimensional vectorial outputs and strictly almost optimal nonlinearity

Resilient substitution boxes (S-boxes) with high nonlinearity are important cryptographic primitives in the design of certain encryption algorithms. There are several trade-offs between the most important cryptographic parameters and their simultaneous optimization is regarded as a difficult task. In this paper we provide a construction technique to obtain resilient S-boxes with so-called strictly almost optimal (SAO) nonlinearity for a larger number of output bits $m$ than previously known. This is the first time that the nonlinearity bound $2^{n-1}-2^{n/2}$ of resilient $(n,m)$ S-boxes, where $n$ and $m$ denote the number of the input and output bits respectively, has been exceeded for $m>\lfloor\frac{n}{4}\rfloor$. Thus, resilient S-boxes with extremely high nonlinearity and a larger output space compared to other design methods have been obtained

Highly Nonlinear t-Resilient Functions

High resilient and high nonlinear Boolean functions are desirable for secure key generators in stream ciphers, for example. This paper first shows that there exists a tradeoff between resiliency and nonlinearity. Then we show a new simple design method for high resilient and high nonlinear Boolean functions. Our method gives higher nonlinearity than [Zhang and Zheng 95] while their method gives larger resiliency than our method. Further, the proposed method provides a tradeo between resiliency t and nonlinearity NF by using an intermediate parameter l. If we choose a large l, then a small t and a large NF are obtained. If we choose a small l, then a large t and a small NF are obtained

Highly Nonlinear t-Resilient Functions

This paper shows a method to design (n; m; t)-resilient functions with high nonlinearity. For fixed n input bits and m output bits, our method gives higher nonlinearity than the method of Zhang et al., while their method gives larger resiliency t than ours. I. Introduction An n-input and m-output function F (x1 ; . . . ; xn) = (f1 ; . . . ; fm ) is called a (n; m; t)-resilient function if any function obtained from F by keeping any t input bits constant is uniformly distributed. Such functions find their applications in key renewal and in stream ciphers. It is known that there exists a linear (n; m; t)-resilient function if and only if there exists a linear [n; m; t + 1]-code. On the other hand, the nonlinearity NF of F is defined as a distance from the set of affine (linear) functions. Ding, Xiao and Shan showed the best affine approximation (BAA) attack against stream ciphers. Matsui showed the linear attack against DES. Therefore, (n; m; t)- resilient functions which possess hi..

Linear codes in generalized construction of resilient functions with very high nonlinearity

In this paper, we provide a new generalized construction method for highly nonlinear t-resilient functions, F: F-2(n) --> F-2(m). The construction is based on the use of linear error-correcting codes together with highly nonlinear multiple output functions. Given a linear [u, m, t + 1] code we show that it is possible to construct n-variable, m-output, t-resilient functions with very high nonlinearity for n > u. The method provides the currently best known nonlinearity results for most of the cases