Construction of Balanced Boolean Functions with High Nonlinearity and Good Autocorrelation Properties
Boolean functions with high nonlinearity and good autocorrelation properties play an important role in the design of block ciphers and stream ciphers. In this paper, we give a method to construct balanced Boolean functions on $n$ variables, where $n\ge 10$ is an even integer, satisfying strict avalanche criterion (SAC). Compared with the known balanced Boolean functions with SAC property, the constructed functions possess the highest nonlinearity and the best global avalanche characteristics (GAC) property.
Balanced Boolean Functions with (Almost) Optimal Algebraic Immunity and Very High Nonlinearity
In this paper, we present a class of $2k$-variable balanced Boolean functions and a class of $2k$-variable $1$-resilient Boolean functions for an integer $k\ge 2$, which both have the maximal algebraic degree and very high nonlinearity. Based on a newly proposed conjecture by Tu and Deng, it is shown that the proposed balanced Boolean functions have optimal algebraic immunity and the $1$-resilient Boolean functions have almost optimal algebraic immunity. Among all the known results of balanced Boolean functions and $1$-resilient Boolean functions, our new functions possess the highest nonlinearity. Based on the fact that the conjecture has been verified for all $k\le 29$ by computer, at least we have constructed a class of balanced Boolean functions and a class of $1$-resilient Boolean functions with the even number of variables $\le 58$, which are cryptographically optimal or almost optimal in terms of balancedness, algebraic degree, nonlinearity, and algebraic immunity.
A Short Signature Scheme in the Standard Model
In this paper, by elaborately choosing the parameters of Waters Hash function, we propose a new efficient signature scheme. It is shown that the scheme is secure against strongly unforgeable chosen-message attacks in the standard model under Computational Diffie-Hellman (CDH) assumption. Further, among all the known secure signatures in the standard model, our scheme is the shortest one and has the efficient security reduction as well.