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Wave is a recent digital signature scheme. It is based on a family of trapdoor one-way Preimage Sampleable Functions and is proven EUF-CMA in the random oracle model under two code-based computational...
Boolean functions used in some cryptosystems of stream ciphers should satisfy various criteria simultaneously to resist some known attacks. The fast algebraic attack (FAA) is feasible if one can find ...
The (fast) algebraic immunity, including (standard) algebraic immunity and the resistance against fast algebraic attacks, has been considered as an important cryptographic property for Boolean functio...
The trace inverse function $\Tr(x^{-1})$ over the finite field $\mathbb{F}_{2^n}$ is a class of very important Boolean functions in stream ciphers, which possesses many good properties, including high...
The incidence matrix between a set of monomials and a set of vectors in $\F_2$ has a great importance in the study of coding theory, cryptography, linear algebra, combinatorics. The rank of these matr...
In this paper, We propose a class of 2k-variable Boolean functions, which have optimal algebraic degree, high nonlinearity, and are 1-resilient. These functions have optimal algebraic immunity when k ...
In this paper, we propose two classes of 2k-variable Boolean functions, which have optimal algebraic immunity under the assumption that a general combinatorial conjecture is correct. These functions a...
In this paper, we present a new combinatorial conjecture about binary strings. Based on the new conjecture, two classes of Boolean functions of $2k$ variables with optimal algebraic immunity are propo...
In this paper, we present a new combinatorial conjecture about binary strings. Based on the new conjecture, two classes of Boolean functions of $2k$ variables with optimal algebraic immunity are propo...
In this paper, three constructions of balanced Boolean functions with optimum algebraic immunity are proposed. The cryptographical properties such as algebraic degree and nonlinearity of the construct...
In this paper, two sufficient conditions for a Boolean function with optimal extended algebraic immunity are given. It is shown that almost all the known functions possess maximum possible algebraic i...
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 algebrai...
In this paper, we propose a class of 1-resilient Boolean function with optimal algebraic degree and high nonlinearity, moreover, based on the conjecture proposed in [4], it can be proved that the al...
In this paper, we propose a combinatoric conjecture on binary string, on the premise that our conjecture is correct we mainly obtain two classes of functions which are both algebraic immunity optima...
This paper proposed a first order recursive construction of Boolean function with optimum algebraic immunity. We also show that the Boolean functions are balanced and have good algebraic degrees.

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