Related papers: Fast Algebraic Attacks and Decomposition of Symmet…
Nowadays, the resistance against algebraic attacks and fast algebraic attacks are considered as an important cryptographic property for Boolean functions used in stream ciphers. Both attacks are very powerful analysis concepts and can be…
From the motivation of algebraic attacks to stream and block ciphers([1,2,7,13,14,15]), the concept of {\em algebraic immunity} (AI) was introduced in [21] and studied in [3,5,10,11,17,18,19,20,21]. High algebraic immunity is a necessary…
To resist algebraic attack, a Boolean function should possess good algebraic immunity (AI). Several papers constructed symmetric functions with the maximum algebraic immunity $\lceil \frac{n}{2}\rceil $. In this correspondence we prove that…
We describe a new class of Boolean functions which provide the presently best known trade-off between low computational complexity, nonlinearity and (fast) algebraic immunity. In particular, for $n\leq 20$, we show that there are functions…
In this paper, we explicitly construct a large class of symmetric Boolean functions on $2k$ variables with algebraic immunity not less than $d$, where integer $k$ is given arbitrarily and $d$ is a given suffix of $k$ in binary…
Algebraic immunity has been proposed as an important property of Boolean functions. To resist algebraic attack, a Boolean function should possess high algebraic immunity. It is well known now that the algebraic immunity of an $n$-variable…
Algebraic immunity of Boolean function $f$ is defined as the minimal degree of a nonzero $g$ such that $fg=0$ or $(f+1)g=0$. Given a positive even integer $n$, it is found that the weight distribution of any $n$-variable symmetric Boolean…
We propose a general approach to construct cryptographic significant Boolean functions of $(r+1)m$ variables based on the additive decomposition $\mathbb{F}_{2^{rm}}\times\mathbb{F}_{2^m}$ of the finite field $\mathbb{F}_{2^{(r+1)m}}$,…
Boolean functions with high algebraic immunity are important cryptographic primitives in some stream ciphers. In this paper, two methodologies for constructing binary minimal codes from sets, Boolean functions and vectorial Boolean…
Boolean functions with good cryptographic properties like high nonlinearity and algebraic degree play an important in the security of stream and block ciphers. Such functions may be designed, for instance, by algebraic constructions or…
One of the major issues of cryptography is the cryptanalysis of cipher algorithms. Cryptanalysis is the study of methods for obtaining the meaning of encrypted information, without access to the secret information that is normally required.…
The algebraic degree of Boolean functions (or vectorial Boolean functions) is an important cryptographic parameter that should be computed by fast algorithms. They work in two main ways: (1) by computing the algebraic normal form and then…
Boolean functions with strong cryptographic properties, such as high nonlinearity and algebraic degree, are important for the security of stream and block ciphers. These functions can be designed using algebraic constructions or…
Constructing $2m$-variable Boolean functions with optimal algebraic immunity based on decomposition of additive group of the finite field $\mathbb{F}_{2^{2m}}$ seems to be a promising approach since Tu and Deng's work. In this paper, we…
With distributed computing and mobile applications, synchronizing diverging replicas of data structures is a more and more common problem. We use algebraic methods to reason about filesystem operations, and introduce a simplified definition…
Suppose a Boolean function $f$ is symmetric under a group action $G$ acting on the $n$ bits of the input. For which $G$ does this mean $f$ does not have an exponential quantum speedup? Is there a characterization of how rich $G$ must be…
In this paper we study the relationship between vectorial (Boolean) functions and cyclic codes in the context of algebraic attacks. We first derive a direct link between the annihilators of a vectorial function (in univariate form) and…
Stream ciphers play an important role in those applications where high throughput remains critical and resources are very restricted e.g. in Europe and North America, A5/1 is widely used stream cipher that ensure confidentiality of…
We describe several families of efficiently implementable Boolean functions achieving provable trade-offs between resiliency, nonlinearity, and algebraic immunity. In particular, the following statement holds for each of the function…
Active learning(AL), which serves as the representative label-efficient learning paradigm, has been widely applied in resource-constrained scenarios. The achievement of AL is attributed to acquisition functions, which are designed for…