Related papers: Degree is Important: On Evolving Homogeneous Boole…
Bent functions, which are maximally nonlinear Boolean functions with even numbers of variables and whose Hamming distance to the set of all affine functions equals $2^{n-1}\pm 2^{\frac{n}{2}-1}$, were introduced by Rothaus in 1976 when he…
A short introduction to quantum error correction is given, and it is shown that zero-dimensional quantum codes can be represented as self-dual additive codes over GF(4) and also as graphs. We show that graphs representing several such codes…
This paper investigates the learnability of the nonlinearity property of Boolean functions using neural networks. We train encoder style deep neural networks to learn to predict the nonlinearity of Boolean functions from examples of…
We propose a multi-bit leveled fully homomorphic encryption scheme using multivariate polynomial evaluations. The security of the scheme depends on the hardness of the Learning with Errors (LWE) problem. For homomorphic multiplication, the…
Submodular function minimization is a key problem in a wide variety of applications in machine learning, economics, game theory, computer vision, and many others. The general solver has a complexity of $O(n^3 \log^2 n . E +n^4 {\log}^{O(1)}…
We consider negabent Boolean functions that have Trace representation. We completely characterize quadratic negabent monomial functions. We show the relation between negabent functions and bent functions via a quadratic function. Using this…
In this technical report, we explore the use of homomorphic encryption (HE) in the context of training and predicting with deep learning (DL) models to deliver strict \textit{Privacy by Design} services, and to enforce a zero-trust model of…
Many underlying structural and functional factors that determine the fault behavior of a combinational network, are not yet fully understood. In this paper, we show that there exists a large class of Boolean functions, called root…
Evolutionary algorithms (EAs), such as the genetic algorithm (GA), offer an elegant way to handle combinatorial optimization problems (COPs). However, limited by expertise and resources, most users do not have enough capability to implement…
Canalization is a key organizing principle in complex systems, particularly in gene regulatory networks. It describes how certain input variables exert dominant control over a function's output, thereby imposing hierarchical structure and…
Polynomial threshold gates are basic processing units of an artificial neural network. When the input vectors are binary vectors, these gates correspond to Boolean functions and can be analyzed via their polynomial representations. In…
In this paper, we study the value distributions of perfect nonlinear functions, i.e., we investigate the sizes of image and preimage sets. Using purely combinatorial tools, we develop a framework that deals with perfect nonlinear functions…
Evolutionary Algorithms (EAs) and other randomized search heuristics are often considered as unbiased algorithms that are invariant with respect to different transformations of the underlying search space. However, if a certain amount of…
Binary linear codes with good parameters have important applications in secret sharing schemes, authentication codes, association schemes, and consumer electronics and communications. In this paper, we construct several classes of binary…
The ability to compose learned skills to solve new tasks is an important property of lifelong-learning agents. In this work, we formalise the logical composition of tasks as a Boolean algebra. This allows us to formulate new tasks in terms…
We investigated the properties of Boolean networks that follow a given reliable trajectory in state space. A reliable trajectory is defined as a sequence of states which is independent of the order in which the nodes are updated. We…
Quantum computations promise the ability to solve problems intractable in the classical setting. Restricting the types of computations considered often allows to establish a provable theoretical advantage by quantum computations, and later…
Here we consider an approach for fast computing the algebraic degree of Boolean functions. It combines fast computing the ANF (known as ANF transform) and thereafter the algebraic degree by using the weight-lexicographic order (WLO) of the…
The trend towards delegating data processing to a remote party raises major concerns related to privacy violations for both end-users and service providers. These concerns have attracted the attention of the research community, and several…
By replacing standard non-linearities with polynomial activations, Polynomial Neural Networks (PNNs) are pivotal for applications such as privacy-preserving inference via Homomorphic Encryption (HE). However, training PNNs effectively…