Related papers: Resilient functions: Optimized, simplified, and ge…
Bent Boolean functions are important objects in cryptography and coding theory, and there are several general approaches for constructing such functions. Metaheuristics proved to be a strong choice as they can provide many bent functions,…
We study the performance of simple quantum error correcting codes with respect to correlated noise errors characterized by a finite correlation strength. Specifically, we consider bit flip (phase flip) noisy quantum memory channels and use…
Reversible computation is one of the most promising emerging technologies of the future. The usage of reversible circuits in computing devices can lead to a significantly lower power consumption. In this paper we study reversible logic…
In quantum computing the decoherence time of the qubits determines the computation time available and this time is very limited when using current hardware. In this paper we minimize the execution time (the depth) for a class of circuits…
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…
The general adversary dual is a powerful tool in quantum computing because it gives a query-optimal bounded-error quantum algorithm for deciding any Boolean function. Unfortunately, the algorithm uses linear qubits in the worst case, and…
Using fault-tolerant constructions, computations performed with unreliable components can simulate their noiseless counterparts though the introduction of a modest amount of redundancy. Given the modest overhead required to achieve…
We address the challenge of implementing reliable computation of Boolean functions in future nanocircuit fabrics. Such fabrics are projected to have very high defect rates. We overcome this limitation by using a combination of cheap but…
We study the next-to-next-to-leading order (NNLO) evolution of flavour singlet parton densities and structure functions in massless perturbative QCD. Present information on the corresponding three-loop splitting functions is used to derive…
We study the quantum query complexity of the Boolean hidden shift problem. Given oracle access to f(x+s) for a known Boolean function f, the task is to determine the n-bit string s. The quantum query complexity of this problem depends…
Gaussian bounds on noise correlation of functions play an important role in hardness of approximation, in quantitative social choice theory and in testing. The author (2008) obtained sharp gaussian bounds for the expected correlation of…
Secure multi-party computation using a physical deck of cards, often called card-based cryptography, has been extensively studied during the past decade. Card-based protocols to compute various Boolean functions have been developed. As each…
The problem of learning Boolean linear functions from quantum examples w.r.t. the uniform distribution can be solved on a quantum computer using the Bernstein-Vazirani algorithm. A similar strategy can be applied in the case of noisy…
We study two conjectures posed in the analysis of Boolean functions $f : \{-1, 1\}^n \to \{-1, 1\}$, in both of which, the Majority function plays a central role: the "Majority is Least Stable" (Benjamini et al., 1999) and the…
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…
Voting is a commonly applied method for the aggregation of the preferences of multiple agents into a joint decision. If preferences are binary, i.e., "yes" and "no", every voting system can be described by a (monotone) Boolean function…
We investigate Boolean degree 1 functions for several classical association schemes, including Johnson graphs, Grassmann graphs, graphs from polar spaces, and bilinear forms graphs, as well as some other domains such as multislices (Young…
Physical implementations of cryptographic algorithms leak information, which makes them vulnerable to so-called side-channel attacks. The problem of secure computation in the presence of leakage is generally known as leakage resilience. In…
A function $f$ is $d$-resilient if all its Fourier coefficients of degree at most $d$ are zero, i.e., $f$ is uncorrelated with all low-degree parities. We study the notion of $\mathit{approximate}$ $\mathit{resilience}$ of Boolean…
We construct and investigate Boolean networks that follow a given reliable trajectory in state space, which is insensitive to fluctuations in the updating schedule, and which is also robust against noise. Robustness is quantified as the…