Related papers: On the differential spectrum of a class of power f…
We investigate the impact of (possible) deviations of the probability distribution of key values from a uniform distribution for the information-theoretic strong, or perfect, message authentication code. We found a simple expression for the…
Proving the unconditional security of a quantum key distribution (QKD) scheme is a highly challenging task as one needs to determine the most efficient attack compatible with experimental data. This task is even more demanding for…
The linear complexity is a measure for the unpredictability of a sequence over a finite field and thus for its suitability in cryptography. In 2012, Diem introduced a new figure of merit for cryptographic sequences called expansion…
We present an efficient, fast and robust Nonlinear Fourier Transform (NFT) algorithm to detect eigenvalues of the discrete spectrum. It outperforms other known NFT algorithms as it detects the eigenvalues from the continuous spectrum, the…
Cloud-based and distributed computations are of growing interest in modern control systems. However, these technologies require performing computations on not necessarily trustworthy platforms and, thus, put the confidentiality of sensitive…
Modular exponentiation is a common mathematical operation in modern cryptography. This, along with modular multiplication at the base and exponent levels (to different moduli) plays an important role in a large number of key agreement…
We prove that a positive-definite measure in $\mathbb{R}^n$ with uniformly discrete support and discrete closed spectrum, is representable as a finite linear combination of Dirac combs, translated and modulated. This extends our recent…
This paper studies a large class of continuous functions $f:[0,1]\to\mathbb{R}^d$ whose range is the attractor of an iterated function system $\{S_1,\dots,S_{m}\}$ consisting of similitudes. This class includes such classical examples as…
Let (k(n)) n=1,2,... be a strictly increasing sequence of positive integers . We consider a specific sequence of differential operators Tk(n),{\lambda} , n=1,2,... on the space of entire functions , that depend on the sequence (k(n))…
We give some coefficient bounds and distortion theorems for a subclass of univalent functions in the unit disk, and defined using the S\^{a}l\^{a}gean differential operator. The results generalize and unify some well known results for…
Decoherence free subspaces (DFS) is a theoretical tool towards experimental implementation of quantum information storage and processing. However, they represent an experimental challenge, since conditions for their existence are very…
We propose a general method for studying properties of quantum channels acting on an n-partite system, whose action is invariant under permutations of the subsystems. Our main result is that, in order to prove that a certain property holds…
The paper introduces new sufficient conditions of strict positive definiteness for kernels on d-dimensional spheres which are not radially symmetric but possess specific coefficient structures. The results use the series expansion of the…
For a real sequence of length of m = nl, we may deduce its congruence derivative sequence with length of l. The discrete Fourier transform of original sequence can be calculated by the discrete Fourier transform of the congruence derivative…
We introduce and study a new class of differential fields in positive characteristic. We call them separably differentially closed fields and demonstrate that they are the differential analogue of separably closed fields. We prove several…
The spectral fluctuations of complex quantum systems, in appropriate limit, are known to be consistent with that obtained from random matrices. However, this relation between the spectral fluctuations of physical systems and random matrices…
We prove a uniform spectral gap for complex transfer operators near the critical line associated to overlapping $C^2$ iterated function systems on the real line satisfying a Uniform Non-Integrability (UNI) condition. Our work extends that…
Nowadays, due to the growing phenomenon of forgery in many fields, the interest in developing new anti-counterfeiting device and cryptography keys, based on the Physical Unclonable Functions (PUFs) paradigm, is widely increased. PUFs are…
With the tremendous benefits of internet and advanced communications, there is a serious threat from the data security perspective. There is a need of secure and robust encryption algorithm that can be implemented on each and diverse…
We prove the security of Gaussian continuous-variable quantum key distribution against arbitrary attacks in the finite-size regime. The novelty of our proof is to consider symmetries of quantum key distribution in phase space in order to…