Related papers: Polynomial-time solutions of computational problem…
In this paper we present a new key establishment protocol based on the decomposition problem in non-commutative groups which is: given two elements $w, w_1$ of the platform group $G$ and two subgroups $A, B \subseteq G$ (not necessarily…
The growing size of modern datasets necessitates splitting a large scale computation into smaller computations and operate in a distributed manner. Adversaries in a distributed system deliberately send erroneous data in order to affect the…
In this paper a variant of nonlinear exponential Euler scheme is proposed for solving nonlinear heat conduction problems. The method is based on nonlinear iterations where at each iteration a linear initial-value problem has to be solved.…
In this work, we introduce a novel variant of the multivariate quadratic problem, which is at the core of one of the most promising post-quantum alternatives: multivariate cryptography. In this variant, the solution of a given multivariate…
Post-quantum cryptography (PQC) must secure large-scale communication systems against quantum adversaries where classical hardness alone is insufficient and purely quantum schemes remain impractical. Lattice-based key encapsulation…
We present a new parallel numerical method for solving the non-stationary Schr\"odinger equation with linear nonlocal condition and time-dependent potential which does not commute with the stationary part of the Hamiltonian. The given…
Several novel imaging and non-destructive testing technologies are based on reconstructing the spatially dependent coefficient in an elliptic partial differential equation from measurements of its solution(s). In practical applications, the…
We investigate a mixed finite element method for the spatial discretization of a time-fractional Allen--Cahn equation defined on a convex polyhedral domain, combined with a nonuniform Alikhanov scheme for the temporal approximation. Under…
In this paper, we study the privacy-preserving distributed optimization problem, aiming to prevent attackers from stealing the private information of agents. For this purpose, we propose a novel privacy-preserving algorithm based on the…
Data compression combined with effective encryption is a common requirement of data storage and transmission. Low cost of these operations is often a high priority in order to increase transmission speed and reduce power usage. This…
Wiesner's unforgeable quantum money scheme is widely celebrated as the first quantum information application. Based on the no-cloning property of quantum mechanics, this scheme allows for the creation of credit cards used in authenticated…
This work explores the behaviour of a noncommutative harmonic oscillator in a time-dependent background, as previously investigated in [1]. Specifically, we examine the system when expressed in terms of commutative variables, utilizing a…
Threshold cryptography has gained momentum in the last decades as a mechanism to protect long term secret keys. Rather than having a single secret key, this allows to distribute the ability to perform a cryptographic operation such as…
Catalano and Fiore propose a scheme to transform a linearly-homomorphic encryption into a homomorphic encryption scheme capable of evaluating quadratic computations on ciphertexts. Their scheme is based on the linearly-homomorphic…
We study the statistical-computational trade-offs for learning with exact invariances (or symmetries) using kernel regression. Traditional methods, such as data augmentation, group averaging, canonicalization, and frame-averaging, either…
The problem of computing posterior functionals in general high-dimensional statistical models with possibly non-log-concave likelihood functions is considered. Based on the proof strategy of Nickl and Wang (2022), but using only local…
Quantum cryptography makes it possible to expand a short shared key (of e.g. 256 bits[1]) into an arbitrary long shared key. The novelty of quantum cryptography is that whenever a spy tries to eavesdrop the communication he causes…
We present two polarization-based protocols for quantum key distribution. The protocols encode key bits in noiseless subspaces or subsystems, and so can function over a quantum channel subjected to an arbitrary degree of collective noise,…
The Cahn-Hilliard equation has been widely employed within various mathematical models in physics, chemistry and engineering. Explicit stabilized time stepping methods can be attractive for time integration of the Cahn-Hilliard equation,…
Quantum cloud computing is emerging as a popular model for users to experience the power of quantum computing through the internet, enabling quantum computing as a service. The question is, when the scale of the computational problems…