arXiv subjects

Avishek Adhikari

Publications and source records attributed to Avishek Adhikari.

4 recordsLinked to original sources

arXiv2026

A Fully Device-Independent Ternary Quantum Key Distribution Protocol Based on the Impossible Colouring Game

We propose a Ternary Fully Device-Independent Quantum Key Distribution (TFDIQKD) protocol based on the two-party Impossible Colouring pseudo-telepathy game, utilizing maximally entangled qutrit states to enable secure key generation between distant parties. The protocol harnesses Bell inequality violations that arise from contextuality in the Kochen-Specker theorem, thereby offering a quantum advantage in a task that is classically impossible and eliminating reliance on assumptions about the internal functioning of quantum devices. A specially designed qutrit quantum circuit is used for state preparation. Security and device independence are rigorously analyzed within a composable framework, employing Bell-inequality violations, smooth min-entropy, von Neumann entropy, and Shannon entropy. The protocol achieves optimal key rates in the ideal case and maintains security under significant noise, with a finite-key analysis that supports its practical viability. Overall, the protocol operates within an adequate security framework and demonstrates an improved key generation rate compared to standard quantum key distribution schemes, highlighting the potential of high-dimensional quantum systems for secure communication.

quant-ph↗

arXiv2024

On metric dimension of cube of trees

Let $G=(V,E)$ be a connected graph and $d_{G}(u,v)$ be the shortest distance between the vertices $u$ and $v$ in $G$. A set $S=\{s_{1},s_{2},\cdots,s_{n}\}\subset V(G)$ is said to be a {\em resolving set} if for all distinct vertices $u,v$ of $G$, there exist an element $s\in S$ such that $d(s,u)\neq d(s,v)$. The minimum cardinality of a resolving set for a graph $G$ is called the {\em metric dimension} of $G$ and it is denoted by $β{(G)}$. A resolving set having $β{(G)}$ number of vertices is named as {\em metric basis} of $G$. The metric dimension problem is to find a metric basis in a graph $G$, and it has several real-life applications in network theory, telecommunication, image processing, pattern recognition, and many other fields. In this article, we consider {\em cube of trees} $T^{3}=(V, E)$, where any two vertices $u,v$ are adjacent if and only if the distance between them is less than equal to three in $T$. We establish the necessary and sufficient conditions of a vertex subset of $V$ to become a resolving set for $T^{3}$. This helps determine the tight bounds (upper and lower) for the metric dimension of $T^{3}$. Then, for certain well-known cubes of trees, such as caterpillars, lobsters, spiders, and $d$-regular trees, we establish the boundaries of the metric dimension. Further, we characterize some restricted families of cube of trees satisfying $β{(T^{3})}=β{(T)}$. We provide a construction showing the existence of a cube of tree attaining every positive integer value as their metric dimension.

math.CO↗

arXiv2014

Multi-Use Multi-Secret Sharing Scheme for General Access Structure

The main aim of this paper is to construct a multi-secret sharing scheme for general access structure in a trusted dealer model using suitable hash function and Lagrange's interpolation method. Even though, the proposed scheme is a multi-secret and multi-use one, each participant has to carry only one share. The suitable use of collision resistant one way hash function makes the scheme efficient and multi-use. Moreover, the scheme has a nice property that secrets, participants or qualified sets of participants may be added to or even may be made inactive dynamically by the dealer to get a new access structure without altering the shares of the existing participants in the old access structure. Finally, in the proposed scheme, both the combiner and the share holders can verify the correctness of the information that they are receiving from each other.

cs.CR↗

arXiv2011

An efficient multi-use multi-secret sharing scheme based on hash function

In this paper, a renewable, multi-use, multi-secret sharing scheme for general access structure based on one-way collision resistant hash function is presented in which each participant has to carry only one share. By applying collision-resistant one-way hash function, the proposed scheme is secure against conspiracy attacks even if the pseudo-secret shares are compromised. Moreover, high complexity operations like modular multiplication, exponentiation and inversion are avoided to increase its efficiency. Finally, in the proposed scheme, both the combiner and the participants can verify the correctness of the information exchanged among themselves.

cs.CR↗