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Algorithms for the synchronisation of clocks across networks are both common and important within distributed systems. We here address not only the formal modelling of these algorithms, but also the formal verification of their behaviour.…
Building upon findings in computational model of handwriting learning and execution, we introduce the concept of stability to explain the difference between the actual movements performed during multiple execution of the subject's…
We take a critical look at the relationship between the security of cryptographic schemes in the Random Oracle Model, and the security of the schemes that result from implementing the random oracle by so called "cryptographic hash…
This paper presents a comprehensive study of matrix Kloosterman sums, including their computational aspects, distributional behavior, and applications in cryptographic analysis. Building on the work of [Zelingher, 2023], we develop…
Motivated by the immense success of random walk and Markov chain methods in the design of classical algorithms, we consider_quantum_ walks on graphs. We analyse in detail the behaviour of unbiased quantum walk on the line, with the example…
With the recent proliferation of distributed systems and networking, remote authentication has become a crucial task in many networking applications. Various schemes have been proposed so far for the two-party remote authentication;…
Most of the information is in the form of electronic data. A lot of electronic data exchanged takes place through computer applications. Therefore information exchange through these applications needs to be secure. Different cryptographic…
A circular-arc graph is the intersection graph of arcs of a circle. It is a well-studied graph model with numerous natural applications. A certifying algorithm is an algorithm that outputs a certificate, along with its answer (be it…
Tensor algebras give rise to one of the most powerful measures of similarity for sequences of arbitrary length called the signature kernel accompanied with attractive theoretical guarantees from stochastic analysis. Previous algorithms to…
The authors present evidence for universality in numerical computations with random data. Given a (possibly stochastic) numerical algorithm with random input data, the time (or number of iterations) to convergence (within a given tolerance)…
RSA is one of the most popular Public Key Cryptography based algorithm mainly used for digital signatures, encryption/decryption etc. It is based on the mathematical scheme of factorization of very large integers which is a…
This paper investigates a variant of the work-stealing algorithm that we call the localized work-stealing algorithm. The intuition behind this variant is that because of locality, processors can benefit from working on their own work.…
The development of large quantum computers will have dire consequences for cryptography. Most of the symmetric and asymmetric cryptographic algorithms are vulnerable to quantum algorithms. Grover's search algorithm gives a square root time…
This paper considers random (non-Hermitian) circulant matrices, and proves several results analogous to recent theorems on non-Hermitian random matrices with independent entries. In particular, the limiting spectral distribution of a random…
Many classical randomized algorithms (e.g., approximation algorithms for #P-complete problems) utilize the following random walk algorithm for {\em almost uniform sampling} from a state space $S$ of cardinality $N$: run a symmetric ergodic…
We consider Markov chains with random transition probabilities which, moreover, fluctuate randomly with time. We describe such a system by a product of stochastic matrices, $U(t)=M_t\cdots M_1$, with the factors $M_i$ drawn independently…
In this paper we study a generalization of distributed conditional gradient method to time-varying network architectures. We theoretically analyze convergence properties of the algorithm and provide numerical experiments. The time-varying…
Encryption study basically deals with three levels of algorithms. The first algorithm deals with encryption mechanism, second deals with decryption Mechanism and the third discusses about the generation of keys and sub keys used in the…
Stern's signature scheme is a historically important code-based signature scheme. A crucial optimization of this scheme is to generate pseudo-random vectors and a permutation instead of random ones, and most proposals that are based on…
Persistent (co)homology is a central construction in topological data analysis, where it is used to quantify prominence of features in data to produce stable descriptors suitable for downstream analysis. Persistence is challenging to…