Related papers: Aryabhata's Mathematics
This article studies the systems of equations appearing in the Susa Mathematical Texts (\textbf{SMT}) and the different approaches used by the Susa scribes to solve them.
The paper is mostly a survey on recent results in Diophantine approximation, with emphasis on properties of exponents measuring various notions of Diophantine <approximation.
Isogenies, the mappings of elliptic curves, have become a useful tool in cryptology. These mathematical objects have been proposed for use in computing pairings, constructing hash functions and random number generators, and analyzing the…
This is a chapter on quantum cryptography for the book "A Multidisciplinary Introduction to Information Security" to be published by CRC Press in 2011/2012. The chapter aims to introduce the topic to undergraduate-level and…
This paper discusses the mechanisms of cryptocurrency, the idea of using security in the system, and the popularity of it. To begin, the authors provide a background on cryptocurrency and how it works. The authors understand that while most…
The methods of quantum cryptography enable one to have perfectly secure communication lines, whereby the laws of quantum physics protect the privacy of the data exchanged. Each quantum-cryptography scheme has its own security criteria that…
In this article, we propose a method to construct self orthogonal matrix, orthogonal matrix and anti orthogonal matrix over the finite field. Orthogonal matrices has numerous applications in cryptography, so here we demonstrate the…
This article, intended for a general mathematical audience, is an informal review of some of the many interesting links which have developed between quantum cohomology and "classical" mathematics. It is based on a talk given at the Autumn…
Although recent advances of blockchain systems, notably in the form of cryptocurrency, have drawn tremendous interests from both researchers and practitioners, limited studies existed toward the theoretical foundation of blockchains. This…
This paper focuses on greedy expansions, one possible representation of numbers, and on arithmetical operations with them. Performing addition or multiplication some additional digits can appear. We study bounds on the number of such digits…
In this paper, we examine the state art of quantum computing and analyze its potential effects in scientific computing and cybersecurity. Additionally, a non-technical description of the mechanics of the listed form of computing is provided…
Uniquely among the sciences, quantum cryptography has driven both foundational research as well as practical real-life applications. We review the progress of quantum cryptography in the last decade, covering quantum key distribution and…
The role of mathematics in a complex system such as the Internet has yet to be deeply explored. In this paper, we summarize some of the important and pressing problems in cyber security from the viewpoint of open science environments. We…
The present work has been designed for students in secondary school and their teachers in mathematics. We will show how with the help of our knowledge of number systems we can solve problems from other fields of mathematics for example in…
In this note I describe reliability standards for writing and reviewing mathematical papers; these standards are (in my opinion) vital for the progress of mathematics. I give examples of applying the described or other reliability…
Elementary review article on quantum cryptography.
The purpose of this article is to discuss recent advances in the growing field of phase retrieval, and to publicize open problems that we believe will be of interest to mathematicians in general, and algebraists in particular.
This paper is an essentially self-contained and rigorous description of the fundamental principles of quantum computing from a mathematical perspective. It is intended to help mathematicians who want to get a grasp of this quickly growing…
This paper gives a short introduction into the metric theory of spaces with dilations.
This paper was presented at the Colloque de Saint-Denis de la Reunion, November 3-7, 1997, and published in the book L'Oc\'ean Indien au carrefour des math\'ematiques arabes, chinoises, europ\'eennes et indiennes (pp. 211-223), Tourn\`es,…