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Prime numbers or primes are man's eternal treasures that have been cherished for several millennia, until today. As their academic ancestors in ancient Mesopotamia, many mathematicians are still trying hard to see primes better. I shall…
Quantum repeaters are used to overcome the exponential photon loss scaling that quantum states acquire as they are transmitted over long distances. While repeaters for discrete variable encodings of quantum information have existed for some…
Quantum key repeater is the backbone of the future Quantum Internet. It is an open problem to determine, for an arbitrary mixed bipartite state shared between the stations of a quantum key repeater, how much key can be generated between its…
This review is aimed to evaluate the importance of Symmetric Key Cryptography for Security in Distributed Systems. Businesses around the world as well as research and other such areas rely heavily on distributed systems these days. Hence,…
[Shortened abstract:] This thesis investigates the importance of quantum memory in quantum cryptography, concentrating on quantum key distribution schemes. In the hands of an eavesdropper -- a quantum memory is a powerful tool, putting in…
We consider the problem of constructing an unconditionally secure cipher for the case when the key length is less than the length of the encrypted message. (Unconditional security means that a computationally unbounded adversary cannot…
We have formerly introduced Deep Random Secrecy, a new cryptologic technique capable to ensure secrecy as close as desired from perfection against unlimited passive eavesdropping opponents. We have also formerly introduced an extended…
An operating system kernel uses cryptographically secure pseudorandom number generator for creating address space localization randomization offsets to protect memory addresses to processes from exploration, storing users' password securely…
We use recurrence equations (alias difference equations) to enumerate the number of formula-representations of positive integers using only addition and multiplication, and using addition, multiplication, and exponentiation, where all the…
Let $a_0\in\{0,\dots,9\}$. We show there are infinitely many prime numbers which do not have the digit $a_0$ in their decimal expansion. The proof is an application of the Hardy-Littlewood circle method to a binary problem, and rests on…
Based on Euclid's algorithm, we find a kind of special sequences which play an interesting role in the study of primes. We call them W Sequences. They not only ties up the distribution of primes in short interval but also enables us to give…
Natural numbers which are nontrivial multiples of some permutation of their base-$b$ digit representations are called permutiples. Specific cases include numbers which are multiples of cyclic permutations (cyclic numbers) and reversals of…
This article bridges the gap between two topics used in sharing an encryption key: (i) Key Consolidation, i.e., extracting two identical strings of bits from two information sources with similarities (common randomness). (ii) Quantum-safe…
Protecting secure random key from eavesdropping in quantum key distribution protocols has been well developed. In this letter, we further study how to detect and eliminate eavesdropping on the random base string in such protocols. The…
Authentication is a process by which an entity,which could be a person or intended computer,establishes its identity to another entity.In private and public computer networks including the Internet,authentication is commonly done through…
Random number generation is a key technology that is useful in a variety of ways. Random numbers are often used to generate keys for data encryption. Random numbers generated at a sufficiently long length can encrypt sensitive data and make…
Since fully homomorphic encryption and homomorphically encrypted computing preserve algebraic identities such as 2*2=2+2, a natural question is whether this extremely utilitarian feature also sets up cryptographic attacks that use the…
A modified Lagrange Polynomial is introduced for polynomial extrapolation, which can be used to estimate the equally spaced values of a polynomial function. As an example of its application, this article presents a prime-generating…
Any system that is used for naming or representing numbers is a number system, also known as numeral system. The modern civilization is familiar with decimal number system using ten digits. However digital devices and computers use binary…
The major system is a mnemonic system that can be used to memorize sequences of numbers. In this work, we present a method to automatically generate sentences that encode a given number. We propose several encoding models and compare the…