Related papers: Using Repeating Decimals As An Alternative To Prim…
There are two basic number sequences which play a major role in the prime number distribution. The first Number Sequence SQ1 contains all prime numbers of the form 6n+5 and the second Number Sequence SQ2 contains all prime numbers of the…
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…
A repdigit is a positive integer that has only one distinct digit in its decimal expansion, i.e., a number has the form $d(10^m-1)/9$ for some $m\geq 1$ and $1 \leq d \leq 9$. Let $\left(T_n\right)_{n\ge0}$ be the sequence of Tribonacci.…
Quantum networks, integrating quantum communication, quantum metrology, and distributed quantum computing, could provide secure and efficient information transfer, high-resolution sensing, and an exponential speed-up in information…
In 1969 J. Verhoeff provided the first examples of a decimal error detecting code using a single check digit to provide protection against all single, transposition and adjacent twin errors. The three codes he presented are length 3-digit…
The notion of chiral prime concatenations is studied as a recursive construction of prime numbers starting from a seed set and with appropriate blocks to define the primality growth, generation by generation, either from the right or from…
Variable-length splittable codes are derived from encoding sequences of ordered integer pairs, where one of the pair's components is upper bounded by some constant, and the other one is any positive integer. Each pair is encoded by the…
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,…
Compression of integer sets and sequences has been extensively studied for settings where elements follow a uniform probability distribution. In addition, methods exist that exploit clustering of elements in order to achieve higher…
In this paper we consider cryptographic applications of the arithmetic on the hyperoctahedral group. On an appropriate subgroup of the latter, we particularly propose to construct public key cryptosystems based on the discrete logarithm.…
Factorization is the most fundamental way to determine if a number $n$ is prime or composite. Yet, this approach becomes impracticable when considering large values of $n$, a difficulty that is exploited by cryptographic protocols. We…
Quantum communication enables the implementation of tasks that are unachievable with classical resources. However, losses on the communication channel preclude the direct long-distance transmission of quantum information in many relevant…
It is known that chaotic systems have widely been used in cryptography. Generally, floating point simulations are used to generate pseudo-random sequence of numbers. Although, it is possible to find some works on the degradation of chaotic…
We develop the theory of cryptographic nondeterministic-secure pseudorandomness beyond the point reached by Rudich's original work (Rudich 1997), and apply it to draw new consequences in average-case complexity and proof complexity.…
Confidentiality was and will always remain a critical need in the exchanges either between persons or the official parties. Recently, cryptology has made a jump, from classical form to the quantum one, we talk about quantum cryptography.…
Quantum protocols for secret sharing usually rely on multi-party entanglement which with present technology is very difficult to achieve. Recently it has been shown that sequential manipulation and communication of a single $d-$ level state…
In this paper, we analyze properties of prime number sequences produced by the alternating sum of higher-order subsequences of the primes. We also introduce a new sieve which will generate these prime number sequences via the systematic…
We investigate quantum repeater protocols that rely on three-qubit repetition codes using nitrogen-vacancy (NV) centers in diamond as quantum memories. NV centers offer a two-qubit register, corresponding to their electron and nuclear…
The appearance of primes in a family of linear recurrence sequences labelled by a positive integer $n$ is considered. The terms of each sequence correspond to a particular class of Lehmer numbers, or (viewing them as polynomials in $n$)…
Sending money in cryptocurrencies is majorly based on public keys or their hashed forms -- "addresses." These long random-looking strings are user unfriendly for transferring by other means than via copy-and-paste or QR codes. Replacing…