Related papers: Using Repeating Decimals As An Alternative To Prim…
In quantum communication via noisy channels, the error probability scales exponentially with the length of the channel. We present a scheme of a quantum repeater that overcomes this limitation. The central idea is to connect a string of…
This paper deals with products of moderate-size primes, familiarly known as smooth numbers. Smooth numbers play a crucial role in information theory, signal processing and cryptography. We present various properties of smooth numbers…
This work presents some novel techniques to enhance an encryption scheme motivated by classical McEliece cryptosystem. Contributions include: (1) using masking matrices to hide sensitive data, (2) allowing both legitimate parties to…
Cryptography is the science of encrypting the information so that it is rendered unreadable for an intruder. Cryptographic techniques are of utmost importance in today's world as the information to be sent might be of invaluable importance…
We propose a multi-scale analysis method for studying arithmetic properties of integer sets, such as primality. Our approach organizes information through a hierarchy of nested sequences, where each level enables a hierarchical expression…
In this paper we deal with a classical problem in elementary number theory, namely repeating decimals. We show how the digits of the period of the decimal representation of any fraction $\frac{k}{m}$, where $k$ and $m$ are positive integers…
In this paper we consider the problem of encoding data into \textit{repeat-free} sequences in which sequences are imposed to contain any $k$-tuple at most once (for predefined $k$). First, the capacity of the repeat-free constraint are…
This paper examines the randomness of d-sequences, which are decimal sequences to an arbitrary base. Our motivation is to check their suitability for application to cryptography, spread-spectrum systems and use as pseudorandom sequence.
A major problem in using iterative number generators of the form x_i=f(x_{i-1}) is that they can enter unexpectedly short cycles. This is hard to analyze when the generator is designed, hard to detect in real time when the generator is…
The decimal digits of $\pi$ are widely believed to behave like as statistically independent random variables taking the values $0, 1, 2, 3, 4, 5$, $6, 7, 8, 9$ with equal probabilities $1/10$. In this article, first, another similar…
This paper discusses the application of known techniques, knowledge and technology in a novel way for encryption. Two distinct and separate methods are presented. Method 1: Alter the symbol set of the language by adding additional redundant…
The prime number 357686312646216567629137 is notable because of the unusual property that it remains prime successively on removing the left digit until there are no remaining digits. We explore here the distributions of the number of left…
In this note we describe a method for finding prime numbers as fixed points of particularly simple sequences. Some basic calculations show that success rates for identifying primes this way are over 99.9%. In particular, it seems that the…
Personal Identification Numbers (PINs) are commonly used as an authentication mechanism. An important security requirement is that PINs should be hard to guess for an attacker. On the other hand, remembering several random PINs can be…
A recursive random number generator using prime reciprocals is described.
Data privacy and data security are always on highest priority in the world. We need a reliable method to encrypt the data so that it reaches the destination safely. Encryption is a simple yet effective way to protect our data while…
Currently there is no known efficient formula for primes. Besides that, prime numbers have great importance in e.g., information technology such as public-key cryptography, and their position and possible or impossible functional generation…
We formally study iterated block ciphers that alternate between two sequences of independent and identically distributed (i.i.d.) rounds. It is demonstrated that, in some cases the effect of alternating increases security, while in other…
Identifiers and sequence numbers make up a large part of the protocol overhead in certain low-power wide-area networks. The requirement for cryptographic nonces in authentication and encryption schemes often demands excessively long…
The statistical distribution, when determined from an incomplete set of constraints, is shown to be suitable as host for encrypted information. We design an encoding/decoding scheme to embed such a distribution with hidden information. The…