Related papers: Using Repeating Decimals As An Alternative To Prim…
Classical crystals are solid materials containing arbitrarily long periodic repetitions of a single motif. In this paper, we study the maximal possible repetition of the same motif occurring in beta-integers -- one dimensional models of…
We give a~detailed construction of the complete ordered field of real numbers by means of infinite decimal expansions. We prove that in the canonical encoding of decimals neither addition nor multiplication is {\em computable}, but that…
The Advanced Encryption Standard (AES) is widely recognized as the most important block cipher in common use nowadays. This high assurance in AES is given by its resistance to ten years of extensive cryptanalysis, that has shown no…
Eavesdropping attacks in inference systems aim to learn not the raw data, but the system inferences to predict and manipulate system actions. We argue that conventional information security measures can be ambiguous on the adversary's…
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…
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…
A block cipher is intended to be computationally indistinguishable from a random permutation of appropriate domain and range. But what are the properties of a random permutation? By the aid of exponential and ordinary generating functions,…
Research on the distribution of prime numbers has revealed a dual character: deterministic in definition yet exhibiting statistical behavior reminiscent of random processes. In this paper we show that it is possible to use an image-focused…
Data deduplication saves storage space by identifying and removing repeats in the data stream. Compared with traditional compression methods, data deduplication schemes are more time efficient and are thus widely used in large scale storage…
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…
In a system that performs both encryption and lossy compression, the conventional way is to compress first and then encrypt the compressed data. This separation approach proves to be optimal. In certain applications where sensitive…
We develop matrix cryptography based on linear recurrent sequences of any order that allows securing encryption against brute force and chosen plaintext attacks. In particular, we solve the problem of generalizing error detection and…
A permutiple is a number which is an integer multiple of some permutation of its digits. A well-known example is 9801 since it is an integer multiple of its reversal, 1089. In this paper, we consider the permutiple problem in an entirely…
Homomorphic encryption is a sophisticated encryption technique that allows computations on encrypted data to be done without the requirement for decryption. This trait makes homomorphic encryption appropriate for safe computation in…
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…
We establish quantum uncloneable encryption with unconditional security, preventing two non-communicating adversaries from simultaneously decrypting a single ciphertext $-$ even when both are given the key. Our construction achieves…
Unclonable encryption, first introduced by Broadbent and Lord (TQC'20), is a one-time encryption scheme with the following security guarantee: any non-local adversary (A, B, C) cannot simultaneously distinguish encryptions of two equal…
Iterative methods play an important role in science and engineering applications, with uses ranging from linear system solvers in finite element methods to optimization solvers in model predictive control. Recently, a new computational…
This note considers reciprocal of primes in binary representation and shows that the conjecture that 0s exceed 1s in most cases continues to hold for primes less one million. The conjecture has also been tested for ternary representation…
Long-distance quantum communication requires quantum repeaters to overcome photon loss in optical fibers. Here we demonstrate a repeater node with two memory atoms in an optical cavity. Both atoms are individually and repeatedly entangled…