Related papers: Using Repeating Decimals As An Alternative To Prim…
Assuming that we have a soft-decision list decoding algorithm of a linear code, a new hard-decision list decoding algorithm of its repeated code is proposed in this article. Although repeated codes are not used for encoding data, due to…
The secret sharing schemes are the important tools in cryptography that are used as building blocks in many secured protocols. It is a method used for distributing a secret among the participants in a manner that only the threshold number…
Quantum repeaters hold the promise to prevent the photon losses in communication channels. Most recently, the serious efforts have been applied to achieve scalable distribution of entanglement over long distances. However, the probabilistic…
Past work has shown that large language models are susceptible to privacy attacks, where adversaries generate sequences from a trained model and detect which sequences are memorized from the training set. In this work, we show that the…
Prime numbers have fascinated mathematicians since antiquity, with ongoing efforts to uncover both their properties and ever-larger examples. While giant primes rarely aid cryptography, they find use in areas such as locally decodable…
Secret-message transmission by echoing encrypted probes (STEEP) is discussed as an alternative to quantum key distribution (QKD). The former only needs classic or non-quantum channels while the latter needs both quantum and classic channels…
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.…
Pseudo-random number generators are widely used in many branches of science, mainly in applications related to Monte Carlo methods, although they are deterministic in design and, therefore, unsuitable for tackling fundamental problems in…
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…
This paper puts a new light on secure data storage inside distributed systems. Specifically, it revisits computational secret sharing in a situation where the encryption key is exposed to an attacker. It comes with several contributions:…
Random numbers play a crucial role in science and industry. Many numerical methods require the use of random numbers, in particular the Monte Carlo method. Therefore it is of paramount importance to have efficient random number generators.…
Tao has shown that in any fixed base, a positive proportion of prime numbers cannot have any digit changed and remain prime. In other words, most primes are "digitally delicate". We strengthen this result in a manner suggested by Tao: A…
We study, from the viewpoint of metrical number theory and (infinite) ergodic theory, the probabilistic laws governing the occurrence of prime numbers as digits in continued fraction expansions of real numbers.
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…
The distribution of quantum states over long distances is limited by photon loss. Straightforward amplification as in classical telecommunications is not an option in quantum communication because of the no-cloning theorem. This problem…
In this work, we established symmetric representation of numbers where one can use any of 9 digits giving the same number. The representations of natural numbers from 0 to 1000 are given using only single digit in all the nine cases, i.e.,…
A symmetric key encryption scheme is described for blocks of general size N that is a product of powers of many prime numbers. This is accomplished by realising each number (representing a message unit) as a point in a product of affine…
We investigate the construction of weakly-secure index codes for a sender to send messages to multiple receivers with side information in the presence of an eavesdropper. We derive a sufficient and necessary condition for the existence of…
Unclonable encryption, introduced by Broadbent and Lord (TQC'20), is an encryption scheme with the following attractive feature: given a ciphertext, an adversary cannot create two ciphertexts both of which decrypt to the same message as the…
Prime number multiplet classifications and patterns are extended to negative integers. The extension from prime numbers to single prime powers is also studied. Prime number septets at equal distance are given. It is also shown that each…