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Large language models (LLMs) frequently make errors when handling even simple numerical problems, such as comparing two small numbers. A natural hypothesis is that these errors stem from how LLMs represent numbers, and specifically, whether…
A new cryptographic approach -- Iterated Random Encryption (IRE) -- is presented here. Although it is very simple, and easy to implement, it provides a very high level of security. According to this approach, a sequence of operations…
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…
Quantum communication is at the forefront of quantum technology, enabling the development of absolutely secure encryption, distributed quantum computing, teleportation and more. Whilst quantum communication has been experimentally…
Natural numbers can be divided in two non-overlapping infinite sets, primes and composites, with composites factorizing into primes. Despite their apparent simplicity, the elucidation of the architecture of natural numbers with primes as…
When elementary quantum systems, such as polarized photons, are used to transmit digital information, the uncertainty principle gives rise to novel cryptographic phenomena unachievable with traditional transmission media, e.g. a…
To determine whether a number is congruent or not is an old and difficult topic and progress is slow. The paper presents a new theorem when a prime number is a congruent number or not. The proof is not necessarily any simpler or shorter…
Ultrafast physical random bit generation at hundreds of Gb/s rates, with verified randomness, is a crucial ingredient in secure communication and have recently emerged using optics based physical systems. Here we examine the inverse problem…
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…
One-time-pad (OTP) encryption simply cannot be cracked, even by a quantum computer. The need of sharing in a secure way supplies of symmetric random keys turned the method almost obsolete as a standing-alone method for fast and large volume…
Ciphers are a powerful tool for encrypting communication. There are many different cipher types, which makes it computationally expensive to solve a cipher using brute force. In this paper, we frame the decryption task as a classification…
Several recently proposed code-based cryptosystems base their security on a slightly generalized version of the classical (syndrome) decoding problem. Namely, in the so-called restricted (syndrome) decoding problem, the error values stem…
We show that encrypted cloning of unknown quantum states is possible. Any number of encrypted clones of a qubit can be created through a unitary transformation, and each of the encrypted clones can be decrypted through a unitary…
Quantum cryptography leverages many unique features of quantum information in order to construct cryptographic primitives that are oftentimes impossible classically. In this work, we build on the no-cloning principle of quantum mechanics…
Security against simple eavesdropping attacks is demonstrated for a recently proposed quantum key distribution protocol which uses the Fibonacci recursion relation to enable high-capacity key generation with entangled photon pairs. No…
Threshold cryptography has gained momentum in the last decades as a mechanism to protect long term secret keys. Rather than having a single secret key, this allows to distribute the ability to perform a cryptographic operation such as…
The evolution of encryption algorithms have led to the development of very complicated and highly versatile algorithms that sacrifice efficiency for better and harder to decrypt results. But by the application of a genetic schema to the…
This paper presents a new chaining technique for the use of Hadamard transforms for encryption of both binary and non-binary data. The lengths of the input and output sequence need not be identical. The method may be used also for hashing.
Quantum communications promise to revolutionise the way information is exchanged and protected. Unlike their classical counterpart, they are based on dim optical pulses that cannot be amplified by conventional optical repeaters.…
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…