Related papers: Advances in Factoring and Primality Testing: From …
In this work we initiate the question of whether quantum devices can provide us with an almost perfect source of classical randomness, and more generally, suffice for classical cryptographic tasks, such as encryption. Indeed, it is well…
For the last few decades, classical machine learning has allowed us to improve the lives of many through automation, natural language processing, predictive analytics and much more. However, a major concern is the fact that we're fast…
Lectures on quantum computing. Contents: Algorithms. Quantum circuits. Quantum Fourier transform. Elements of number theory. Modular exponentiation. Shor`s algorithm for finding the order. Computational complexity of Schor`s algorithm.…
Shor's quantum algorithm is very important for cryptography, since it can factor large numbers much faster than classical algorithms. In this study, we implement a simulator for Shor's quantum algorithm on graphic processor units (GPU) and…
We show that $n$-bit integers can be factorized by independently running a quantum circuit with $\tilde{O}(n^{3/2})$ gates for $\sqrt{n}+4$ times, and then using polynomial-time classical post-processing. The correctness of the algorithm…
Shor's algorithm efficiently solves factoring and discrete logarithm problems using quantum computers, compromising all public key schemes used today. These schemes rely on assumptions on their computational complexity, which quantum…
Classical and quantum information are very different. Together they can perform feats that neither could achieve alone, such as quantum computing, quantum cryptography and quantum teleportation. Some of the applications range from helping…
An overarching milestone of quantum machine learning (QML) is to demonstrate the advantage of QML over all possible classical learning methods in accelerating a common type of learning task as represented by supervised learning with…
A fundamental problem in statistics and learning theory is to test properties of distributions. We show that quantum computers can solve such problems with significant speed-ups. In particular, we give fast quantum algorithms for testing…
The task of factoring integers poses a significant challenge in modern cryptography, and quantum computing holds the potential to efficiently address this problem compared to classical algorithms. Thus, it is crucial to develop quantum…
This article proposes a new method to inject backdoors in RSA and other cryptographic primitives based on the Integer Factorization problem for balanced semi-primes. The method relies on mathematical congruences among the factors of the…
Integer factorization is a fundamental problem in algorithmic number theory and computer science. It is considered as a one way or trapdoor function in the (RSA) cryptosystem. To date, from elementary trial division to sophisticated methods…
Traditional cryptography is suffering a huge threat from the development of quantum computing. While many currently used public-key cryptosystems would be broken by Shor's algorithm, the effect of quantum computing on symmetric ones is…
The advancements in quantum computing are a threat to classical cryptographic systems. The traditional cryptographic methods that utilize factorization-based or discrete-logarithm-based algorithms, such as RSA and ECC, are some of these.…
Shor's shockingly fast quantum algorithm for solving the period-finding problem is a threat for the most common public-key primitives, as it can be efficiently applied to solve both the Integer Factorisation Problem and the Discrete…
Quantum computing provides a new way for approaching problem solving, enabling efficient solutions for problems that are hard on classical computers. It is based on leveraging how quantum particles behave. With researchers around the world…
Machine Learning algorithms are extensively used in an increasing number of systems, applications, technologies, and products, both in industry and in society as a whole. They enable computing devices to learn from previous experience and…
Demonstrating quantum advantage has been a pressing challenge in the field. Most claimed quantum speedups rely on a subroutine in which classical information can be accessed in a coherent quantum manner, which imposes a crucial constraint…
In this paper we generalize the quantum algorithm for computing short discrete logarithms previously introduced by Eker{\aa} so as to allow for various tradeoffs between the number of times that the algorithm need be executed on the one…
Shor's algorithm for the prime factorization of numbers provides an exponential speedup over the best known classical algorithms. However, nontrivial practical applications have remained out of reach due to experimental limitations. The…