Related papers: Quantum security of subset cover problems

Hidden shift problems are relevant to assess the quantum security of various cryptographic constructs. Multiple quantum subexponential time algorithms have been proposed. In this paper, we propose some improvements on a polynomial quantum…

This review examines how quantum computing and artificial intelligence challenge current cryptographic systems. We analyze the literature to assess the resilience of algorithms against quantum attacks (Shor's and Grover's algorithms) and…

Shor's quantum factoring algorithm and a few other efficient quantum algorithms break many classical crypto-systems. In response, people proposed post-quantum cryptography based on computational problems that are believed hard even for…

This paper introduces a completely new approach to encryption based on group theoretic quantum framework. Quantum cryptography has essentially focused only on key distribution and proceeded with classical encryption algorithm with the…

Solving random subset sum instances plays an important role in constructing cryptographic systems. For the random subset sum problem, in 2013 Bernstein et al. proposed a quantum algorithm with heuristic time complexity…

In order to research the security of the knapsack problem under quantum algorithm attack, we study the quantum algorithm for knapsack problem over Z_r based on the relation between the dimension of the knapsack vector and r. First, the…

Post-quantum cryptography (PQC) must secure large-scale communication systems against quantum adversaries where classical hardness alone is insufficient and purely quantum schemes remain impractical. Lattice-based key encapsulation…

With the advancement of quantum computing, symmetric cryptography faces new challenges from quantum attacks. These attacks are typically classified into two models: Q1 (classical queries) and Q2 (quantum superposition queries). In this…

One of the most promising and versatile approaches to creating new quantum algorithms is based on the quantum hidden subgroup (QHS) paradigm, originally suggested by Alexei Kitaev. This class of quantum algorithms encompasses the…

Let U be a universe on n elements, let k be a positive integer, and let F be a family of (implicitly defined) subsets of U. We consider the problems of partitioning U into k sets from F, covering U with k sets from F, and packing k…

Quantum no-cloning theorem gives rise to the intriguing possibility of quantum copy protection where we encode a program or functionality in a quantum state such that a user in possession of k copies cannot create k+1 copies, for any k.…

Quantum computer is no longer a hypothetical idea. It is the worlds most important technology and there is a race among countries to get supremacy in quantum technology. Its the technology that will reduce the computing time from years to…

Several algorithms with an approximation guarantee of $O(\log n)$ are known for the Set Cover problem, where $n$ is the number of elements. We study a generalization of the Set Cover problem, called the Partition Set Cover problem. Here,…

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…

This paper describes the work carried out by the Inter-American Development Bank, the IDB Lab, LACChain, Cambridge Quantum Computing (CQC), and Tecnologico de Monterrey to identify and eliminate quantum threats in blockchain networks. The…

Quantum computing devices are believed to be powerful in solving the prime factorization problem, which is at the heart of widely deployed public-key cryptographic tools. However, the implementation of Shor's quantum factorization algorithm…

We study the classic set cover problem from the perspective of sub-linear algorithms. Given access to a collection of $m$ sets over $n$ elements in the query model, we show that sub-linear algorithms derived from existing techniques have…

Quantum secure signature schemes have a lot of attention recently, in particular because of the NIST call to standardize quantum safe cryptography. However, only few signature schemes can have concrete quantum security because of technical…

A $k$-collision for a compressing hash function $H$ is a set of $k$ distinct inputs that all map to the same output. In this work, we show that for any constant $k$, $\Theta\left(N^{\frac{1}{2}(1-\frac{1}{2^k-1})}\right)$ quantum queries…

Let $({\bf U},{\bf S},d)$ be an instance of Set Cover Problem, where ${\bf U}=\{u_1,...,u_n\}$ is a $n$ element ground set, ${\bf S}=\{S_1,...,S_m\}$ is a set of $m$ subsets of ${\bf U}$ satisfying $\bigcup_{i=1}^m S_i={\bf U}$ and $d$ is a…