相关论文: Simulation of Shor algorithm for discrete logarith…

Precise suites of benchmarks are required to assess the progress of early fault-tolerant quantum computers at economically impactful applications such as cryptanalysis. Appropriate challenges exist for factoring but those for elliptic curve…

This work presents a generalized period decomposition approach, significantly improving the practical reliability of Shor's quantum factoring algorithm. Although Shor's algorithm theoretically enables polynomial-time integer factorization,…

Shor's factorisation algorithm is a combination of classical pre- and post-processing and a quantum period finding (QPF) subroutine which allows an exponential speed up over classical factoring algorithms. We consider the stability of this…

We try to minimize the number of qubits needed to factor an integer of n bits using Shor's algorithm on a quantum computer. We introduce a circuit which uses 2n+3 qubits and O(n^3 lg(n)) elementary quantum gates in a depth of O(n^3) to…

We give precise quantum resource estimates for Shor's algorithm to compute discrete logarithms on elliptic curves over prime fields. The estimates are derived from a simulation of a Toffoli gate network for controlled elliptic curve point…

Improving over an earlier construction by Kaye and Zalka, Maslov et al. describe an implementation of Shor's algorithm which can solve the discrete logarithm problem on binary elliptic curves in quadratic depth O(n^2). In this paper we show…

For $q$ a prime power, the discrete logarithm problem (DLP) in $\mathbb{F}_{q}$ consists in finding, for any $g \in \mathbb{F}_{q}^{\times}$ and $h \in \langle g \rangle$, an integer $x$ such that $g^x = h$. We present an algorithm for…

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…

With the development of Shor's algorithm, some nondeterministic polynomial (NP) time problems (e.g. prime factorization problems and discrete logarithm problems) may be solved in polynomial time. In recent years, although some homomorphic…

Quantum computers pose a fundamental threat to widely deployed public-key cryptosystems, such as RSA and ECC, by enabling efficient integer factorization using Shor's algorithm. Theoretical resource estimates suggest that 2048-bit RSA keys…

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…

The quantum algorithm with polynomial time for discrete logarithm problem proposed by Shor is one of the most significant quantum algorithms, but a large number of qubits may be required in the Noisy Intermediate-scale Quantum (NISQ) era.…

We perform logical and physical resource estimation for computing binary elliptic curve discrete logarithms using Shor's algorithm on fault-tolerant quantum computers. We adopt a windowed approach to design our circuit implementation of the…

The semidirect discrete logarithm problem (SDLP) in finite groups was proposed as a foundation for post-quantum cryptographic protocols, based on the belief that its non-abelian structure would resist quantum attacks. However, recent…

Recently, Cai showed that Shor's quantum factoring algorithm fails to factor large integers when the algorithm's quantum Fourier transform (QFT) is corrupted by a vanishing level of random noise on the QFT's precise controlled rotation…

This paper studies the limitations of the generic approaches to solving cryptographic problems in classical and quantum settings in various models. - In the classical generic group model (GGM), we find simple alternative proofs for the…

Shor's algorithm is one of the most important quantum algorithm proposed by Peter Shor [Proceedings of the 35th Annual Symposium on Foundations of Computer Science, 1994, pp. 124--134]. Shor's algorithm can factor a large integer with…

The security of messages encoded via the widely used RSA public key encryption system rests on the enormous computational effort required to find the prime factors of a large number N using classical (i.e., conventional) computers. In 1994,…

We formulate and numerically simulate the single control qubit Shor algorithm for the case of static imperfections induced by residual couplings between qubits. This allows us to study the accuracy of Shor's algorithm with respect to these…

Shor's factoring algorithm (SFA), by its ability to efficiently factor large numbers, has the potential to undermine contemporary encryption. At its heart is a process called order finding, which quantum mechanics lets us perform…