Related papers: Factoring semi-primes with (quantum) SAT-solvers
We report a proof-of-concept demonstration of a quantum order-finding algorithm for factoring the integer 21. Our demonstration involves the use of a compiled version of the quantum phase estimation routine, and builds upon a previous…
It is commonly assumed that Shor's quantum algorithm for the efficient factorization of a large number $N$ requires a pure initial state. Here we demonstrate that a single pure qubit together with a collection of $log_2 N$ qubits in an…
We present a distributed implementation of Shor's quantum factoring algorithm on a distributed quantum network model. This model provides a means for small capacity quantum computers to work together in such a way as to simulate a large…
Pollard's Rho is a method for solving the integer factorization problem. The strategy searches for a suitable pair of elements belonging to a sequence of natural numbers that given suitable conditions yields a nontrivial factor. In…
A precise estimation of the computational complexity in Shor's factoring algorithm under the condition that the large integer we want to factorize is composed by the product of two prime numbers, is derived by the results related to number…
Prime factorization has been a buzzing topic in the field of number theory since time unknown. However, in recent years, alternative avenues to tackle this problem are being explored by researchers because of its direct application in the…
This work focuses on quantum methods for cryptanalysis of schemes based on the integer factorization problem and the discrete logarithm problem. We demonstrate how to practically solve the largest instances of the factorization problem by…
We show that given the order of a single element selected uniformly at random from $\mathbb Z_N^*$, we can with very high probability, and for any integer $N$, efficiently find the complete factorization of $N$ in polynomial time. This…
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…
A number of elegant approaches have been developed for the identification of quantum circuits which can be efficiently simulated on a classical computer. Recently, these methods have been employed to demonstrate the classical simulability…
In quantum information processing (QIP), the quantum Fourier transform (QFT) has a plethora of applications [1] [2] [3]: Shor's algorithm and phase estimation are just a few well-known examples. Shor's quantum factorization algorithm, one…
Properties of Shor's algorithm and the related period-finding algorithm could serve as benchmarks for the operation of a quantum computer. Distinctive universal behaviour is expected for the probability for success of the period-finding…
The factorization of a large digit integer in polynomial time is a challenging computational task to decipher. The exponential growth of computation can be alleviated if the factorization problem is changed to an optimization problem with…
An efficient integer factorization algorithm would reduce the security of all variants of the RSA cryptographic scheme to zero. Despite the passage of years, no method for efficiently factoring large semiprime numbers in a classical…
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.…
In the last decade, public and industrial research funding has moved quantum computing from the early promises of Shor's algorithm through experiments to the era of noisy intermediate scale quantum devices (NISQ) for solving real-world…
A major obstacle to implementing Shor's quantum number-factoring algorithm is the large size of modular-exponentiation circuits. We reduce this bottleneck by customizing reversible circuits for modular multiplication to individual runs of…
In ensemble (or bulk) quantum computation, measurements of qubits in an individual computer cannot be performed. Instead, only expectation values can be measured. As a result of this limitation on the model of computation, various important…
Determining the prime factors of a given number N is a problem, which requires super-polynomial time for conventional digital computers. A polynomial-time algorithm was invented by P. Shor for quantum computers. However, the realization of…
Quantum computing is a significant risk to classical cryptographic, especially RSA, which depends on the difficulty of factoring large numbers. Classical factorization methods, such as Trial Division and Pollard's Rho, are inefficient for…