Related papers: Prime Factorization Using Magnonic Holographic Dev…
We introduce a prime number generator in the form of a stochastic algorithm. The character of such algorithm gives rise to a continuous phase transition which distinguishes a phase where the algorithm is able to reduce the whole system of…
Holography is a technique based on the wave nature of light which allows us to utilize wave interference between the object beam and the coherent background. Holography is usually associated with images being made from light, however, this…
We revisit the problem of integer factorization with number-theoretic oracles, including a well-known problem: can we factor an integer $N$ unconditionally, in deterministic polynomial time, given the value of the Euler totient $$\Phi$(N)$?…
Let $n = \mathrm{p}\!\cdot\!\mathrm{q}$ (p < q) and $\Delta = \lvert p-q \rvert$, where p,q are odd integers, then, it is hypothesized that factorizing this composite n will take O(1) time once the steady state value is reached for any…
Classical public-key cryptography standards rely on the Rivest-Shamir-Adleman (RSA) encryption protocol. The security of this protocol is based on the exponential computational complexity of the most efficient classical algorithms for…
The effects of imperfect gate operations in implementation of Shor's prime factorization algorithm are investigated. The gate imperfections may be classified into three categories: the systematic error, the random error, and the one with…
The effects of imperfect gate operations in implementation of Shor's prime factorization algorithm are investigated. The gate imperfections may be classified into three categories: the systematic error, the random error, and the one with…
In this paper, we intend to present a new algorithm to factorize large numbers. According to the algorithm proposed here, we prove that there is a common factor between p and q. With this procedure, the time of factorization considerably…
We study the influence of errors and decoherence on both the performance of Shor's factoring algorithm and Grover's search algorithm, and on the amount of interference in these algorithms using a recently proposed interference measure. We…
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 paper proposes a new factorization algorithm for computing the phase factors of quantum signal processing. The proposed algorithm avoids root finding of high degree polynomials by using a key step of Prony's method and is numerically…
Non-negative Matrix Factorization (NMF) asks to decompose a (entry-wise) non-negative matrix into the product of two smaller-sized nonnegative matrices, which has been shown intractable in general. In order to overcome this issue, the…
We demonstrate that a modification of the classical index calculus algorithm can be used to factor integers. More generally, we reduce the factoring problem to finding an overdetermined system of multiplicative relations in any factor base…
The security of RSA algorithm depends upon the positive integer N, which is the multiple of two precise large prime numbers. Factorization of such great numbers is a problematic process. There are many algorithms has been implemented in the…
Integer factorization has been one of the cornerstone applications of the field of quantum computing since the discovery of an efficient algorithm for factoring by Peter Shor. Unfortunately, factoring via Shor's algorithm is well beyond the…
Quantum random number generators employ the inherent randomness of quantum mechanics to generate truly unpredictable random numbers, which are essential in cryptographic applications. While a great variety of quantum random number…
High-order methods gain more and more attention in computational fluid dynamics. However, the potential advantage of these methods depends critically on the availability of efficient elliptic solvers. With spectral-element methods, static…
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 the near-term, hybrid quantum-classical algorithms hold great potential for outperforming classical approaches. Understanding how these two computing paradigms work in tandem is critical for identifying areas where such hybrid algorithms…
The integer factorization problem (IFP) underpins the security of RSA, yet becomes efficiently solvable on a quantum computer through Shor's algorithm. Regev's recent high-dimensional variant reduces the circuit size through lattice-based…