Related papers: MapReduce for Integer Factorization
Clustering problems have numerous applications and are becoming more challenging as the size of the data increases. In this paper, we consider designing clustering algorithms that can be used in MapReduce, the most popular programming…
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…
This paper elaborates on a sieving technique that has first been applied in 2018 for improving bounds on deterministic integer factorization. We will generalize the sieve in order to obtain a polynomial-time reduction from integer…
MapReduce is a technique used to vastly improve distributed processing of data and can massively speed up computation. Hadoop and its MapReduce relies on JVM and Java which is expensive on memory. High Performance Computing based MapReduce…
Quantum computing is a winsome field that concerns with the behaviour and nature of energy at the quantum level to improve the efficiency of computations. In recent years, quantum computation is receiving much attention for its capability…
Two prominent methods for integer factorization are those based on general integer sieve and elliptic curve. The general integer sieve method can be specialized to quadratic integer sieve method. In this paper, a probability analysis for…
The two currently fastest general-purpose integer factorization algorithms are the Quadratic Sieve and the Number Field Sieve. Both techniques are used to find so-called smooth values of certain polynomials, i.e., values that factor…
Undoubtedly, the MapReduce is the most powerful programming paradigm in distributed computing. The enhancement of the MapReduce is essential and it can lead the computing faster. Therefore, here are many scheduling algorithms to discuss…
The Apriori algorithm that mines frequent itemsets is one of the most popular and widely used data mining algorithms. Now days many algorithms have been proposed on parallel and distributed platforms to enhance the performance of Apriori…
A new asymmetric cryptosystem based on the Integer Factorization Problem is proposed. It posses an encryption and decryption speed of $O(n^2)$, thus making it the fastest asymmetric encryption scheme available. It has a simple mathematical…
Distributed processing frameworks, such as MapReduce, Hadoop, and Spark are popular systems for processing large amounts of data. The design of efficient algorithms in these frameworks is a challenging problem, as the systems both require…
Numerous methods have been considered to create a fast integer factorization algorithm. Despite its apparent simplicity, the difficulty to find such an algorithm plays a crucial role in modern cryptography, notably, in the security of RSA…
Particle filtering is a numerical Bayesian technique that has great potential for solving sequential estimation problems involving non-linear and non-Gaussian models. Since the estimation accuracy achieved by particle filters improves as…
MapReduce is a programming system for distributed processing large-scale data in an efficient and fault tolerant manner on a private, public, or hybrid cloud. MapReduce is extensively used daily around the world as an efficient distributed…
Integer factorization is a famous computational problem unknown whether being solvable in the polynomial time. With the rise of deep neural networks, it is interesting whether they can facilitate faster factorization. We present an approach…
An algorithm is given to factor an integer with $N$ digits in $\ln^m N$ steps, with $m$ approximately 4 or 5. Textbook quadratic sieve methods are exponentially slower. An improvement with the aid of an a particular function would provide a…
Matrix factorization is an important mathematical problem encountered in the context of dictionary learning, recommendation systems and machine learning. We introduce a new `decimation' scheme that maps it to neural network models of…
The purpose of this text is to provide an accessible introduction to a set of recently developed algorithms for factorizing matrices. These new algorithms attain high practical speed by reducing the dimensionality of intermediate…
In addition to recent developments in computing speed and memory, methodological advances have contributed to significant gains in the performance of stochastic simulation. In this paper, we focus on variance reduction for matrix…
The bound to factor large integers is dominated by the computational effort to discover numbers that are smooth, typically performed by sieving a polynomial sequence. On a von Neumann architecture, sieving has log-log amortized time…