Related papers: Performance Analysis of Parallel Pollard's Rho Alg…
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…
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…
One of the most significant challenges on cryptography today is the problem of factoring large integers since there are no algorithms that can factor in polynomial time, and factoring large numbers more than some limits(200 digits) remain…
With the advancement of quantum technologies, there is a potential threat to traditional encryption systems based on integer factorization. Therefore, developing techniques for accurately measuring the performance of associated quantum…
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…
Quantum algorithms are at the heart of the ongoing efforts to use quantum mechanics to solve computational problems unsolvable on ordinary classical computers. Their common feature is the use of genuine quantum properties such as…
The theoretical aspects of four integer factorization algorithms are discussed in details in this note. The focus is on the performances of these algorithms on the subset of hard to factor balanced integers N = pq, p < q < 2p. The running…
A digital computer is generally believed to be an efficient universal computing device; that is, it is believed able to simulate any physical computing device with an increase in computation time of at most a polynomial factor. This may not…
We describe a novel analogue algorithm that allows the simultaneous factorization of an exponential number of large integers with a polynomial number of experimental runs. It is the interference-induced periodicity of "factoring"…
Modern-day computer security relies heavily on cryptography as a means to protect the data that we have become increasingly reliant on. The main research in computer security domain is how to enhance the speed of RSA algorithm. The…
As multicore systems continue to gain ground in the High Performance Computing world, linear algebra algorithms have to be reformulated or new algorithms have to be developed in order to take advantage of the architectural features on these…
The assumed computationally difficulty of factoring large integers forms the basis of security for RSA public-key cryptography, which specifically relies on products of two large primes or semi-primes. The best-known factoring algorithms…
Lenstra's integer factorization algorithm is asymptotically one of the fastest known algorithms, and is ideally suited for parallel computation. We suggest a way in which the algorithm can be speeded up by the addition of a second phase.…
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…
Pollard's rho method finds a prime factor $p$ of an integer $N$ by searching for a collision in a map of the form $x \mapsto x^{2k} + c$ modulo $N$. This search can be parallelized to multiple machines, which may use distinct parameters $k$…
Integer factorization is a significant problem, with implications for the security of widely-used cryptographic schemes. No efficient classical algorithm for polynomial-time integer factorization has been found despite extensive research.…
As multicore systems continue to gain ground in the High Performance Computing world, linear algebra algorithms have to be reformulated or new algorithms have to be developed in order to take advantage of the architectural features on these…
Integer factorization is a very hard computational problem. Currently no efficient algorithm for integer factorization is publicly known. However, this is an important problem on which it relies the security of many real world cryptographic…
Sorting is one of the most fundamental problems in the field of computer science. With the rapid development of manycore processors, it shows great importance to design efficient parallel sort algorithm on manycore architecture. This paper…
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…