منابع مشابه
Integer factorization
“The problem of distinguishing prime numbers from composite numbers, and of resolving the latter into their prime factors, is known to be one of the most important and useful in arithmetic,” Gauss wrote in his Disquisitiones Arithmeticae in 1801. “The dignity of the science itself seems to require that every possible means be explored for the solution of a problem so elegant and so celebrated.”...
متن کاملOn the WZ Factorization of the Real and Integer Matrices
The textit{QIF} (Quadrant Interlocking Factorization) method of Evans and Hatzopoulos solves linear equation systems using textit{WZ} factorization. The WZ factorization can be faster than the textit{LU} factorization because, it performs the simultaneous evaluation of two columns or two rows. Here, we present a method for computing the real and integer textit{WZ} and textit{ZW} factoriz...
متن کاملFaster deterministic integer factorization
The best known unconditional deterministic complexity bound for computing the prime factorization of an integer N is O(Mint(N 1/4 logN)), where Mint(k) denotes the cost of multiplying k-bit integers. This result is due to Bostan–Gaudry–Schost, following the Pollard–Strassen approach. We show that this bound can be improved by a factor of √
متن کاملMapReduce for Integer Factorization
Integer factorization is a very hard computational problem. Currently no e cient algorithm for integer factorization is publicly known. However, this is an important problem on which it relies the security of many real world cryptographic systems. I present an implementation of a fast factorization algorithm on MapReduce. MapReduce is a programming model for high performance applications develo...
متن کاملDeterministic Integer Factorization Algorithms
This note presents a deterministic integer factorization algorithm of running time complexity O(N), ε > 0. This improves the current performances of deterministic integer factorization algorithms rated at O(N) arithmetic operations. Equivalently, given the least (log N)/6 bits of a factor of N = pq, where p and q are primes, the algorithm factors the integer in polynomial time O(log(N)), c ≥ 0 ...
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ژورنال
عنوان ژورنال: DAIMI Report Series
سال: 1983
ISSN: 2245-9316,0105-8517
DOI: 10.7146/dpb.v11i144.7419