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- Title
The new integer factorization algorithm based on fermat's factorization algorithm and euler's theorem.
- Authors
Somsuk, Kritsanapong
- Abstract
Although, Integer Factorization is one of the hard problems to break RSA, many factoring techniques are still developed. Fermat's Factorization Algorithm (FFA) which has very high performance when prime factors are close to each other is a type of integer factorization algorithms. In fact, there are two ways to implement FFA. The first is called FFA-1, it is a process to find the integer from square root computing. Because this operation takes high computation cost, it consumes high computation time to find the result. The other method is called FFA-2 which is the different technique to find prime factors. Although the computation loops are quite large, there is no square root computing included into the computation. In this paper, the new efficient factorization algorithm is introduced. Euler's theorem is chosen to apply with FFA to find the addition result between two prime factors. The advantage of the proposed method is that almost of square root operations are left out from the computation while loops are not increased, they are equal to the first method. Therefore, if the proposed method is compared with the FFA-1, it implies that the computation time is decreased, because there is no the square root operation and the loops are same. On the other hand, the loops of the proposed method are less than the second method. Therefore, time is also reduced. Furthermore, the proposed method can be also selected to apply with many methods which are modified from FFA to decrease more cost.
- Subjects
EULER theorem; SQUARE root; INTEGERS; ALGORITHMS
- Publication
International Journal of Electrical & Computer Engineering (2088-8708), 2020, Vol 10, Issue 2, p1469
- ISSN
2088-8708
- Publication type
Article
- DOI
10.11591/ijece.v10i2.pp1469-1476