Integer Factorization

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. 1. INTRODUCTION Nowadays, the significant information is always exchanged via the communication channel connected to computer system such as internet. Generally, this channel is the insecure channel. That means attackers can access data easily by using various techniques. With this reason, security for the information becomes very important. At present, many security algorithms were introduced to protect the secret data sending over insecure channel. Cryptography is one of techniques to defend data from attackers by using encryption and decryption processes. In addition, there are two types about cryptography. The first is symmetric key cryptography using the same key which is called secret key for encryption and decryption processes. The second is asymmetric key cryptography (or public key cryptography) [1] using a pair of keys for encryption and decryption. In addition, one key which is always distributed to keep in the key center is called public key. On the other hand, the other key which is always kept secretly by owner's key is called private key. RSA [2] is the most well-known public key cryptography used for both of digital signature and data encryption. This algorithm is one-way function. That means it is very easy to compute the production of