Notice of Violation of IEEE Publication Principles: Modified Integer Factorization Algorithm Using V-Factor Method

Sharma, Prashant; Gupta‬‬‬‬‬‬‬‬‬‬‬‬‬‬‬‬‬‬‬‬‬‬‬‬‬‬‬‬‬‬, Amit Kumar; Vijay, Ashish

doi:10.1109/acct.2012.73

Cited by 15 publications

(5 citation statements)

References 14 publications

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“…In fact, if attackers can recover two large prime factors of the modulus, then RSA is broken. Although, Integer Factorization is one of the hard problems to break RSA, many integer factorization algorithms, such as [4][5][6][7][8][9][10] are still developing to find the weakness of RSA which is not still disclosed. In general, the efficiency of each algorithm is based on characteristic of prime factors.…”

Section: Introductionmentioning

confidence: 99%

The new integer factorization algorithm based on Fermat’s Factorization Algorithm and Euler’s theorem

Somsuk¹

2020

IJECE

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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 that 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.

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Section: Introductionmentioning

confidence: 99%

The new integer factorization algorithm based on Fermat’s Factorization Algorithm and Euler’s theorem

Somsuk¹

2020

IJECE

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“…The aim of this paper is to modify one of the factoring algortihms which is suitable for the small result of p-q. The algorithm is called VFactor [15]. Both of two initial values are usually assigned for VFactor, x and y.…”

Section: Introductionmentioning

confidence: 99%

Improving the initial values of VFactor suitable for balanced modulus

Somsuk

2020

IJECE

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The aim of this study is to estimate the new initial values of VFactor. In general, this algorithm is one of the members in a group of special proposed integer factorization algorithm. It has very high performance whenever the result of the difference between two prime factors of the modulus is a little, it is also called as balanced modulus. In fact, if this situation is occurred, RSA which is a type of public key cryptosystem will be broken easily. In addition, the main process of VFactor is to increase and decrease two odd integers in order to compute the multiplication until the targets are found. However, the initial values are far from the targets especially that the large value of the difference between two prime factors that is not suitable for VFactor. Therefore, the new initial values which are closer to the targets than the traditional values are proposed to decrease loops of the computation. In experimental results, it is shown that the loops can be decreased about 26% for the example of 256 bits-length of modulus that is from the small result of the difference between prime factors.

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“…Many factorization algorithms have been still developed continuously such as Trial Division algorithm (TDM) [2,3], Pollard's p-1 algorithm [2,3], Quadratic Sieve (QS) [4,5], Vfactor [6], Fermat's Factorization algorithm (FFM) [2,7] and Modified Fermat Factorization (MFF) [2] modified from FFM. For MFF, we have to compute the difference between two integers and the square root of the result to find the integer result for every iteration.…”

Section: Introductionmentioning

confidence: 99%

MFFV3: An Improved Integer Factorization Algorithm to Increase Computation Speed

Somsuk

Kasemvilas

2014

AMR

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RSA, a public key cryptosystem, was proposed to protect the information in the insecure channel. The security of RSA relies on the difficulty of factoring the modulus which is the product of two large primes. We proposed Modified Fermat Factorization Version 2 (MFFV2) modified from Modified Fermat Factorization (MFF) to break RSA. The key of MFFV2 is to decrease the number of times of MFF for computing an integers square root. However, MFFV2 is still time-consuming to some extent due to computation time of the subtraction of two integers for all iterations. Thus, this paper aims to propose Modified Fermat Factorization Version 3 (MFFV3) to increase the computation speed when compared with MFFV2. For MFFV3, we can ignore computing the difference between two integers when we know that the subtractions result is certainly not a perfect square. Hence, we develop the Differences Least Significant Digit Table (DLSDT), the information table used to analyze the least significant digit of the subtractions result. Experimental results show that the computation time of MFFV3 for factoring the modulus is substantially reduced in comparison to MFF and MFFV2 respectively.

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Notice of Violation of IEEE Publication Principles: Modified Integer Factorization Algorithm Using V-Factor Method

Cited by 15 publications

References 14 publications

The new integer factorization algorithm based on Fermat’s Factorization Algorithm and Euler’s theorem

The new integer factorization algorithm based on Fermat’s Factorization Algorithm and Euler’s theorem

Improving the initial values of VFactor suitable for balanced modulus

MFFV3: An Improved Integer Factorization Algorithm to Increase Computation Speed

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