MVFactor: A method to decrease processing time for factorization algorithm

Somsuk, Kritsanapong; Kasemvilas, Sumonta

doi:10.1109/icsec.2013.6694805

Cited by 7 publications

(8 citation statements)

References 12 publications

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“…In addition, the method is from the combination between euler's theorem and FFA. In fact, (8) is rewritten as following: a n-(p +q) +1  1 mod n (9)  mod n and b is recomputed by using modular multiplication with c 2 mod n whenever the result which is equal to 1 is not found as follow: b=b*c 2 mod n (10) From (10), the result is certainly equal to 1 whenever the process is repeated l u times.…”

Section: The Proposed Methodsmentioning

confidence: 99%

“…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%

“…Because, l u is represented as loops of the proposed method and the increasing step is 2, it implies that loops between the method and FFA-1 are same. In addition, c 2 mod n should be calculated as the constant at first, because it is often operated in (10). Furthermore, it should be assigned as small integer to decrease the cost.…”

mentioning

confidence: 99%

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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: The Proposed Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Somsuk¹

2020

IJECE

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“…On the other hand, one of them must be changed until the target is found. In addition, the improvement of VFactor [27], [28] were proposed to skip some loops to decrease computation time.…”

Section: ) Vfactormentioning

confidence: 99%

The new Weakness of RSA and The Algorithm to Solve this Problem

2020

KSII TIIS

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RSA is one of the best well-known public key cryptosystems. This methodology is widely used at present because there is not any algorithm which can break this system that has all strong parameters within polynomial time. However, it may be easily broken when at least one parameter is weak. In fact, many weak parameters are already found and are solved by some algorithms. Some examples of weak parameters consist of a small private key, a large private key, a small prime factor and a small result of the difference between two prime factors. In this paper, the new weakness of RSA is proposed. Assuming Euler's totient value, Φ (n), can be rewritten as Φ (n) = ad + b, where d is the private key and , a b ∈  , if a divides both of Φ (n) and b and the new exponent for the decryption equation is a small integer, this condition is assigned as the new weakness for breaking RSA. Firstly, the specific algorithm which is created for this weakness directly is proposed. Secondly, two equations are presented to find a, b and d. In fact, one of two equations must be implemented to find a and b at first. After that, the other equation is chosen to find d. The experimental results show that if this weakness has happened and the new exponent is small, original plaintext, m, will be recovered very fast. Furthermore, number of steps to recover d are very small when a is large. However, if a is too large, d may not be recovered because m which must be always written as m = h a is higher than modulus.

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“…Moreover, the modified algorithms of VFactor were proposed to remove some loops and time. MVFactor [20] is the technique to decrease both of x and y out of the computation when the last digit is equal to 5. In fact, the odd integers which the last digit is equal to 5, except 5, are not certainly a prime number, because 5 divides all of them.…”

Section: Vfactor and Improvementmentioning

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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MVFactor: A method to decrease processing time for factorization algorithm

Cited by 7 publications

References 12 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

The new Weakness of RSA and The Algorithm to Solve this Problem

Improving the initial values of VFactor suitable for balanced modulus

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