A Modified Non-Sieving Quadratic Sieve For Factoring Simple Blur Integers

Huang, Qingfeng; Li, Zhitang; Zhang, Yejing; Lu, Chuiwei

doi:10.1109/mue.2007.28

Cited by 9 publications

(5 citation statements)

References 2 publications

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“…In fact, when two prime factors are close in proximity to one another, they can be computed rapidly. Furthermore, other FFA-improved algorithms such as [22], [23], [24], [25], [26] were proposed to increase computation speed.…”

Section: Overviews Of Some Algorithms To Break Rsamentioning

confidence: 99%

The Improved Estimation of the Least Upper Bound to Search for RSA’s Private key

2022

KSII TIIS

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RSA is known as one of the best techniques for securing secret information across an unsecured network. The private key which is one of private parameters is the aim for attackers. However, it is exceedingly impossible to derive this value without disclosing all unknown parameters. In fact, many methods to recover the private key were proposed, the performance of each algorithm is acceptable for the different cases. For example, Wiener's attack is extremely efficient when the private key is very small. On the other hand, Fermat's factoring can quickly break RSA when the difference between two large prime factors of the modulus is relatively small. In general, if all private parameters are not disclosed, attackers will be able to confirm that the private key is unquestionably inside the scope [3, n -2], where n is the modulus. However, this scope has already been reduced by increasing the greatest lower bound to [dil, n -2], where dil ≥ 3. The aim of this paper is to decrease the least upper bound to narrow the scope that the private key will remain within this boundary. After finishing the proposed method, the new scope of the private key can be allocated as [dil, dir], where dir ≤ n -2. In fact, if the private key is extremely close to the new greatest lower bound, it can be retrieved quickly by performing a brute force attack, in which dir is decreased until it is equal to the private key. The experimental results indicate that the proposed method is extremely effective when the difference between prime factors is close to each other and one of two following requirement holds: the first condition is that the multiplier of Euler totient function is very close to the public key's small value whereas the second condition is that the public key should be large whenever the multiplier is far enough.

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Section: Overviews Of Some Algorithms To Break Rsamentioning

confidence: 99%

The Improved Estimation of the Least Upper Bound to Search for RSA’s Private key

2022

KSII TIIS

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“…This method does not need to use a factor base. For this method, n is distinguished in two forms: n = 6k -1 and n = 6k + 1 [3]. The algorithms of each form is as follows:…”

Section: Modified Non -Sieving Quadratic Sievementioning

confidence: 99%

“…The idea of RSA is that finding the product of the large two primes is very simple, but finding the factors which are the product of these primes is computationally much harder. The security of RSA is based on the difficulty of factorization problem [3]. If some malicious persons can find the factors of the modulus n, then RSA is broken.…”

Section: Introductionmentioning

confidence: 99%

“…Recently, there are many factorization algorithms such as Trial division algorithm [8], Fermat factorization algorithm [2,3] and Monte Carlo factorization algorithm [8]. Trial division is the simplest factorization algorithm [7].…”

Section: Introductionmentioning

confidence: 99%

“…This method can finish all trivial and nontrivial value of n, called Modified Fermat Factorization (MFF). Qingfend Huange et al [3] proposed the factorization method modified from Primitive Non -sieving Quadratic Sieve (PNQS), called Modified Non -sieving Quadratic Sieve (MNQS). Both PNQS and MNQS must use the difference of squares equation.…”

Section: Introductionmentioning

confidence: 99%

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MFFV2 and MNQSV2: Improved Factorization Algorithms

Somsuk

Kasemvilas

2013

2013 International Conference on Information Science and Applications (ICISA)

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we propose a method to decrease processing time for two factorization algorithms. One is Modified Fermat Factorization Version 2 (MFFV2) modified from Modified Fermat Factorization (MFF). The other is Modified Non -sieving Quadratic Sieve Version 2 (MNQSV2) modified from Modified Non -Sieving Quadratic Sieve (MNQS). A key concept of this method is to decrease processing time to compute an integer's square root. This method can be used with all factorization algorithms which the modulus is written as the difference of squares. The experiments showed that the speed of MFFV2 increases when compares with MFF and the speed of MNQSV2 increases when compares with MNQS. In addition, if two primes' differences are small, the factorization speed of MNQSV2 is faster than the factorization speed of MFFV2.

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Possible Prime Modified Fermat Factorization: New Improved Integer Factorization to Decrease Computation Time for Breaking RSA

Somsuk

Kasemvilas

2014

Advances in Intelligent Systems and Computing

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A Modified Non-Sieving Quadratic Sieve For Factoring Simple Blur Integers

Cited by 9 publications

References 2 publications

The Improved Estimation of the Least Upper Bound to Search for RSA’s Private key

The Improved Estimation of the Least Upper Bound to Search for RSA’s Private key

MFFV2 and MNQSV2: Improved Factorization Algorithms

Possible Prime Modified Fermat Factorization: New Improved Integer Factorization to Decrease Computation Time for Breaking RSA

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