Modified trial division algorithm using KNJ-factorization method to factorize RSA public key encryption

Lal, Nidhi; Singh, Anurag Prakash; Kumar, Shishupal

doi:10.1109/ic3i.2014.7019588

Cited by 10 publications

(5 citation statements)

References 12 publications

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“…Trial division algorithm (TDA) is the method for discovering p and q by for factoring n. It is divided into two techniques. The first way [19] is to select 3 as the initial divisor which is always increased by two when the remainder exists. This approach can quickly discover p and q when p is a small integer, as it is particularly efficient when p is small.…”

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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“…Beragam kajian telah membahas tentang kombinasi dan improvisasi untuk menambahkan tingkat keamanan RSA [5], [10]- [14]. Namun, penelitian tersebut hanya membahas pengembangan algoritme RSA dengan menggunakan satu metode saja.…”

Section: Pendahuluanunclassified

“…Lal dkk. [14] mengembangkan faktorisasi KNJ untuk mempercepat kinerja RSA dengan mengecek faktor yang bernilai ganjil dan prima.…”

Section: Pendahuluanunclassified

RSA algorithm using key generator ESRKGS to encrypt chat messages with TCP/IP protocol

Aminudin

Aditya

Arifianto

2020

Jurnal Teknologi dan Sistem Komputer

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This study aims to analyze the performance and security of the RSA algorithm in combination with the key generation method of enhanced and secured RSA key generation scheme (ESRKGS). ESRKGS is an improvement of the RSA improvisation by adding four prime numbers in the property embedded in key generation. This method was applied to instant messaging using TCP sockets. The ESRKGS+RSA algorithm was designed using standard RSA development by modified the private and public key pairs. Thus, the modification was expected to make it more challenging to factorize a large number n into prime numbers. The ESRKGS+RSA method required 10.437 ms faster than the improvised RSA that uses the same four prime numbers in conducting key generation processes at 1024-bit prime number. It also applies to the encryption and decryption process. In the security testing using Fermat Factorization on a 32-bit key, no prime number factor was found. The test was processed for 15 hours until the test computer resource runs out.

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“…Trial division algorithm (TDA) [18], [19] is the simplest integer factorization algorithm and it is divided into two techniques. The concept of this algorithm is to find the correct divisor of n. First, the divisor is begun as 3 and it is increased whenever the result is not the target answer.…”

Section: ) Trial Division Algorithmmentioning

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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Modified trial division algorithm using KNJ-factorization method to factorize RSA public key encryption

Cited by 10 publications

References 12 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

RSA algorithm using key generator ESRKGS to encrypt chat messages with TCP/IP protocol

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

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