Performance Analysis of 128-bit Modular Inverse Based Extended Euclidean Using Altera FPGA Kit

Asad, Mohammad M.; Marouf, Ibrahim; Al‐Haija, Qasem Abu; AlShuaibi, Abdullah

doi:10.1016/j.procs.2019.11.050

Cited by 7 publications

(3 citation statements)

References 7 publications

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“…Step 5: Compute private key, d, from the following equation: ed  1 mod (n). In fact, the key to find the result in this step is to use extended Euclidean algorithm [16][17][18]. Process 2 (Encryption Process): it is the process to transform plaintext, m, where 0 < m < n, as unreadable message or ciphertext, c, before sending to receiver by using the following equation:…”

Section: Related Work 21 Rsamentioning

confidence: 99%

Authentication system for e-certificate by using RSA’s digital signature

Somsuk

Thakong

2020

TELKOMNIKA

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Online learning and teaching become the popular channel for all participants, because they can access the courses everywhere with the high-speed internet. E-certificate is being prepared for everyone who has participated or passed the requirements of the courses. Because of many benefits from e-certificate, it may become the demand for intruders to counterfeit the certificate. In this paper, Rivest-Shamir-Adleman (RSA)'s digital signature is chosen to sign e-certificate in order to avoid being counterfeited by intruders. There are two applications to manage ecertificate. The first application is the signing application to sign the sub image including only participant's name in e-certificate. In general, the file of digital signature is divided from e-certificate. That means, both of them must be selected to compare each other in checking application. In fact, the solution will be approved when each pixel of participant's name is equal to each part from the decrypted message at the same position. In experimental session, 40 e-certificates are chosen for the implementation. The results reveal that the accuracy is 100% and both of signing and checking processes are completed rapidly fast, especially when signing application is applied with Chinese remainder theorem (CRT) or the special technique of CRT. Therefore, the proposed method is one of the best solutions to protect e-certificate from the forgery by intruders.

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Section: Related Work 21 Rsamentioning

confidence: 99%

Authentication system for e-certificate by using RSA’s digital signature

Somsuk

Thakong

2020

TELKOMNIKA

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“…Computing d, from e*d mod Φ (n) = 1, is performed in the last step. In fact, Extended Euclidean Algorithm or the improved methods [14], [15] are the method to calculate d. The second process is the encryption process. It will convert the original plaintext, m, as unreadable message or ciphertext, c, from the equation: c = m e mod n. However, m will be recovered by using the decryption equation: m = c d mod n in the last process.…”

Section: Rsamentioning

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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“…The next step is to select a public key, t, with the following condition, 1<t<  (n) and gcd(t,  (n) )=1. After that, a private key, h, can be computed from t*h mod  (n)=1 by using some of extended euclidean algorithms [16][17][18][19]. The second process is an encryption process to convert original plaintext, m, as ciphertext, c, from the equation: c=m t mod n. The last process is a decryption process to recover m by using the equation: m=c h mod n. Generally, it is very difficult to break this system when bit-length of n is at least 1024 and all parameters are strong.…”

Section: Related Work 21 Rsamentioning

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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Performance Analysis of 128-bit Modular Inverse Based Extended Euclidean Using Altera FPGA Kit

Cited by 7 publications

References 7 publications

Authentication system for e-certificate by using RSA’s digital signature

Authentication system for e-certificate by using RSA’s digital signature

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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