How to securely outsource the extended euclidean algorithm for large-scale polynomials over finite fields

Zhou, Qiang; Tian, Chengliang; Zhang, Hanlin; Yu, Jia; Li, Fengjun

doi:10.1016/j.ins.2019.10.007

Cited by 26 publications

(12 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…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

View full text Add to dashboard Cite

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.

show abstract

Section: Related Work 21 Rsamentioning

confidence: 99%

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

Somsuk

Thakong

2020

TELKOMNIKA

View full text Add to dashboard Cite

show abstract

“…Due to the above-mentioned tremendous benefits of cloud computing, designing secure and efficient outsourcing algorithms for various of computation-extensive tasks, such as large-scale linear algebraic operations [3,14], modular exponentiations and modular inverse operations in cryptography [18,27,45,56], large-scale graph operations [54], heavy computations in artificial intelligence (AI) and internet of things (IoT) [28,51,52], has become a popular topic. Out of which, the outsourcing of matrix-related operations is closely related with our work.…”

Section: A Related Workmentioning

confidence: 99%

Securely and Efficiently Computing the Hermite Normal Form of Integer Matrices via Cloud Computing

Wei

Tian

et al. 2020

IEEE Access

Self Cite

View full text Add to dashboard Cite

The prevalence of cloud computing greatly promotes the traditional computing paradigm. With the assistance of a cloud, the light-weight device can achieve computation-intensive tasks which may not be done on its own. While, computing the Hermite Normal Form (HNF), which is a standard form of integer matrices, not only is inescapable when solving the linear system of equations over integers, but also has lots of applications in many other fields, such as integer programming and latticebased cryptography. However, the fast blowup phenomenon of intermediate numbers makes the HNF computation time-consuming. In this paper, we initialize the study of the cloud-assisted HNF computation and design an efficient outsourcing algorithm that enables the resource-constrained client to securely delegate this heavy computation to a resource-abundant yet maybe untrusted cloud server. The main idea involved in our algorithm is a novel matrix encryption method based on random permutation, unimodular matrix transformation and triangular matrix transformation, which makes our algorithm protect the client's input/output information with the one-way notion and enable the client to detect the cloud's deception with the optimal probability 1. Besides, rigorous theoretical analysis and extensive experimental evaluation validate the efficiency and the practical performance of our design, and the substantial client-side savings are remarkable as the problem size increases.

show abstract

“…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

View full text Add to dashboard Cite

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.

show abstract

How to securely outsource the extended euclidean algorithm for large-scale polynomials over finite fields

Cited by 26 publications

References 21 publications

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

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

Securely and Efficiently Computing the Hermite Normal Form of Integer Matrices via Cloud Computing

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

Contact Info

Product

Resources

About