%0 Journal Article
%T A modification of the Cayley-Purser algorithm
%J International Journal of Nonlinear Analysis and Applications
%I Semnan University
%Z 2008-6822
%A Khlebus, Sameerah Faris
%A Hasoun, Rajaa K.
%A Sabri, Bassam Talib
%D 2022
%\ 03/01/2022
%V 13
%N 1
%P 707-716
%! A modification of the Cayley-Purser algorithm
%K cryptography
%K Cayley- Purser Algorithm
%K Galois field $ GF(p^{n})$
%K General Linear group over $ GF(p^{n})(GL_{m}(GF(p^{n}))$
%K Encryption, Decryption
%R 10.22075/ijnaa.2022.5559
%X Cayley- Purser Algorithm is a public key algorithm invited by Sarah Flannery in 1998. The algorithm of Cayley-Purser is much faster than some public key methods like RSA but the problem of it is that it can be easily broken especially if some of the private key information is known. The solution to this problem is to modify this algorithm to be more secure than before so that it gives its utilizers the confidence of using it in encrypting important and sensitive information. In this paper, a modification to this algorithm based on using general linear groups over Galois field $GF(p^n)$, which is represented by $GL_m(GF(p^n))$ where $n$ and $m$ are positive integers and $p$ is prime, instead of $GL_2(Z_n)$ which is General linear set of inverted matrices $2 \times 2$ whose entries are integers modulo $n$. This $GL_m(GF(p^n))$ ensures that the secret key of this algorithm would be very hard to be obtained. Therefore, this new modification can make the Cayley-Purser Algorithm more immune to any future attacks.
%U https://ijnaa.semnan.ac.ir/article_5559_772471a8e73f526c502cf6b19f2f7be1.pdf