A Public-Key Cryptosystem Using Cyclotomic Matrices
This work addresses confidentiality and integrity in information and communication technology, but appears incremental as it builds on existing arithmetic approaches for cryptography.
The authors tackled the problem of designing asymmetric key cryptography by proposing a cyclotomic asymmetric cryptosystem (CAC) based on cyclotomic matrices, achieving encryption and decryption with asymptotic complexity of O(e^2.373).
Confidentiality and Integrity are two paramount objectives in the evaluation of information and communication technology. In this paper, we propose an arithmetic approach for designing asymmetric key cryptography. Our method is based on the formulation of cyclotomic matrices correspond to the diophantine system. The proposed cyclotomic asymmetric cryptosystem (CAC) utilizes the cyclotomic matrices, whose entries are cyclotomic numbers of order $2l^{2}$, $l$ be prime over a finite field $\mathbb{F}_{p}$ of $p$ elements. The method utilize cyclotomic matrices to design a one-way function. The outcome of a one-way function that is efficient to compute however difficult to compute its inverse unless if secret data about the trapdoor is known. We demonstrate that the encryption and decryption can be efficiently performed with asymptotic complexity of $\mathcal{O}(e^{2.373})$. Besides, we study the computational complexity of the CAC.