Department of Mathematics, College of Science, King Saud University, Riyadh, Saudi Arabia.
Department of Mathematics, Government College University, Faisalabad, Pakistan.
PLoS One. 2024 Sep 27;19(9):e0308140. doi: 10.1371/journal.pone.0308140. eCollection 2024.
The field of cryptography has grown significantly with the advent of information and communication technologies due to the increasing complexity of cyber threats and rising security requirements. This evolution has come with the creation of new cryptosystems and improvements to current ones. This study is the first to explore the RSA approach in the framework of t-intuitionistic fuzzy subgroups. This technique makes group-based cryptographic operations safer when there are unclear relationships and hesitations. This supports the complex and uncertain nature of subgroup membership, allowing for much more significant representations of the degrees of belonging, non-belonging, and hesitancy for the group elements along parameter 't'. The t-intuitionistic fuzzy RSA technique employs a t-intuitionistic fuzzy subgroup to address cryptosystem ambiguity, fuzziness, and imprecision. Consequently, inaccurate cryptographic data is more effectively represented, manipulated, and protected. Furthermore, this technique enhances the current level of fuzzy cryptography. The t-intuitionistic fuzzy RSA algorithms are of theoretical and practical value, as they significantly contribute towards developing fuzzy cryptography, fuzzy algebraic structures, and decision support systems. In this paper, the notions of t-intuitionistic fuzzy numbers and triangular t-intuitionistic fuzzy numbers are introduced. A new RSA cryptosystem based on a t-intuitionistic fuzzy subgroup is proposed in which the plaintext and the ciphertext are obtained in terms of t-intuitionistic fuzzy numbers and triangular t-intuitionistic fuzzy numbers. In addition, the significance of the concept of the t-intuitionistic fuzzy subgroup is highlighted as a suitable alternative tool to secure the data under consideration. In addition, the practical effect of the proposed methods is also investigated in this study. A mathematical mechanism is presented to implement the t-intuitionistic fuzzy RSA algorithm. Finally, a comparative analysis of the developed technique is presented with some existing methods to showcase the applicability and superiority of the recently developed method.
随着信息和通信技术的发展，密码学领域得到了显著发展，因为网络威胁的日益复杂和安全要求的不断提高。这种发展带来了新的密码系统的创建和现有密码系统的改进。本研究首次探索了在 t-直觉模糊子群框架内的 RSA 方法。当存在不明确的关系和犹豫时，这种技术使基于群组的密码操作更加安全。这支持了子群成员关系的复杂性和不确定性，允许对子群元素的归属、非归属和犹豫程度进行更有意义的表示，参数为't'。t-直觉模糊 RSA 技术采用 t-直觉模糊子群来解决密码系统的模糊性、不精确性和歧义性。因此，可以更有效地表示、操作和保护不准确的密码数据。此外，这项技术提高了当前的模糊密码学水平。t-直觉模糊 RSA 算法具有理论和实际价值，因为它们为开发模糊密码学、模糊代数结构和决策支持系统做出了重要贡献。本文引入了 t-直觉模糊数和三角 t-直觉模糊数的概念。提出了一种基于 t-直觉模糊子群的新 RSA 密码系统，其中明文和密文是通过 t-直觉模糊数和三角 t-直觉模糊数来获得的。此外，强调了 t-直觉模糊子群概念的重要性，作为一种合适的替代工具来保护所考虑的数据。此外，本研究还研究了所提出方法的实际效果。提出了一种数学机制来实现 t-直觉模糊 RSA 算法。最后，与一些现有方法进行了比较分析，展示了最近开发的方法的适用性和优越性。
