Mitigating security flaws in Baptista’s chaotic cryptosystem through superior and alternated logistic map approaches

Abstract

This research delves into the concerns raised by numerous researchers regarding the security of Baptista’s chaotic cryptosystem. The paper scrutinizes two fundamental issues in the Baptista algorithm: the imperfect distribution of chaotic data and the constraints of a single attractor. To address these issues, we propose a novel approach that leverages Parrondo’s paradox to switch between two chaotic attractors and integrates a more robust logistic map into the Baptista algorithm by introducing additional parameters to the secret key. The two innovative methods, Superior Baptista and alternated Superior Baptista cryptosystems, are proposed to yield improved chaotic data or two new chaotic attractors. Therefore, the security features of the cryptosystem are enhanced by increasing the number of system iterations used for encryption. Experimental evaluations show that the Superior Baptista Algorithm required iteration counts up to 2,823, while the Alternated variant reached 86,556 iterations for specific characters, significantly improving randomness and diffusion. Furthermore, the entropy values of these algorithms are calculated 67.35% and 42.86% higher than those of the Baptista algorithm, respectively. These findings demonstrate the superiority of the proposed cryptosystems over the base algorithm.