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

Area of Science:

• Cryptography
• Chaos Theory
• Information Security

Background:

• Concerns exist regarding the security of the Baptista chaotic cryptosystem.
• Key issues include imperfect chaotic data distribution and single attractor limitations.

Purpose of the Study:

• To address security vulnerabilities in the Baptista cryptosystem.
• To propose novel methods for enhancing chaotic cryptosystem security and performance.

Main Methods:

• Leveraging Parrondo's paradox to switch between two chaotic attractors.
• Integrating a robust logistic map with additional secret key parameters.
• Developing Superior Baptista and alternated Superior Baptista cryptosystems.
• Increasing system iterations for encryption.

Main Results:

• Proposed cryptosystems yield improved chaotic data and new attractors.
• Superior Baptista Algorithm required up to 2,823 iterations.
• Alternated variant reached 86,556 iterations for specific characters.
• Entropy values increased by 67.35% and 42.86% compared to the base algorithm.

Conclusions:

• The proposed Superior Baptista and alternated Superior Baptista cryptosystems significantly enhance security.
• These novel methods demonstrate superior randomness and diffusion over the original Baptista algorithm.