Research on Password Algorithms based on Chaos and Algebraic Groups

As information technology advances rapidly, the demand for data security continues to grow. Chaos theory and algebraic groups have become a focal point in cryptographic research, providing a foundation for designing more robust block cipher algorithms. This article introduces a password algorithm based on chaos and algebraic groups, proposing the Lorenz chaos-geometric Goppa code composite password algorithm that has demonstrated significant achievements in image processing. In comparison to traditional methods, this algorithm exhibits the shortest key length and reduced error rates in image processing, offering a more reliable data protection solution for practical applications. This research opens up new possibilities for enhancing the security and performance in the field of cryptography.