Today the Genetic Algorithm (GA) tops all the standard algorithms in solving complex nonlinear equations based on the laws of nature. However, permute convergence is considered one of the most significant drawbacks of GA, which is known as increasing the number of iterations needed to achieve a global optimum. To address this shortcoming, this paper proposes a new GA based on chaotic systems. In GA processes, we use the logistic map and the Linear Feedback Shift Register (LFSR) to generate chaotic values to use instead of each step requiring random values. The Chaos Genetic Algorithm (CGA) avoids local convergence more frequently than the traditional GA due to its diversity. The concept is using chaotic sequences with LFSR to generate seed values for genetic algorithms, which can generate keys with a high degree of randomness. The quality of key (generated sequence) was tested using known standard tests, then a comparison table is presented to show the increase in ratios in the test before and after applying GA, demonstrating that the proposed system generates sequence (key) with high randomness degree, The proposed system achieved an increase in the randomness rate by four degrees on average and thus it solves the problem of repetition and linearity, Finally, The system is built in the Java environment.