## 4 Experimental Analysis
A critical metric for evaluating the encryption performance of the generalized two-dimensional polynomial chaotic mapping involves analyzing the distribution characteristics of plaintext and ciphertext, as well as the randomness of ciphertext binary sequences (0-1). Non-random or non-uniform ciphertext distributions could enable attackers to compromise the encrypted data. To rigorously evaluate this method's encryption performance, we encrypted an 8 KB English text, with the resulting plaintext and ciphertext distributions illustrated in Figures 7 and 8, respectively. Figures 7 and 8 reveal significant spatial distribution differences in ASCII values between plaintext and ciphertext. While the original plaintext displays distinct statistical patterns, the ciphertext processed by the proposed encryption method demonstrates uniform distribution characteristics. This transformation effectively obscures the original data features, preventing potential ciphertext-only attacks through statistical analysis and consequently enhancing data security. Figure 8: Ciphertext histogram. Figure 6: Bifurcation diagram of state variables with control parameters \(\alpha_{1}\) and \(\mu\). Figure 7: Plain text histogram. Using this method, the information for this typical building power system is transmitted securely by high-speed power line carrier communication, with secure transmission results shown in Table 1.  
As indicated in Table 1, this method effectively employs the generalized two-dimensional polynomial chaotic mapping technique to achieve deep information encryption, significantly enhancing the confidentiality level during transmission. Moreover, this method has been successfully implemented in high-speed power line carrier communication to ensure secure data transmission, guaranteeing that the received information remains intact and free from decryption or tampering, thereby further strengthening the system's security. The encryption time varies between 8.9 ms and 15.2 ms, averaging approximately 11.4 ms, while the transmission delay ranges from 6.2 ms to 9.1 ms, with an average of 7.9 ms. All information categories are transmitted successfully, and the security performance is confirmed (including leakage prevention, tamper resistance, and timely response). The generalized two-dimensional polynomial chaotic mapping encryption significantly enhances data security and effectively resists ciphertext-only attacks. The encryption time and transmission delay, measured in milliseconds, meet the real-time requirements of high-speed power line carrier communication. The proposed method demonstrates excellent performance in security, real-time capability, and reliability, making it suitable for applications with strict data confidentiality requirements, such as smart grids, industrial monitoring, and smart home systems. The bit error rate (BER) between the received data and the original data is calculated to verify the secure transmission performance of this method in high-speed power line carrier communication. Furthermore, the secure transmission performance of this method is compared with that of two-dimensional logistic mapping, the method in reference [6], and the method in reference [7] under different noise levels. The analysis results are shown in Figure 9.  
As can be seen from Figure 9, when the signal-to-noise ratio is small and different chaotic maps are used, the method in this paper can obtain almost the same bit error rate, with a maximum value of 0.051. However, with the increase in signal-to-noise ratio, using the generalized two-dimensional polynomial chaotic mapping proposed in this paper can obtain a smaller bit error rate than using the two-dimensional logistic mapping, reference [6]'s method, and reference [7]'s method. The minimum bit error rate obtained by