*4.3. Time Consumption*

The framework's time performance analysis was performed on a CentOS server with an Intel® Xeon® Gold 6248 CPU @ 2.50 GHz and 8 GB of RAM using Python 3. The time is taken to compute the three critical stages of data resampling, multiple linear regression modeling, and a bitwise inversion was calculated separately during the evaluation. Table 8 shows the execution time results for each phase. The shortest time-consuming stage is the bit-inverse stage, which requires no more than 25 us in the longest case and can be completed within 7 us in the fastest case. The most time-consuming phase is the data resampling phase. The execution time of the data resampling phase varies from 1.15 s to 190.67 s, with an average time of 37.23 s, which is because this stage resamples the sensor data based on the number of IDs that occur. The essential linear regression phase does not take more than 0.84 s. Overall, the time required to reverse the content of a message correctly averages 37.41 s and does not exceed 191.5 s at most.

**Table 8.** Implementation time of each stage.


### *4.4. Result of Comparison with Other Methods*

This section presents the performance comparison results between the bit-level reverse framework proposed in this study and other CAN message reverse methods. Nowadays, the effective CAN message reversal algorithms are READ [30], LibreCAN [31], ReCAN, and Bram's proposed reversal algorithm based on the correlation coefficient [30]. Among them, READ, ReCAN [32], and LibreCAN algorithms use bit-flip rates to delimit CAN message data fields; LibreCAN and Bram's scheme [37] use correlation coefficients to find the message IDs describing specific vehicle behavior. The differences between the existing algorithms and the linear regression framework in reverse results are given in Table 9. Our proposed scheme is the only one that enables boundary delineation, correlated message identification, and bit reverse. READ and ReCAN only perform CAN message data boundary delineation, Bram's scheme only addresses correlated message screening, and LibreCAN achieves both results but cannot achieve bit-level inversion. Therefore, this section only compares the performance of this framework with existing algorithms in terms of boundary delineation, correlated message filtering, and execution complexity.


**Table 9.** Reverse function compared with existing algorithms.
