To authenticate a controller area network (CAN) data frame, a message authentication code (MAC) must be sent along with the CAN frame, but there is no space reserved for the MAC in the CAN frame. Recently, difference-based compression (DBC) algorithms have been used to create a space inside the frame. DBC has the advantage of being very efficient, but its drawback is that, if an error occurs in one frame, the effects of that error propagate to subsequent frames. In this paper, a CAN data compression algorithm is proposed that compresses the current frame without relying on previous frames. Therefore, an error generated in one frame cannot be propagated to subsequent frames. In addition, a CAN signal grouping technique is proposed based on entropy analysis. To efficiently authenticate CAN frames, the length of the compressed data must be 4 bytes or less (4BL). Simulation shows that the 4BL-compression ratio of a Kia Sorento vehicle is 99.36% in the DBC method, but 100% in the proposed method. In an LS Mtron tractor, the 4BL-compression ratio is 98.58% in the DBC method, but 100% in the proposed method. In addition, the execution time of the proposed compression algorithm is only 27.39% of that of the DBC algorithm. The results show that the proposed algorithm has better compression characteristics for CAN security than the DBC algorithms.