Over the past 20 years, numerous papers have been written on various aspects of ECC implementation. In this paper, the authors investigate the superiority of the arithmetic data compression technique over the Huffman data compression technique in reducing the channel bandwidth and the transmission time. The main purpose of data compression is to reduce the memory space or transmission time, while that of cryptography is to ensure the security of the data. Applying data compression techniques not only reduces the bandwidth but also enhances the strength of the cryptosystem.