Improved security of short message services (SMS) can be obtained using cryptographic methods, both symmetric and asymmetric, but must remain efficient. This paper aims to study the performance and efficiency of the symmetric crypto of AES-128 and asymmetric crypto of RSA with message compression in securing SMS messages. The ciphertext of RSA and AES were compressed using the Huffman algorithm. The average AES encryption time for each character is faster than RSA, which is 5.8 and 24.7 ms/character for AES and AES+Huffman encryption and 8.7 and 45.8 ms/character for RSA and RSA+Huffman, from messages with 15, 30, 60 and 90 characters. AES decryption time is also faster, which is 27.2 ms/character compared to 47.6 ms/character in RSA. Huffman compression produces an average efficiency of 24.8 % for the RSA algorithm, better than 17.35 % of AES efficiency for plaintext of 1, 16, 45, and 88 characters.