A New Modified MD5-224 Bits Hash Function and an Efficient Message Authentication Code Based on Quasigroups

In this paper, we have proposed  (i) a hash function and (ii) an efficient message authentication code based on quasigroup. We refer to these as QGMD5 and QGMAC, respectively. The proposed new hash function QGMD5 is an extended version of MD5 that uses an optimal quasigroup along with two operations named as QGExp and QGComp. The operations quasigroup expansion (QGExp) and the quasigroup compression (QGComp) are also defined in this paper. QGMAC is designed using the proposed hash function QGMD5 and a quasigroup of order 256 as the secret key. The security of QGMD5 is analyzed by comparing it with both the MD5 and the SHA-244. It is found that the proposed QGMD5 hash function is more secure. Also, QGMAC is analyzed against the brute-force attack. It is resistant to this attack because of the exponential number of quasigroups of its order. It is also analyzed for the forgery attack, and it is found to be resistant. In addition, we compared the performance of the proposed hash function to that of the existing MD5 and SHA-224. Similarly, the performance of the proposed QGMAC is compared with that of the existing HMAC-MD5 and HMAC-SHA-224. The results show that the proposed QGMD5 would take around 2 \(\mu s\) additional execution time from that of MD5 but not more than SHA-224, while QGMAC always takes less time than that of both the HMAC-MD5 and the HMAC-SHA-224. So, our schemes can be deployed in all the applications of hash functions, such as in blockchain and for verifying the integrity of messages.