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These days the need for securing a message has been increasing and with that there has been a tremendous need for new hashing techniques and message authentication codes. This paper proposes an efficient message authentication code named here as QGMAC-384. It is based on a quasigroup of order 256 and QGMD5-384. The QGMD5-384 is a new hash function which is also proposed in this paper. This article is an extension of the work previously presented in ICSPN 2021 (Kumar, U. & Venkaiah, V. Ch., 2021). A keyed hash function (also known as a message authentication code or MAC) is a cryptographic tool. It is used to validate the sender of a message as well as to confirm that the message has not been modified in transit. The secret input (key) to the MAC is a crucial aspect of a message authentication code. By definition, a MAC's output (known as an authentication tag) must be easy to compute with the secret key but computationally hard to compute without it. For a MAC to be useful, the key must take less amount of storage space but the number of possible keys must be large enough to avoid MAC attacks. There are various ways to design a MAC. Some are based on cryptographic primitives, such as a hash function or a block cipher. The security of these MACs depends on the security of the hash function or the block cipher employed in their design. However, MAC algorithms can be designed without the use of any cryptographic primitive. They can instead be designed based on some other algebraic structure. In this case, the MAC's security is determined by the properties of the underlying algebraic structure, and one such MAC is based on Latin squares given in (Bakhtiari, 1997).
Nowadays, one of the mathematical objects called a quasigroup (Shcherbacov,2003; Teseleanu, 2020), popularly known as Latin square (Dénes & Keedwell, 1991), has received lots of attention. It is widely used in the design of various cryptographic applications (Chauhan et al., 2021), such as stream cipher (Kumar et al., 2021), secret sharing scheme (Ashwini et al., 2021), hash functions (Kumar, U. & Venkaiah, V. Ch., 2021; Dvorsky et al., 2000, 2002), and message authentication codes (Kumar, U. & Venkaiah, V. Ch., 2021; Bakhtiari, 1997). This is because; the number of quasigroups grows exponentially with the size (Velammal & Arockiadoss, 2014). So, they make an important case for the design of cryptosystems. The quasigroups are very simple non-associative algebraic structures. Using quasigroups, simple and efficient hash and MAC algorithms can be produced. One of the factors that favor quasigroups is that they can be efficiently stored. Also, quasigroup based cryptosystems are suitable for low resource devices such as smart phones, sensors, tablets, etc. Previous works done by Dvorsky et al. (2000, 2002) that use quasigroups in the design of hash functions are vulnerable to the preðx and suffix attacks (Slaminkova & Vojvoda, 2010). That is, an attacker can create a false message by adding a prefix or suffix to the original message, such that the hash values of both the messages would be same. The new hash function QGMD5-384 resists these kinds of attacks.