Currently, there are around 4.95 billion people who use the internet, which creates a large audience with an increasing demand for activities that can be done online. Some examples of these activities include social networking, information sharing, and online shopping. Therefore, there is an urgent need for improved levels of secrecy and privacy. It has recently come to light that one of the most serious challenges to the mainstream adoption of business apps is that of online fraud. As a direct consequence of this, issues pertaining to authentic cation, authorization, and identification have emerged as critical considerations in today's open and accessible society. The act of recognizing an entity, whether it be a human, a computer, or a software program, is referred to as the identification process. Authentication and authorization are complementary processes that are used in security systems to decide which persons are permitted to access information resources over a network. Authentication is performed by the user's device, while authorization is performed by the security system. However, a variety of potential solutions have been suggested, one of which is the use of parallelism in order to boost the efficiency of authentication methods. This work proposes a new message authentication algorithm that is applied in parallel over a multicore processor. The proposed message authentication algorithm uses two PNGRs and two substitution boxes to encrypt and authenticate the plain message. The encryption process has a one-round operation, making it a fast technique to encrypt and decrypt blocks of messages. In comparison to the existing method, the proposed authentication method outperforms the parallel speck-based authentication method by an average of 3.27 times faster when executed over a multicore CPU. The average speedup compared to the sequential version of the proposed algorithm and its parallel implementation is 2.99. The proposed method passes the most difficult randomness test, and the obtained MAC values are tested further to meet other security measurements.