Nowadays, physical unclonable functions (PUFs) are emerging as one of the key building blocks for device authentication and key generation. Although PUF is very useful in the area of hardware security, it is vulnerable to machine learning modelling attacks (ML-MA) by modelling the challenge-response pairs (CRPs) behaviour. To this end, this study proposes a novel PUF named MARPUF, which gives good resistance to machine learning (ML) attacks. The study proposed a MARPUF design, where the mapping of CRPs is randomized by implementing two-round challenges to meet the randomness requirements for ML resistance. Ssome of the popular ML techniques are used to test the ML attack resistance and compare the results with some existing PUFs. We evaluate the performance of the PUF against various parameters like reliability, uniformity, uniqueness, etc. The hardware cost analysis shows that MARPUF requires lesser hardware than the existing ML-MA resistant PUFs. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.