Arnold Map (AM) is a very useful chaotic transformation used in several encryption schemes. However, this map is not employed to its full strength in the literature due to the needless constraint that it should be area preserving (i.e., its determinant should be \(\pm 1\) ). Very recently, Turan et al. (2024 Multimed Tools Appl 83:70921–70935) discovered some new AMs with large periods and no such restriction on their determinant. In this paper, we put-forward a new authenticated encryption scheme pertaining to these newly discovered AMs, classical modified two-square cipher (MTSC) and Poly1305 MAC. The AMs are applied adaptively on the image with different moduli so as to minimize the overlapping of pixels for encryption. We demonstrate that our scheme has large key space and it is extremely responsive to a minor variation in the keys. Moreover, we perform a thorough robustness analysis of our scheme with respect to certain prominent attacks. We also compare our scheme with several other schemes in the literature, especially, with the schemes of Kumar et al. (2017 Multimed Tools Appl 76:8757–8779) and Tang et al. (2015 Multimed Tools Appl 74(15):5429–5448). Finally, we show that our scheme outperforms all the other existing schemes in terms of time taken for encryption and decryption phases.
