In this work, we propose a new public-key cryptosystem whose security is based on the computational intractability of the following problem: Given a Mersenne number
$$p = 2^n - 1$$
p=2n-1, where n is a prime, a positive integer h, and two n-bit integers T, R, decide whether their exist n-bit integers F, G each of Hamming weight less than h such that
$$T = F\cdot R + G$$
T=F·R+G modulo p.

@article{crypto-2018-28795,
title={A New Public-Key Cryptosystem via Mersenne Numbers},
booktitle={Advances in Cryptology – CRYPTO 2018},
series={Lecture Notes in Computer Science},
publisher={Springer},
volume={10993},
pages={459-482},
doi={10.1007/978-3-319-96878-0_16},
author={Divesh Aggarwal and Antoine Joux and Anupam Prakash and Miklos Santha},
year=2018
}