A New Public-Key Cryptosystem via Mersenne Numbers

Summary

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, 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 R + G modulo p.