A New Public-Key Cryptosystem via Mersenne Numbers

Divesh Aggarwal, Antoine Joux, Anupam Prakash, Miklos Santha

Abstract: 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 $$T = F\cdot R + G$$ modulo p.