Section: New Results

A New Public-Key Cryptosystem via Mersenne Numbers

In [13], 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 , find two n -bit integers F,G each of Hamming weight at most h such that T = F ·R+G modulo p , under the promise that they exist.