On a new fast public key cryptosystem

Abstract

This paper presents a new fast public key cryptosystem namely : a key exchange algorithm, a public key encryption algorithm and a digital signature algorithm, based on the difficulty to invert the following function : $F(x) =(a\times x)Mod(2^p)Div(2^q)$ .\\* Mod is modulo operation , Div is integer division operation , a , p and q are integers where $( p > q )$ .\\* In this paper we also evaluate the hardness of this problem by reducing it to SAT