On a new fast public key cryptosystem

This paper presents a new fast public key cryptosystem namel : 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 $( p > q )$. We define p and q values for which ModDiv2Inv can be the hardest. We then present ModDiv2Kex, a new fast key exchange algorithm based on ModDiv2Inv. In this paper we also evaluate the hardness of this problem by reducing it to SAT .