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: $$F(x) =(atimes
x)Mod(2^p)Div(2^q).$$ 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 .

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