International Association
for Cryptologic Research

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 a the difficulty to invert the following function :

$F(X) =(A\\times X)Mod(2^r)Div(2^s)$ .\\\\* Mod is modulo operation , Div is integer division operation , A , r and s are known natural numbers while $( r > s )$ .\\\\* In this paper it is also proven that this problem is equivalent to SAT problem which is NP complete .