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 known natural numbers while $( p > q )$ .\\* In this paper it is also proven that this problem is equivalent to SAT problem which is NP complete .
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