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 diculty to
invert the following function : F(x) = (a * x)Mod(2 power p)Div(2 power 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 .
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