1 research outputs found
Family of PRGs based on Collections of Arithmetic Progressions
We consider the mathematical object: \textit{collection of arithmetic progressions}
with elements satisfying the property:
\textit{ terms of and progressions of
the collection are multiplicative inverses of each other modulo the
term of progression}.
Under a \textit{certain} condition on the common differences of the progressions,
such a collection is {\em uniquely}
generated from a pair of co-prime seed integers. The object is
closely connected to the standard Euclidean gcd algorithm.
In this work, we present
one application of this object to a novel construction of a new family of pseudo random number
generators (PRG) or symmetric key ciphers. We present an
authenticated encryption scheme which is another application of
the defined object.
In this paper, we pay our attention to a basic symmetric key method of the new family.
The security of the method is based on a well-defined hard problem.
Interestingly, a special case of the hard problem (defined as Problem A)
is shown to be computationally equivalent to the problem of factoring integers.
The work leaves some open issues, which are being addressed in our ongoing work