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AMC

In this paper we study the hardness of some discrete logarithm
like problems defined in linear recurring sequences over finite
fields from a point of view as general as possible. The
intractability of these problems plays a key role in the security
of the class of public key cryptographic constructions based on
linear recurring sequences. We define new discrete logarithm,
Diffie-Hellman and decisional Diffie-Hellman problems for any
nontrivial linear recurring sequence in any finite field whose
minimal polynomial is irreducible. Then, we prove that these
problems are polynomially equivalent to the discrete logarithm,
Diffie-Hellman and decisional Diffie-Hellman problems in the
subgroup generated by any root of the minimal polynomial of the
sequence.

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