dissertacao.pdf

4 Conclusions
The several attacks presented in this work, or any other known attack, have
not rendered the RSA cryptosystem unsafe. There is good prospects that some
attacks, specially the ones by Boneh and Durfee and Blomer and May will
become more powerful as soon as we get more knowledge on what we called The
Coppersmith Method Conjectures. These conjectures seem to be closely related
with the security of RSA and proving them would be definitely useful.
However, none of these heuristic attacks seems to threat RSA security com-
pletely. New bounds will be set and new precautions will be needed. But the
most important criteria for the RSA safety is still the Large Integer Factorization
Problem. Though there have been several advances in this area, an algorithm
running in polynomial time to factor large integers is still not known.
The experiments on this work have not led to any new results but we hope
that, along with the simple implementations presented, they can motivate the
reader to further explore the existing attacks on RSA and to think how one can
improve them.
One topic that deserves more study is the variants of RSA. They present
exciting new possibilities but their security has not yet been as analysed as
thoroughly as that of standard RSA. Its probably in them that the future of
cryptography lies, so the sooner we understand them, the sooner it will be safer
for us to rely on them.
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