dissertacao.pdf
dissertacao.pdf
dissertacao.pdf
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key, have lead to restrictions over the choice of the four parameters mentioned<br />
above and to limitations to the use of RSA. However, the set of these attacks has<br />
not led to contradictory restrictions on the parameters, so the system has not<br />
been proven to be unsafe. It is possible, so far, to choose the right parameters<br />
so that all the known attacks become infeasible. In fact, the deep knowledge<br />
we have about its weaknesses makes it more reliable, since less surprises are<br />
expected than they were 30 years ago.<br />
Since it has not been proven unsafe and it is not generally believed that it<br />
will be so, RSA is presently the most used public-key cryptosystem in the world.<br />
For this reason, its safe implementation is a matter of extreme importance. As<br />
this depends mostly on the choice of the four parameters mentioned above,<br />
every survey and new result about this topic will lead to a greater safety on<br />
the transmission of information online, preventing cyber crime and providing<br />
greater confidentiality to internet users.<br />
1.4 Objective<br />
The reliability of any cryptosystem relies mainly on how much it has been<br />
analysed. RSA has been the subject of numerous analysis and that is one of its<br />
strengths: no devastating attack has been found yet.<br />
This work results from an analysis on several known mathematical attacks<br />
on the RSA cryptosystem and their respective complexity. The objective is<br />
that someone who wishes to implement RSA has a brief and clear summary of<br />
the main precautions to have especially when it comes to choosing the gener-<br />
ating primes and the encryption/decryption exponents. Besides the theoretical<br />
complexity of the attacks we present the mathematical basis for the results<br />
presented, experimental results and the implementation of some of the attacks,<br />
with the aim of motivating people to improve the known attacks and to discover<br />
new ones.<br />
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