dissertacao.pdf

3.2.3 Cycling Attack
The Cycling Attack was one of the first attacks on RSA to be described [43].
As the name of this attack suggests, the way this attack works is by repeatedly
encrypting the cypher text. When Marvin gets c ∼ = m e (mod N), he will en-
crypt the cypher text with the public key and this will lead him to, eventually,
getting an encryption which will be the original cypher text. That is, after l + 1
encryptions, he will have:
c el+1 ∼ = c ∼ = m e
(mod N) (46)
so he will know that the previous encryption is the original plain text, that is:
c el ∼ = m (mod N) (47)
The implementation of this attack resulted in the experimental results shown
in Table 6.
Table 6: Cycling Attack’s Experimental Results
size of N average running time (seconds)
8 0.000012
16 0.000010
32 0.000008
64 0.000010
128 0.000011
256 0.000013
512 0.000011
1024 0.000011
2048 0.000016
4096 0.000015
These results reveal little dependence on N.
This means that, after l encryptions of the cypher text, he finds the plain
text. For this reason, the value l is called the recovery exponent for the
plain text m. So, given a plain text m, all Marvin needs to do is to find its
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