Reputation
Top tag
Next privilege 150 Rep.
Create new tags
Badges
5
Impact
~1k people reached

  • 0 posts edited
  • 0 helpful flags
  • 2 votes cast
Sep
24
awarded  Autobiographer
Jun
18
awarded  Popular Question
Jan
5
comment Cycle attack on RSA
@PeterTaylor Yes, by " $k$ might have not much to do with the order of $\mathbb{Z}_{\phi(n)}^{\times}$" I meant in terms of magnitude - it could be a divisor and still be small.
Jan
5
comment Cycle attack on RSA
Thank you for your answer, this is what I was looking for. I still don't understand one thing though: why is the probability of $|e|$ not being a multiple of $r$ at most $1/r$?
Jan
5
awarded  Scholar
Jan
5
accepted Cycle attack on RSA
Jan
5
comment Cycle attack on RSA
By $<e>$ i mean the group generated by $e$, $<e>=\{1,e,e^2,...,e^{k-1} \}$ (yes, $|e|$=k). I don't see the connection with factoring or with evaluating $\phi(n)$ (which are computationally equivalent, up to polynomial transformations), since in theory $k$ could be much smaller than $|\mathbb{Z}_{\phi(n)}^{\times}|=\phi(\phi(n))$ (I'm guessing it probably isn't - this is the type of result I was looking for).
Jan
5
awarded  Supporter
Jan
5
comment Cycle attack on RSA
Then regarding the first highlighted part you quoted: I am not wondering about the order of $\space$ $\mathbb{Z}_{\phi(n)}^{\times}$ (which of course is fixed), but about the order of $e$ in $\mathbb{Z}_{\phi(n)}^{\times}$, that is the order of the subgroup $<e>$ of $\mathbb{Z}_{\phi(n)}^{\times}$. This might not have much to do with the order of $\mathbb{Z}_{\phi(n)}^{\times}$ : for example the group $\mathbb{Z}_{8}^{\times}$ has order 4, but the only possible orders of elements are $1$ or $2$, since it is the klein group.
Jan
5
comment Cycle attack on RSA
Thank you for your answer. I was expecting th first objection you made: even if I came across $m$ I might not be able to tell it's the plaintext, and distinguish it from any other element in $\mathbb{Z_n}$. I don't know much about padding, and I can see how this is possible.
Jan
4
awarded  Student
Jan
4
asked Cycle attack on RSA