138 reputation
5
bio website
location Florence, Italy
age 24
visits member for 2 years, 9 months
seen Aug 15 at 15:14

I got my BSc in Florence, Italy and I'm currently an MSc student in Bonn, Germany. My main interest is algebraic and differential topology. I'm writing my master thesis on surgery theory.


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