# Emilio Ferrucci

reputation
3
bio
website
location       Florence, Italy
age            23
member for     1 year, 4 months
seen           Jan 29 '12 at 15:36
profile views  3

Master's student in Florence, Italy, currently on an ERASMUS program at FU Berlin. My main interest is Algebraic Topology. I wrote my bachelor degree project on Morse Theory. Here are some of my favourite quotes:

• "To ask the right question is harder than to answer it." - Georg Cantor

• "Reductio ad absurdum, which Euclid loved so much, is one of a mathematician's finest weapons. It is a far finer gambit than any chess gambit: a chess player may offer the sacrifice of a pawn or even a piece, but a mathematician offers the game." (G. H. Hardy)

• "We say that a proof is beautiful when it gives away the secret of the theorem, when it leads us to perceive the inevitability of the statement being proved." (Giancarlo Rota)

• "A mathematician is a device for turning coffee into theorems." (Alfréd Rényi)

• "Mathematicians may turn coffee into theorems, but with an american coffee the most you'll get out of me is a lemma." (a Professor at my university)

• A topologist is someone who can't tell his ass from a hole in the ground, but can tell his ass from two holes in the ground.

|          |                | bio             | visits   |                     |                  |
|----------|----------------|-----------------|----------|---------------------|------------------|
|          | 123 reputation | website         |          | member for          | 1 year, 4 months |
| 3 badges | location       | Florence, Italy | seen     | Jan 29 '12 at 15:36 |                  |

# 10 Actions

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| Jan5 | 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.                                                                                                                                                                                                                                                                                                                                                                  |
| Jan5 | comment  | Cycle attack on RSAThank 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 $1/r$?                                                                                                                                                                                                                                                                                                                                                                   |
| Jan5 | awarded  | Scholar                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               |
| Jan5 | accepted | Cycle attack on RSA                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   |
| Jan5 | comment  | Cycle attack on RSABy $<e>$ 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).                                                                                                                        |
| Jan5 | awarded  | Supporter                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             |
| Jan5 | comment  | Cycle attack on RSAThen 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. |
| Jan5 | comment  | Cycle attack on RSAThank 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.                                                                                                                                                                                                                                                                |
| Jan4 | awarded  | Student                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               |
| Jan4 | asked    | Cycle attack on RSA                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   |
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