I was just going through RSA encryption scheme and was trying to figure out how to do all maths. I was suddenly struck by the question that (e,n) is public to the people. How easy it becomes to attack one's system if you find out that you are using same n as someone else?
I know that there exist some attack when using same modulus.      But with a little modification, $m$ is the plain-text $N$ is the RSA modulus $r_1, r_2$ is the random padding $e, s$ is the public exponent $C_e, C_s$ is the cipher-text  encrypt as follow $$С_e = (m + r_1)^e   \bmod N$$ $$С_s = (m + r_2)^s   \bmod N$$  If attacker only knows $C_e, C_s, r_1, r_2, e, s, N$. Is it possible to know $m$?  It seems the  does not work?
I'm trying to  when I run into this:     "You have already deleted 5 of your own posts today; further deletes are blocked"      I found conflicting information on this very annoying limit:   This post from May 25, 2010: . This is marked . If this is no longer the case, please edit that question and flag it as . Then , indicates that the problem has risen from the dead -- despite :     Each time that I've seen it (pruning subpar answers), it's been a user who is deleting their own redundant zero-upvote answers. Can you tweak the algorithm slightly so answers with less than one upvote don't count towards tripping this flag?     (Emphasis added.) :     I don't mind it when         cleaning up redundant answers on questions that have multiple alternate good answers   cleaning up old, "less awesome" answers that are no longer reflective of the user's current skill level         (Emphasis added.)     So why do we have barriers in place, to making SO answers less, "less awesome"?      Proposed Solution:  Please let us (¿once again?) delete an unlimited number of our own answers, when they have zero up-votes and are not marked as the answer.  Otherwise, please edit the linked questions to clear up the confusion. Deleting an element from an array in PHP Regex matches but shouldn't Why won't my taskbar display on my secondary monitor? On my secondary monitor (currently using Windows 10), my taskbar will barely show up. I've tried adjusting the resolution to lower ones (it recommends 1920x1080) and it doesn't do much. Is there a way to adjust the taskbar so I can see it?  That is about what I see. I could make it bigger via Snipping Tool and see my entire desktop on the picture but not normally. How can I set Excel to always import all columns of CSV files as Text? Though I try to avoid it, I occasionally have to open a CSV file in Excel. When I do, it formats columns containing numbers, which makes them useless for my purposes. As far as I can tell, the only way to prevent this from happening on import is to rename the file so the extension isn't .csv and use the import wizard to specify the format of each column individually. For files with 50-60 columns, this is impractical.  Since every answer for this oft-asked question on the internet suggests either some means of converting the formatted numbers back once the file is open (which won't work for me - I want to solve the general problem, not a few specific cases) or manually selecting the format type of each column (which I don't want to do), I'm looking for a way to set a global preference or style such that all columns of all CSV files opened are always formatted as text.  I know about "armoring" the numbers with quotes, too, but the files I get don't come like that and I was hoping to avoid having to pre-process the files so Excel doesn't screw them up.  Is there a way to do specifically this: Always format all columns in opened CSV files as text, without manually selecting each column every time during import?  I'm using Excel 2003, but I'll take answers for 2007 if that's what you know. The only solution that I have been able to come up with is $d=1$, but because $d&gt;2$, I can't seem to figure out how to find a solution. Differential equation: autonomous system This isn't homework. I have no idea what theorems I should be looking at to solve this. Guidance, partial and total solutions are all welcomed.     Let $f$ be a locally lipschitz function in an open set $G\subseteq \Bbb R^n$. Consider the autonomous system $y'=f(y)$.      Let $y(x,\xi)$ be the value at point $x$ of the maximal solution that satisfies the initial condition $y(0)=\xi$.         Prove that the domain of $y(\cdot, y(s, \xi))$ is $I-s$, where $I$ is the domain of $y(\cdot ,\xi)$.   Prove that for all $s, t$ such that $y(s, \xi)$ and $y(t+s, \xi)$ exist, then $y(t,y(s,\xi))$ also exists and $y(t,y(s,\xi))=y(t+s, \xi)$.   If $y$ is a maximal solution and there exists $T&gt;0$ such that $y(0)=y(T)$ and $f(y(0))\neq 0$, then $y$ is a periodic solution and not constant.   If $y$ is a solution whose domain is $(a,+\infty)$, if $\eta:=\lim _{x\to +\infty}y(x)$ and $\eta \in G$, then $f(\eta)=0$.      EDIT  I found an alternative solution for 3. Please check my proof and give feedback in comments:  let $u$ be the restriction of $y$ to $[0,T]$, now let $\overline u$ be the periodic extension of $u$ to $\mathbb R$. It is easy to see that $\overline u$ is a solution to the given differential equation. But since $f$ is locally lipschitz, $\overline u$ must coincide with $y$ wherever they are both defined. Since $y$ is a maximal solution, it must be $\overline u$, so $y$ is defined on $\mathbb R$. I want a green for "correct answer" and a red for "wrong answer". My current choice is rgb(144, 238, 144) for the green and rgb(250, 128, 114) for the red. (See wikilearner.net/wiki for the colours in action.)  I have been told that these colors are very close in contrast, making it difficult for a person with red-green color-blindness. What would be a better choice? Edit: The previous title didn't really ask the same thing as the question (sorry about that), so I've changed it. To clarify, I understand that the action isn't always a minimum. My questions are in the points 1. and 2. below.  I understand that &quot;principle of least action&quot; is somewhat of a misnomer, since we find that to determine the path taken by a system, we need only impose the condition that the action be stationary, i.e., that $\delta S$ should vanish to first order for small variations of the path, and this leads to the Euler-Lagrange equations. In The Classical Theory of Fields, Landau &amp; Lifshitz discuss the relativistic action for a free particle:  So for a free particle the action must have the form $$S = -\alpha \int_a^b ds$$ (...) It is easy to see that $\alpha$ must be a positive quantity for all particles. In fact, as we saw [earlier], $\int_a^b ds$ has its maximum value along a straight world line; by integrating along a curved world line we can make the integral arbitrarily small. Thus the integral $\int_a^b ds$ with the positive sign cannot have a minimum; with the opposite sign it clearly has a minimum, along the straight world line.  There is also a footnote, addressed a couple of paragraphs earlier, but which is relevant:  Strictly speaking, the principle of least action asserts that the integral $S$ must be a minimum only for infinitesimal lengths of the path of integration. For paths of arbitrary length we can say only that $S$ must be an extremum, not necessarily a minimum.  I have two questions regarding this:  How is the condition &quot;the action must be a minimum for infinitesimal displacements&quot; formulated? I've never heard of that outside of Landau &amp; Lifshitz's books, and in Mechanics they mention it as well but doesn't go into detail. Is this discussed a bit more somewhere?  If for the whole path the action only needs to be stationary, how can we make the argument for the negative sign? If the action had to be a minimum then it would make sense, but surely the fact that $\delta S$ = 0 isn't affected by an overall sign? Disabling SSLv3 but still supporting SSLv2Hello in Apache Many SSL clients, notably JDK 6, use the SSLv2Hello protocol to handshake with the server.  Using this protocol does not mean you are using SSL 2.0 or 3.0 for that matter; it is merely a handshake to determine which protocol to use.  [  However, in Apache, if you disable SSLv3 support, this apparently removes support for the SSLv2Hello protocol.  Apache Tomcat has explicit support for SSLv2Hello; that is, you can enable that, but not enable SSLv3.    Is there any way to do this in Apache?    [Update]   This is my protocol config:    SSLProtocol +TLSv1 +TLSv1.1 +TLSv1.2 -SSLv3 What is a suitable image resolution for canvas prints? I would like to create a 60 inch x 20 inch canvas print using an image with a resolution of 4759x1798 (240 pixels per inch) and I would like to know if the image quality will still be good at that size.  To generalise the question, what is the recommended maximum size of an enlargement at varying image resolutions?  e.g. 3 megapixel, 5 megapixel, 8 megapixel, etc I get these weird characters when I try to print out a vector element! A linear operator commuting with all such operators is a scalar multiple of the identity. I would like to add my bibliography to my presentation in IEEE format. What should I add to my preamble and code.  \documentclass{beamer} \setbeamertemplate{footline}[page number]  \usepackage{graphicx} \usepackage{booktabs} \begin{document} \section{Reference} \begin{frame} \frametitle{Reference}  \end{frame}   I'm using the same bibTex which I use to make the IEEE paper. Is it possible to flash a custom ROM without a custom recovery image For an un-rooted device, almost all articles/forum posts I've read say that in order to flash a custom ROM you first need to flash (or boot) a custom recovery image like TWRP.   I'm not sure I understand why. If the bootloader is unlocked shouldn't it be possible to manually flash images that make up the custom ROM to the required partitions with fastboot flash &lt;partition&gt; [ &lt;xxxx.img&gt; ], and leave the stock recovery untouched.  I realize that this may be difficult and that there is no benefit in doing it this way, but I'm curious to know whether or not it is possible, and if not, why? Is it true that one should not use NSLog() on production code? I was told this a few times in this very site, but I wanted to make sure this is really the case.  I was expecting to be able to sprinkle NSLog function calls throughout my code, and that Xcode/gcc would automatically strip those calls out when building my Release/Distribution builds.  Should I avoid using this? If so, what alternatives are most common between experienced Objective-C programmers? What is the non-parametric equivalent of a two-way ANOVA that can include interactions? Find the limit $\lim_{n\to\infty} \frac{x_1 y_n + x_2 y_{n-1} + \cdots + x_n y_1}{n}$ When $\lim_{n\to\infty} x_n = a$, and $\lim_{n\to\infty} y_n = b$, find the limit, $$\lim_{n\to\infty} \frac{x_1 y_n + x_2 y_{n-1} + \cdots + x_n y_1}{n}.$$ Thank you for your help in advance. Distance between footnote and the line above it Can others in my party go through TSA PreCheck? If I have  (i.e. I have a KTN from TSA and the "pre-check" logo gets printed on my boarding pass) and a travel companion does not, can they go with me through the PreCheck security lines? This is assuming that the travel companion is booked in the same reservation on the same flights and is also a U.S. citizen and not on any no-fly or otherwise increased scrutiny lists.  I'm guessing the answer is no, but I haven't seen anything from TSA specifically addressing this.