I understand that both an HMAC and digital signature are used to check the integrity and authenticity of a message. Further, I understand that a digital signature is non-repudiatible.   What I do not understand is when to use an HMAC vs a digital signature, in practice. I appreciate the help!
A message may be accompanied with a digital signature, a MAC or a message hash, as a proof of some kind.  Which assurances does each primitive provide to the recipient?  What kind of keys are needed?
I wanted to know how I could configure multi-touch gestures in Ubuntu. In windows I can do this using the synaptics driver software.  I have already used synclient to configure the taps, palmdetect, scroll, etc. But I'd also want gesture support. Is is even possible?  System-Info: Ubuntu 12.10, Synaptics clickpad Viruses in wine? Prove that the subsequence of a convergent series with nonnegative terms converges Disclaimer Yes, I am fully aware that what I am asking about is totally stupid and that anyone who would wish to try such a thing in production code should be fired and/or shot.  I'm mainly looking to see if can be done. Now that that's out of the way, is there any way to access private class members in C++ from outside the class?  For example, is there any way to do this with pointer offsets? (Naive and otherwise non-production-ready techniques welcome) Update As noted in the comments, I asked this question because I wanted to write a blog post on over-encapsulation (and how it affects TDD).  I wanted to see if there was a way to say &quot;using private variables isn't a 100% reliable way to enforce encapsulation, even in C++.&quot;  At the end, I decided to focus more on how to solve the problem rather than why it's a problem, so I didn't feature some of the stuff brought up here as prominently as I had planned, but I still left a link. At any rate, if anyone's interested in how it came out, here it is:   (I suggest reading it before you decide that I'm crazy). Let $a,b,n$ be integers such that  $\gcd(a,n)=\gcd(b,n)=1$. How to show that $\gcd(ab,n)=1$?   In other words, how to show that if two integers $a$ and $b$ each have no non-trivial common divisor with and integer $n$, then their product does no have a non-trivial common divisor with $n$ either.     This is a problem that is an exercise in my course.   Intuitively it seems plausible and it is easy to check in specific cases but how to  give an actual proof is not obvious. Javascript profanity match NOT replace Is it possible to determine the exact date and time (if possible) of creation of an Apple ID?   Is there any official or unofficial way to establish this if you don't have the initial sign up information recorded? Which Content Management System (CMS)/Wiki should I use? This is a general, community wiki  question to address non-specific "I need a CMS or Wiki that does x, y, and z..." questions.  If your question was closed as a duplicate of this question and you feel that the information provided here does not provide a sufficient answer, please open a discussion on .    I have a list of features that I want for my website's Content Management System (CMS) - where can I find a [free] script that includes all of them? If $\int_0^x f \ dm$ is zero everywhere then $f$ is zero almost everywhere I have been thinking on and off about a problem for some time now. It is inspired by an exam problem which I solved but I wanted to find an alternative solution. The object was to prove that some sequence of functions converges weakly to zero in $L^2$.   I managed to show (with some help) that the limit $f$ (of a subsequence) satisfies $\int_0^x f \ dm=0$ for all $x&gt;0 $. From this I want to conclude that $f=0$ a.e. I can do this with the fundamental theorem of calculus in its Lebesgue version but there ought to be a more elementary proof.  Can someone here help me out? Elementary proof for $\lim\limits_{n \to\infty}\frac{n!e^n}{n^n} = +\infty$ As seen in  question, the series $\sum\limits_{n=1}^{\infty} \dfrac{n!e^n}{n^n}$ diverges. (One way to see this is by noting that the terms of the sum are greater than $1$ and, therefore, don't converge to zero.)  However, more is true: not only are the terms greater than $1$, they blow up to $+\infty$! To see this, one can apply Stirling's approximation and get $\dfrac{n!e^n}{n^n} \sim \sqrt{2\pi n}$.  My question is: is there an elementary proof for $\lim_{n \to\infty}\dfrac{n!e^n}{n^n} = +\infty$?  The reason I'm asking this is that I'm taking a Calculus course and I was assigned the exercise of proving the divergence of the series above and I would feel more satisfied if I could prove that its terms go to $+\infty$ (as opposed to merely proving the terms are greater than $1$.) Obviously, things like Stirling's approximation are outside the scope of the course, so I can't really use them.  (To be clear, you can use anything one learns in $4$ semesters of standard Calculus courses. I hope this restriction is not too obscure.) Difficult Polynomial Question Prove that there exist two integers such that i - j is divisible by n. Here's the full question:  Prove that, for any $n + 1$ integers, $\{x_0, x_1, x_2, . . . , x_n\}$, there exist two integers $x_i$ and $x_j$ with $i \neq j$ such that $x_i − x_j$ is divisible by $n$.  Now, the integers aren't necessarily consecutive, positive, or without repeats. I've tried breaking this into cases, such as "$x_i = x_j, \dfrac{0}{n} = 0$" etc. But I don't think it's possible to exhaust the cases.  I feel like there should be an easy way to contradict this one, by saying that $x_i - x_j$ isn't divisible by $n$. But I just wasn't getting anywhere with that one.  I thought about using induction, but I would have just as hard a time proving this for $n$ integers before $n+1$ integers, so I don't think it would be possible for me to do it that way.  If anyone could help out, that would be wonderful. I'm pretty stuck here. Repeating the consonant in many words in a sentence or phrase In the movie 'V for Vendetta' you have for example (bold part):     Evey: Who are you?        V. : Who? Who is but the form following the function of what and what I am is a man in a mask.      Evey: Well I can see that.        V. : Of course you can, I’m not questioning your powers of observation, I’m merely remarking upon the paradox of asking a masked man who he is.      Evey: Oh, right.      V. : But on this most auspicious of nights, permit me then, in lieu of the more commonplace soubriquet, to suggest the character of this dramatis persona.      V. : Voila!   In view humble vaudevillian veteran, cast vicariously as both victim and villain by the vicissitudes of fate. This visage, no mere veneer of vanity, is a vestige of   the “vox populi” now vacant, vanished. However, this valorous visitation of a bygone vexation stands vivified, and has vowed to vanquish these venal and virulent vermin, van guarding vice and vouchsafing the violently vicious and voracious violation of volition. The only verdict is vengeance; a vendetta, held as a votive not in vain, for the value and veracity of such shall one day vindicate the vigilant and the virtuous. Verily this vichyssoise of verbiage veers most verbose, so let me simply add that it’s my very good   honour to meet you and you may call me V.       Evey: Are you like a crazy person?      V. : I’m quite sure they will say so.   What do you call sentences like these? And do you know some other ones? Is there a way to export large multi-layered Illustrator file to Photoshop?  When I export with preserve layers and text edit-ability, the complex layers are flattened. I've reorganized my layers to have simple groupings but that's time consuming.  Is there a more effective way of doing this? Or script to automate it? How to install MySQL workbench? Installing MySQL workbench on 10.04 or 10.10 is not a problem, as the deb packages are available on MySQL's website.  But there is no 11.04 deb package available.  So, how do I install MySQL workbench on 11.04 and keep it updated automatically when updates become available to ubuntu via apt-get update. Segmentation fault error occurs for a simple function I have coded Will taking a gap year after my Master's degree improve or degrade my potential of doing a PhD? I couldn't find much on the new Lucene-based search, and don't know much about the engine in general, so I'm asking this question.  Does anybody have a description of how search results are ranked?  Does the rank calculation include:   rep of post's author? views? unique referers? PageRank of referers? rank of questions that link to the post? whether a question is closed? vote count? answer count? Why are Perl 5's function prototypes bad? With a macro such as:  \def\naive{na\"{\i}ve}   I find that the space which I would hope to follow it, is absent. So, with  the \naive approach   I get     the naïveapproach   in the output. How do I bring back the space?