Are there public key schemes that have perfect secrecy? The perfect secrecy notion is defined for symmetric key encryption. If P is a message and C the corresponding ciphertext then the cipher has perfect secrecy if pr(P|C)=pr(P). This equivalently means in terms of entropy that the conditional entropy H(P|C)=H(P). Originally as defined in Shannon's paper the encryption system is not classified as block or stream cipher. In practice it has to be one of the two and the message length is a priori fixed to a maximum. Hence for a public key scheme with the message length fixed perfect secrecy is still meaningful when probability distribution of the maximum length message is considered. In general H(P|C)&lt; H(P). Since all public key schemes are secured in computational sense H(P|C)=0 which means an infinitely powerful adversary can always break the encryption. Can a perfectly secure public key scheme be defined? If there is one which scheme is it?
Assume there is a public-key encryption scheme $(KeyGen, Enc, Dec)$ with perfect correctness (i.e., for all messages M and valid key-pairs (PK,SK), we have $Dec_{SK}(Enc_{PK}(M))=M$).  Will there always be a function $A$ such that for all messages M and valid public-keys PK, $A_{PK}(Enc_{PK}(M))=M$?  In other words, can a computationally unbounded adversary decrypt the message, having only the public key?
I work on a HP laptop plugged in most of the time, and after a few months the battery went off-duty.  Of course, I could remove the battery each time the laptop is plugged and replace it each time I must move to where no sockets are around. But I think that:   It would be really BORING! The computer would not avail itself of the useful backup power supply a battery can provide in case of black out.   It should simply switch off the battery charging when a safe power level is reached (i.e. 95%) and start recharging it, not every five minutes, but only under a certain safe threshold (i.e. 40% - 50%).  In its energy-saving profiles, Windows 7 only allows for setting up screen brightness, screen fadeout, screen deactivation and the suspension, not managing any charging issue.  Is there a way to accomplish this? Finding acute triangle probability A stick is broken in three parts of any length ,  if we join the pieces then what's the probability of getting a acute angled triangle? I've found several posts with this same question, but the answers always diverge to some other topic or they don't work for my needs.  After a node is saved, I want my custom module to insert a row into one of my custom tables which contains the nid of the new node. When hook_node_submit is called, the nid doesn't exist yet. hook_node_insert does have the nid, but only gets called the first time the node is saved, but I potentially need to take action each time the node is saved.   My plan is to separate my functionality into its own method and implement both hooks, but I'm trying to learn to do things properly with Drupal and so I'm wondering if there is a hook that actually fits with my requirements.  Is there a hook which is called every time a node is saved and called AFTER the save is complete? java.io.Console support in Eclipse IDE I use the Eclipse IDE to develop, compile, and run my Java projects. Today, I'm trying to use the java.io.Console class to manage output and, more importantly, user input.  The problem is that System.console() returns null when an application is run "through" Eclipse. Eclipse run the program on a background process, rather than a top-level process with the console window we're familiar with.  Is there a way to force Eclipse to run the program as a top level process, or at least create a Console that the JVM will recognize? Otherwise, I'm forced to jar the project up and run on a command-line environment external to Eclipse. Suppose $L=\mathbb{Q}(\sqrt{a+b\sqrt{d}})$,($d$ and $a+b\sqrt{d}$ are square free algebraic integers) when is $L/\mathbb{Q}$ a normal extension? When does $Aut(L/\mathbb{Q})=\mathbb{Z}/4\mathbb{Z}$ or $Aut(L/\mathbb{Q})=\mathbb{Z}/2\mathbb{Z}\times \mathbb{Z}/2\mathbb{Z}$? Want to fill line with repeating string Similar to the \dotfill command, but with your own text, rather than dots.  If the string was: kitty!  The entire line would look like the following: kitty!kitty!kitty!kitty!kitty!kitty!kitty!kitty!kitty!  Is there any way to do this? Globally disable "include online search results" Ckeditor toolbar not entirely showing up Steady-State Current I am in the process of completing some homework and have come across a question that says: "What is the steady-state current?" It is asking in reference to a circuit that includes two capacitors in parrallel and a DC source of 24V and an AC source given by $\epsilon = 20 \cos(120 \pi t)\ \text{V}$, where $t$ is in seconds. I assume that it is asking when the current is constant. Because naturally the current is not constant due to the AC source, would I just consider the DC source for this? Why does $\sqrt{n\sqrt{n\sqrt{n \ldots}}} = n$? Ok, so I've been playing around with radical graphs and such lately, and I discovered that if the   nth x = √(1st x √ 2nd x ... √nth x);   Then  $$\text{the "infinith" } x = x$$  Example:   $$\sqrt{4\sqrt{4\sqrt{4\sqrt{4\ldots}}}}=4$$ Try it yourself, type calc in Google search, hit  then a number, such as $4$, and repeat, ending with $4$, (or press the buttons instead).  I'm a math-head, not big enough though, I think this sequence is divergent or convergent or whatever, too lazy to search up the difference.  However, can this be explained to me? Like how the Pythagorean Theorem can be explained visually. How do I post code in chat? I would like to be able to post code in chat. I know that I can post inline snippets of code by using backticks, but I don't know how to post blocks of code, with the entire chat message formatted as code, and indentation respected. I am aware of . After reading the comments, I found out that I could format in "fixed width", but I can't see a "fixed width" button anywhere. What should I do? How unique is the php session id How can I make extra money with photography? I have photos in Getty Images, in Shutterstock, Imagekind and I recently added some to RedBubble, but I'm not having the expected results.  Does anyone have some history of success selling photographs or working as a photographer?  Examples of my work are available in .    Also asked by   I am an amateur who sometimes takes pictures of nature or random things. I've been told by several people that my pictures are worth money.  How can I monetize my best shots?  I don't really want to do a lot of work, editing, SEO or whatever. I'm looking for an easy way where I would just upload my pictures somewhere and let it go.  Maybe stock photos? People buying prints? I have no idea how that works...  EDIT: maybe a link to see which type of photography I do can help I would like to have multiple bibliographies (reference lists) as described in   ().   However, I'd like to use with a single .tex file, which would contain the bibliography database embedded, as in  ...   Now, I want to use letter documentclass, for which the bibliography needs to be defined ()   So what I end up is with this example (code below, compiled with just pdflatex, no bibtex(which I'd like to avoid in this case)):     ... obviously, something works (multibib recognized primary and secondary cites, assigning them number "1" as start) -- however I don't get two, separate primary and secondary list of references; would that be possible in this context? (doesn't have to be with multibib, but I'd like to avoid a separate .bib file and a bibtex call)  EDIT: I'd also like separate cite keys (i.e. rendered as [a1] and [b1]; not yet sure if multibib can do that; edit: no it cant,  says "You can also edit the .bbl files created by BibTEX and add 'a', 'b',. . . to the labels, but your changes will be overwritten by subsequent BibTEX runs." and recommends \cite[a]{key}) - how possible would that be?  &nbsp;  The code is this:   \documentclass{letter}  % Environment thebibliography undefined when using letter: http://www.latex-community.org/forum/viewtopic.php?f=4&amp;t=3359 \makeatletter \setlength \labelsep {.5em} \newcommand\newblock{\hskip   .11em\@plus.33em\@minus.07em} \let\@openbib@code\@empty \newcommand\refname{References} \newcommand\section{\@startsection   {section}{1}{\z@}%   {-3.5ex \@plus -1ex \@minus -.2ex}%   {2.3ex \@plus.2ex}%   {\normalfont\Large\bfseries}} \newenvironment{thebibliography}[1] {\section*{\refname}%   \@mkboth{\MakeUppercase\refname}{\MakeUppercase\refname}%   \list{\@biblabel{\@arabic\c@enumiv}}%   {\settowidth\labelwidth{\@biblabel{#1}}%     \leftmargin\labelwidth \advance\leftmargin\labelsep \@openbib@code     \usecounter{enumiv}%     \let\p@enumiv\@empty \renewcommand\theenumiv{\@arabic\c@enumiv}}%   \sloppy \clubpenalty4000 \@clubpenalty \clubpenalty   \widowpenalty4000%   \sfcode`\.\@m} {\def\@noitemerr {\@latex@warning{Empty       `thebibliography' environment}}%       \endlist} \makeatother  \usepackage{multibib} \newcites{pri}{Primary sources} \newcites{sec}{Secondary sources}  \begin{document}   \begin{letter}{Addressee} Blah, blah - content...  Primary cite: \citepri{lamport94} ...  Secondary cite: \citesec{lamport94} ...   \begin{thebibliography}{9}  \bibitem{lamport94}   Leslie Lamport,   \emph{\LaTeX: A Document Preparation System}.   Addison Wesley, Massachusetts,   2nd Edition,   1994.  \bibitem{lamport95}   Leslie Lamport,   \emph{\LaTeX: A Document Preparation System}.   Addison Wesley, Massachusetts,   2nd Edition,   1995.  \end{thebibliography}  \end{letter}   \end{document} How to install Ubuntu on portable external Hard Drive? I am new to Stack  Exchange and I think it's very impressive.  One thing bothers me is that because it is so far down the line, I don't think beginners stand a chance of growing.  As time goes on, more and more questions are being answered and therefore if someone asks something with a really basic answer you can just comment. However, beginners can't comment until they have a reputation of 50. The only way they can build up is by answering questions. But if they answer a basic question long winded, they will be voted down because not so much effort was needed or because its already a duplicate and will lose the bit of reputation they have earned.  Can you tell me the future for beginners? Where in the world is tikzlibraryhobby.code.tex? I was trying to reproduce Claudio Fiandrino's answer to .  However, I do not have the hobby package by Andrew Stacey in my local distribution.  After reading  and , I looked at the latest  (build on December 7, 2012) but could not located the hobby package in it.  I found  but do not know where each file is supposed to go in my distribution.  How do I add the hobby package? In general, what would be the easy way to get any new TikZ package installed in a Mac?  EDIT:  I have used the drag-and-drop (mac) method as described below.  (1) Drag pml3array.sty file to /Users/Username/Library/texmf/tex/latex folder. (2) Drag hobby.code.tex file to /Users/Username/Library/texmf/tex/generic/pgf/math folder. (3) Drag pgflibraryfpu.code.tex to /Users/Username/Library/texmf/tex/generic/pgf/libraries folder. (4) Drag tikzlibraryhobby.code.tex to /Users/Username/Library/texmf/tex/generic/pgf/frontendlayer/tikz/libraries folder.  I no longer get the hobby cannot be found error message.  But, is this correct? I have to import large Shapefiles (> 1 million records) into PostGIS, and I have been wondering about the best way to do it.    In my question I used the word "hack", instead of tool, on purpose because I think this is not so much a matter of which tool, but which set of steps, or configuration settings to use. So far, I have tried the  plugin (QGIS), the  Postgis tool and the GDAL  tool. You can view my full review on  post. So far, I find all of them really unresponsive, when dealing with a large dataset. I was wondering if someone experienced a similar issue, and if you could share something about the approach. I was reading a bit of Landau and Lifshitz's Mechanics the other day and ran into the following part, where the authors are about to derive the kinetic energy of a free particle. They use the fact that the Lagrangian of this particle must be the same (or at most, differ by the total time derivative of a function of co-ordinates and time) in different inertial frames.     We have $L'=L(v'^2)=L(v^2+2\mathbf{v}\cdot\boldsymbol{\epsilon}+\boldsymbol{\epsilon}^2)$. Expanding this expression in powers of $\boldsymbol{\epsilon}$ and neglecting terms above the first order, we obtain    $$L(v'^2)=L(v^2)+\frac{\partial L(v^2)}{\partial (v^2)}2\mathbf{v}\cdot\boldsymbol{\epsilon}.$$   I think I'm ok with all the physics in this section. What I don't get is just the part I quoted above (so maybe this post is better suited for the math site, but since this is book is so physics-y I thought I'd post it here). My math is pretty rusty, so I'm not really sure- how do the authors expand the function to arrive at the above expression? It reminds me a bit of a Taylor expansion, but not very much. What's the process used to arrive at it? How can I get my graphics card to be recognized in System Info?