Are all public-key encryption protocols based on one-way functions?
What primitives are needed to generically implement public-key cryptography?
Here's a question I've been asked;  Given distinct primes $p,q,r$, show that any group $G$ of order $pqr$ is not simple.   So far, my idea has been to individually check each possible proper subgroup, since by Lagrange there are only $$\dbinom{3}{2} + \dbinom{3}{1} + 1$$ of them, and show that at least one of them other than the trivial group is normal. Surely there is a smarter way, since generalizing this approach wouldn't work so well if I wanted to show similar results for groups who's order is a product of $n$ distinct primes.  Is there some other approach? Thanks for any insights Before the seasonal flu vaccine was recommended for all healthy adults, people in developed countries might get vaccinated against on the order of 10 different pathogens and develop immunity for some more via natural exposure.  Now the same person is expected to take a seasonal flu vaccine for a new strain every year - won't this put them in an uncharted territory as far as effects on the immune systems are concerned within a couple of decades? When should I make explicit use of the `this` pointer? Is it possible to use a laptop as an external monitor? I need to create a multi-monitor setup for my desktop computer but I have no additional monitors with me right now, aside from my laptop. Is it possible to use my laptop screen as an external monitor?  Note that I am not trying to connect a monitor to my laptop, rather, I am trying to connect my laptop screen to a desktop video card (if this is possible). I need to add a new field in the @book or @InProceedings entries: this field is "tome", for I have for instance the following title:  Francesco Bertolini, Società di trasmissione orale: mito e folclore, in Lo spazio letterario della Grecia antica, a cura di G. Cambiano, L. Canfora e D. Lanza, vol. I, tomo I, Salerno, Roma 1992, pp. 47--75.   So the following code is not enough:  @InProceedings{ bertolini:1992,   author                   = "Francesco Bertolini",   title                    = "Società di trasmissione orale: mito e folclore",   booktitle                = "Lo spazio letterario della Grecia antica",   editor                   = "G. Cambiano and L. Canfora and D. Lanza",   publisher                = "Salerno",   location                 = "Roma",   year                     = "1992",   volume                   = "1,   pages                    = "47--75", }   Using othes codes, I was able only to produce the "tome" field, but with a general trouble about the other fields:  \DeclareSourcemap{   \maps[datatype=bibtex]{     \map{       \step[fieldsource=tome,fieldtarget=usera]     }   } } \DeclareFieldFormat{usera}{tomo\space{#1}}   \DeclareBibliographyDriver{book}{%   \usebibmacro{author/editor}%   \setunit{\labelnamepunct}\newblock   \usebibmacro{title}%   \newunit\newblock   \usebibmacro{journal+issuetitle}%   \setunit{\bibpagespunct}%   \printfield{pages}%   \newunit\newblock   \printfield{usera}%   \usebibmacro{finentry}} \renewcommand*{\finentrypunct}{}   (useful for articles, but not for my case). By real, I'm not able to understand  which bibmascros I have to invocate...  I tried to write a biblatex-tome.dbx:  \ProvidesFile{biblatex-tome.dbx}   \DeclareDatamodelFields[type=field,datatype=literal,skipout=false]{tome}   \DeclareDatamodelEntryfields{tome}   Inside the main .tex file I put just this code:  \DeclareFieldFormat{tome}{\mkbibacro{tome}\addcolon\space #1} \newcommand*{\patchmoretome}[1]{   \xpatchbibdriver{#1}%     {\printfield{tome}}     {\printfield{tome}%           \newunit\newblock      \printfield{tome}}%     {\typeout{patching #1 to include more tome succeded}}%     {\typeout{patching #1 to include more tome failed}}% } % patch all drivers \patchmoretome{article} \patchmoretome{book} \patchmoretome{collection} \patchmoretome{inbook} \patchmoretome{incollection} \patchmoretome{inproceedings} \patchmoretome{manual} \patchmoretome{periodical} \patchmoretome{proceedings} \patchmoretome{report} \patchmoretome{thesis}   but it doesn't print the field in bibliographic entry. So I'm very confused about a (re)writing of driver I was just reviewing my "capitalization standards" for titles and such and was wondering if there's a macro to do the same thing I'm forced to do by hand nowadays. My personal rules (feel free to disagree/comment on them) are as follows:   the first letter (a number is a letter too for the sake of these rules) always gets capitalized, every word gets capitalized individually, the exception to the rule above (and just the rule above) are  such as prepositions and the like.   In other words: I'd like a capitalization command (like \MakeUppercase) that will capitalize every word not included in a list of words and that will always capitalize the first word of its argument.  Doable?  PS: one such "list" of closed class words (also known as "function words") can be found . I have a Python script that will need to be given to a client.   We are currently evaluating what license level the client will need in order to run the script for their software acquisition purposes.   We all have ArcGIS 10.1 Advanced license in our company.   I checked all the tools and extensions used in the script against the web help and found that they should work on the Standard license level.   Is there a way I can test the script against the Standard license level, when we have no Standard license level in or company (only the higher Advanced level)? 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? If I was at point $A$ and I wanted to walk directly to point $B$, I would have to walk half way to point $B$, but before that I would have to walk half way to halfway to halfway to point $B$ and half of that again and so on and so fourth. if I halved this distance an infinite amount of times then there would be an infinite amount of actions I would need to perform in order to cross from $A$ to $B$. Therefore, if each action took any quantity of time at all, then it would take me an infinite amount of time to cross from $A$ to $B$, even if $A$ and $B$ were only a few centimetres apart!   Because I am not infinitely old and I can move, there must be a flaw in this logic. Where is it? Start TOC from chapter 1 and also page numbering I am writing a bash script to look for a file if it doesn't exist then create it and append this to it:  Host localhost     ForwardAgent yes   So "line then new line 'tab' then text" I think its a sensitive format.  I know you can do this:  cat temp.txt &gt;&gt; data.txt   But it seems weird since its two lines. Is there a way to append that in this format:  echo "hello" &gt;&gt; greetings.txt How can I create a text input box with Pygame? How do you display a photo map tip in QGIS 3 on Windows?  As a new user I'm not sure if this is my lack of experience or a bug, so I've tried to simplify it as far as I can:  This is the contents of the Layer Display properties.    &lt;div style="width:400;height:400"&gt; &lt;p&gt;test&lt;/p&gt; &lt;div&gt;&lt;img src="C:\Local\aa.jpg" width="350" /&gt;&lt;/div&gt; &lt;/div&gt;   and this is how it appears:    C:\Local\aa.jpg is real file I'm using to try to figure out what the problem is. What am I doing wrong? I asked this question  but I haven't gotten a useful answer. Could you tell me the difference in meaning between these sentences?        Do you think you will visit them next week?     Will you visit them next week?     Are you going to visit them next week?     Are you visiting them next week?     Are you going to be visiting them next week?     Are you planning to be visiting them next week?     Do you plan to visit them next week?      Will there be any difference in the answers?        I think I will visit them next week.     I will visit them next week.     I am going to visit them next week.     I am visiting them next week.     I am going to be visiting them next week.     I am planning to be visiting them next week.     I plan to visit them next week.      Can I use "planning to" instead of "going to"?  (E.g. "Are you planning to visit them next week? — Yes, I am planning to visit them next week.") Which of these sentences show that the subject of conversation has already been discussed? For example, I talked with a friend of mine about my plans to visit somebody. So my friend is aware of my plans.  And my last question. Which of these seven sentences express that the action will certainly take place? Schadenfreude is the joy or pleasure derived from the misfortunes of others. What is the word for joy or pleasure derived from the happiness of others? For example, on this page:   I see the following:   What does this 499 mean? I can't seem to correlate it with upvotes, posts, edits or anything else. How to draw open-close interval in LaTeX I am using the following commands to have half-open interval in a real line:   \begin{tikzpicture}[scale=7] \draw[-&gt;, thick] (-0.1,0) -- (1.7,0); \foreach \x/\xtext in {0/8,0.2/$S_1$,0.4/$T_4$,0.6/$S_3$,0.8/$T_2$,1/$S_3$,1.2/14,1.4/$S_3$,1.6/16}     \draw[thick] (\x,0.5pt) -- (\x,-0.5pt) node[below] {\xtext}; \draw (0.2,0.5pt) node[above] {$c$}; \draw[[-), ultra thick, blue] (0.2,.01) -- (.4,0.01); \draw[(-, ultra thick, green] (0.6,.02) -- (1,0.02); \end{tikzpicture}   Now, I need to have an open-close interval, but I am not able to have that close interval at the end, using the following command:  \begin{tikzpicture}[scale=7] \draw[-&gt;, thick] (-0.1,0) -- (1.7,0); \foreach \x/\xtext in {0/8,0.2/$S_1$,0.4/$T_4$,0.6/$S_3$,0.8/$T_2$,1/$S_3$,1.2/14,1.4/$S_3$,1.6/16}     \draw[thick] (\x,0.5pt) -- (\x,-0.5pt) node[below] {\xtext}; \draw (0.2,0.5pt) node[above] {$c$}; \draw[(-], ultra thick, green] (0.6,.02) -- (1,0.02); \end{tikzpicture}   May I ask for anybody help? How do I overload the square-bracket operator in C#? DataGridView, for example, lets you do this:  DataGridView dgv = ...; DataGridViewCell cell = dgv[1,5];   but for the life of me I can't find the documentation on the index/square-bracket operator.  What do they call it?  Where is it implemented?  Can it throw?  How can I do the same thing in my own classes?  ETA: Thanks for all the quick answers.  Briefly: the relevant documentation is under the "Item" property; the way to overload is by declaring a property like public object this[int x, int y]{ get{...}; set{...} }; the indexer for DataGridView does not throw, at least according to the documentation.  It doesn't mention what happens if you supply invalid coordinates.  ETA Again: OK, even though the documentation makes no mention of it (naughty Microsoft!), it turns out that the indexer for DataGridView will in fact throw an ArgumentOutOfRangeException if you supply it with invalid coordinates.  Fair warning. PostgreSQL, SELECT from max id Can ASP.NET MVC generate elements with lower case name and id attributes