Is there any proof of correct work of RSA algorithm, if p is not a prime number? For example: n = p*q, p = p1*p2, where p1 and p2 are primes.  Edit: I found that it's called Multiprime RSA, but i didnt find proof of Correctness for it.
It has been said that RSA uses a modulus product of two prime numbers for security reasons. But does RSA even work correctly if we allow composite integers instead?  I think that the answer is "NO".  Define “work correctly” as:   allows encryption and decryption to be carried out as in normal RSA, yielding the original message (message padding and unpadding can remain unspecified, or absent as in texbook RSA); a security level can be given in terms of the key generation process (which may have alternate requirements to testing that $p$ and $q$ are prime).
Expectation and variance of the geometric distribution How can one use memorylessness and the  and the  to find the expectation and variance of the geometric distribution?  I will post my own answer, but as always, that shouldn't stop anyone else from posting theirs. What are the blue dots next to App names in iOS and macOS? They disappear once you open the apps and then return to the home screen, but I can't tell what they indicate.  Are they apps that haven't been opened since an app update? Or that it thinks have never been opened (not accurate in my case, but that could be a function of a "restore" confusing the phone). Steps for going from Polyakov action to low-energy effective action (SUGRA?) in String Theory A lot of string-theory questions have been asked here. This one is, hopefully, different in that this inquiry is specific and the expected answer would be more mathematical than philosophical in character.  To give some context, I'm familiar with LQG, QFT etc. I'm a beginner in CFT and string-theory. On reading papers on AdS/CFT and String Theory the following sentence often appears: "The low-energy effective action for $x$ dimensional ST of type $y$ reduces to that of supergravity (SUGRA) in $z$ dimensions with matter fields of types $a$, $b$ and $c$".  The $64,000 dollar question any noob, such as me, wants answered is what are the mathematical/technical steps or arguments which lead us from the fundamental action of string-theory (the Polyakov/Nambu-Goto action) to a low-energy effective description. Of course, I might be asking a question for which the only concise answer is: "go read GSW". Here's hoping otherwise ;) Does registering [name]overflow.com violate Stack Overflow's trademark? Plotting function defined with Lua doesn't do anything Theoretically possible to run two operating systems simultaneously? A friend of mine asked a question that got me thinking. Is it possible (theoretically, I assume it hasn't been done) to run two operating systems simultaneously on the same computer? Not in the sense of multitasking in one window, but being able to quickly switch from one to the other without restarting. Could something low-level be created that would intercept system calls (or whatever needs to be done) to make each OS think it is running alone? Or hardware itself that would accomplish this?  I'm not talking about dual booting or using virtual machines, but actually running two OS's side-by-side. How can I make my ad hoc iPhone application's icon show up in iTunes? I've got an iPhone app with icon file Icon.png.  This icon shows up properly when the app is on the phone itself, but it doesn't show up in the applications pane in iTunes.  What do I need to do to get it to show up properly? I am doing some arcpy -functions and afterwards I'm trying to add the calculated results from one table to another table. I'm using the arcpy.AddJoin_management() function.   As input table I'm using a table which is stored in a personal geodatabase. The personal geodatabase is not the workspace environment! As "JoinTable" a Table of a file geodatabase is used. This file geodatabase is the workspace geodatabase environment.  The initialized function looks like this:  (%self.getWorkspaceEnvironment => "W:/a18fb/data/mypersonalgeodatabase.mdb" and tFactsheetHochwasser => table in the personal geodatabase)  arcpy.AddJoin_management("%s/tFactsheetHochwasser"%self.getWorkspaceEnvironment(),"KPG", "GebaeudeKtn_BWVred1Stat","KPG","KEEP_ALL")  If the code is executed the following error-message appears:  Failed to execute.Parameters are not valid. The value cannot be a table     ERROR 000840: The value is not a Raster Layer.      ERROR 000840: The value is not a Raster Catalog Layer.      ERROR 000840: The value is not a Mosaic Layer.      Failed to execute (AddJoin)`. There is a statement that maximizing the likelihood is equivalent to minimizing the cross-entropy.  Are there any proof for this statement? Why does the /winsxs folder grow so large, and can it be made smaller? A Vista virtual machine I use only has a 10 GB virtual hard disk -- and I'm worried about it running out of space over time. I used  to check for the culprits..  And the primary culprit is that /winsxs or &quot;Windows Side-By-Side&quot; folder.  What is the Windows Side By Side folder? Well, that's .  All of the components in the operating system are found in the WinSxS folder – in fact we call this location the component store.  Each component has a unique name that includes the version, language, and processor architecture that it was built for.  The WinSxS folder is the only location that the component is found on the system, all other instances of the files that you see on the system are “projected” by hard linking from the component store.  Let me repeat that last point – there is only one instance (or full data copy) of each version of each file in the OS, and that instance is located in the WinSxS folder.   So looked at from that perspective, the WinSxS folder is really the entirety of the whole OS, referred to as a &quot;flat&quot; in down-level operating systems.  This also accounts for why you will no longer be prompted for media when running operations such as System File Checker (SFC), or when installing additional features and roles. That explains why the folder starts off big, but not why it gets larger over time – the answer to that question is servicing.   In previous versions of Windows the atomic unit of servicing was the file, in Windows Vista it’s the component.  When we update a particular binary we release a new version of the whole component, and that new version is stored alongside the original one in the component store.  The higher version of the component is projected onto the system, but the older version in the store isn’t touched.  The reason for that is the third part of why the component store gets so large.  Lots of other people :  A coworker recently received his every two year work laptop refresh and was in the middle of loading his new laptop with Vista. For some reason, his hard drive C: was partitioned to only 25GB and the rest of the space reserved for a much larger drive D:. Anyway, after loading many Windows Updates, he was left with hardly any drive space left on C:, and for some reason, the WinSxS directory had ballooned to over 8GB. While I knew what the WinSxS (Windows Side-by-Side) directory was for, I wasn't quite sure why that directory would explode in size so fast with normal operating system updates.  I don't really care about having all these duplicate files for safety, but I do care about the VM exploding due to an out of disk space error. So.. can /winsxs be safely pared down in any way? ..  Administrators should not, for any reason, take it upon themselves to clean out the /winsxs directory - doing so may prevent Windows Update and MSI from functioning properly afterwards.  Preventing accidental deletion from the directory is accomplished by putting a strong security descriptor on the directory that inherits to its children.  If this /winsxs folder gets any larger, I'm going to have to re-image this virtual machine.. which I really don't want to do! I know this sounds like a stupid question, but I just wanted to confirm if they are the same thing. In new canon, anti-gravity is never mentioned. Nielsen & Chuang Exercise 2.2 - “Matrix representations: example” Reproduced from Exercise 2.2 of Nielsen &amp; Chuang's Quantum Computation and Quantum Information (10th Anniversary Edition):     Suppose $V$ is a vector space with basis vectors $|0\rangle$ and $|1\rangle$, and $A$ is a linear operator from $V$ to $V$ such that $A|0\rangle = |1\rangle$ and $A|1\rangle = |0\rangle$. Give a matrix representation for $A$, with respect to the input basis $|0\rangle, |1\rangle$, and the output basis $|0\rangle, |1\rangle$. Find input and output bases which give rise to a different matrix representation of $A$.   Note: This question is part of a series attempting to provide worked solutions to the exercises provided in the above book. Duplicate auxiliary verbs in a sentence (may we / should we delete the second?) Wubi with 14.10 doesn't work - failed to partition the selected disk I tried to install Ubuntu 14.10 on my computer with Wubi. The installation appeared to work in Windows, and told me to reboot.   After rebooting the Ubuntu installer continued the installation, until it stopped with an error message: Failed to partition the selected disk with the detail This probably happened because are too many primary partitions in the partition table. Update Eclipse with Android development tools v. 23 What is the function of "do" in this sentence? Let $d=(a^n,b^n), d_1=(a,b)^n$; need show $d\mid d_1$ &amp; $d_1\mid d$ to prove.  For the general case of $(a,b)\ne 1, (a,b)= (d_1)^\frac{1}{n}$, else $(a,b)=d_1$.  Let, $d_2= (a,b)=d_1^\frac{1}{n}\implies a=a'd_2, b = b'd_2\implies a^n= (a')^nd_2^n, b^n= (b')^nd_2^n$  Unable to progress further. Proving $\int_{0}^{\infty} \mathrm{e}^{-x^2} dx = \frac{\sqrt \pi}{2}$ Is there such a thing as a European SIM card? This summer I will go on a road trip from West to East Europe and back. Being able to call and especially access the internet is useful on the road, so it made me wonder whether I could buy a European SIM card or something that would let me access the web or make calls regardless of the country I was in.  I know of the provider Mobile Vikings that offers a . Are there any other alternatives? Data is the main priority because calling or texting within Europe isn't that expensive to begin with, with recent regulations. Also I could use the data to call using VOIP anyway, which is even cheaper. How to have full bleed between two facing pages Indesign