implementing a cryptographic hash with a block cipher How can a cryptographic hash function be implemented/created using the block cipher?  I was wondering if we can use AES in cipher block chaining mode to implement it.
Turning a cipher into a hashing function This is theoretical question. I'd like to know if it's possible (and what are eventually the consequences), not that I'm going to do it in one of my projects. ;)  The first hashing functions created were based on a symmetric cipher (just like the first Unix crypt was based on DES). The idea was simple. Use the password as key to encode a constant.  I'd like to know if it's still possible to convert any modern symmetric cipher into a hashing function (and second question: into a cryptographic hashing function). Is it possible (easier) to guess the key, when you have an encoded and decoded messages?
Is the set of all finite sequences of letters of Latin alphabet countable/uncountable? How to prove either? Today in Coding/Cryptography class, we were talking about basic definitions, and the professor mentioned that for a set $A=\left \{ \left. a, b, \dots, z \right \} \right.$ (the alphabet) we can define a set $A^{*}=\left \{ \left. a, ksdjf, blocks, coffee, maskdj, \dots, asdlkajsdksjfs \right \} \right.$ (words) as a set that consists of all finite sequences of the elements/letters from our $A$/alphabet. My question is, is this set $A^{*}$ countably or uncountably infinite? Does it matter how many letters there are in your alphabet? If it was, say, $A=\left \{ \left. a \right \} \right.$, then the words in $A^{*}$ would be of form $a, aa, aaa, \dots$ which, I think, would allow a bijection $\mathbb{N} \to A^{*}$ where an integer would signify the number of a's in a word. Can something analogous be done with an alphabet that consists of 26 letters (Latin alphabet), or can countability/uncountability be proved otherwise? And as mentioned before, I am wondering if the number of elements in the alphabet matters, or if all it does is change the formula for a bijection.   P.S. Now that I think of it, maybe we could biject from $\underset{n}{\underbrace{\mathbb{N}\times\mathbb{N}\times\mathbb{N}\times\dots\times\mathbb{N}}}$ to some set of words $A^{*}$ whose alphabet $A$ has $n$ elements? Thanks! Show that   $$\displaystyle1 - \frac{x^2}2\leq\cos x\quad\forall x \in \mathbb{R}$$   Let $f(x) = \cos x - 1 + \frac{x^2}2$; then we need to show that $f(x) \geq 0\quad\forall x \in \mathbb{R}$.  Since $$\lim_{x \to \pm\infty} f(x) = +\infty$$ and $$\operatorname{im}f'' = [0, 2]$$ (as $f''(x) = 1 -\cos x$), it remains to show that $x = 0$ is a minimum for $f(x)$, but I cannot do that because I would need to solve $f'(x) = x -\sin x = 0$, which I cannot. I think it would suffice to show that plugging in $x = 0$ we have that $f'(x) = 0$, and combining it with the fact that the function $f$ is convex, we would be done.    Is it enough? What's a better proof?  EDIT: It just occurred to me that there is a way to solve $f'(x) = 0$. Just observe that $f'(x)$ is an odd function and that $f''(x) \geq 0$ implies that $f'(x)$ is monotonically increasing. Since an odd function, if defined at $x = 0$, must be $0$ there, $x = 0$ is a solution to the equation and it's the only one. How can I quickly know the rank of this / any other matrix? In the C and C++ programming languages, what is the difference between using angle brackets and using quotes in an include statement, as follows?   #include &lt;filename&gt;  #include "filename" Rule of thumb for choosing an implementation of a Java Collection? Anyone have a good rule of thumb for choosing between different implementations of Java Collection interfaces like List, Map, or Set?  For example, generally why or in what cases would I prefer to use a Vector or an ArrayList, a Hashtable or a HashMap? How to handle a native OS (Ubuntu) file upload window in selenium webdriver with python? This is my first time here but I have already posted this question on SO. I keep getting solutions for Windows + Java and not for Linux or python for that matter.  I am using Selenium and Python to automate a file upload application for the past many hours but nothing helpful!   The HTML DOM structure for this file upload is an input tag with its type attribute value = 'file'. I know I can make use of the send_keys.   The problem is I am not supposed to use send_keys() (as per the question I am trying to solve). The assumption is there are other ways of doing it.  Can anyone suggest me alternative ways to upload the file? I do get solutions for windows but not for Linux(Ubuntu). I know there are applications/tools to automate GUI components like AutoIt but there is nothing for Linux close to AutoIt.  I can say I have done my homework to find a solution. Only after not finding anything useful, I am asking this question, please help! How to get client date and time in ASP.NET? I can't seem to find info on installing a Swedish language package on my machine. The language is not listed  and the hits on Google I got led nowhere (or, rather, to the said page).  Where can I ask such a question (within the realm of Stack Exchange)? Roots of $\,ax^2+bx+c\,$ are irrational if $a,b,c$ are odd integers How would I show the following.  For all odd integers a,b, and c if z is a solution of $ax^2+bx+c=0$ the z is not rational.  How would I show this? This is what I did  Let a be an odd integer then for a integer k it has the form $a=2k+1$  then $b=2t+1$ for if c integer.  then $c=2r+1$ if s is an integer then I do  $(2k+1)(x)^2+2t+1(x)+(2r+1)=0$  But I find my self stuck on what to do any hint are appreciated. butt, bottom, buttock and ass? A woman's butt was allegedly touched by a man several times during a commute on the MRT.   How to use butt, bottom, buttock and ass? I am confusing with these words. Attribution alignment and order should be consistent with the website After logging in on terminal with user name and password, how do I start the GUI? I am new to Ubuntu, and I am working on a Mac. The Ubuntu installation was done by someone else. I logged in with the user name and password, but I'm not sure what next to do in the terminal to get to the graphical interface. Could someone assist or point me in a direction where I can get useful guidelines? I have done research, but nothing I found helped me.   When I tried to start the lightdm greeter, I got the following message:  lightdm.service not found     Update: My understanding is that Ubuntu Server is installed. Is there a word for happiness made possible by a tragic situation? I frequently find myself needing a word to express happiness that acknowledges a tragic or unfortunate circumstance underpinning that happiness. Preferably the word could have both adjective and verb forms. For example, "Gregory [verb-ed | felt adjective about] the balmy February day, suspecting it was yet another consequence of catastrophic and irreversible climate change."  "Bittersweet" is close, but not precisely right. It implies ambivalence rather than genuine gladness. "Schadenfreude" is also in the neighborhood, but I don't want to imply that the tragic part of the situation is what causes the pleasure. (Also, I recognize that the word may not quite exist in English, and I don't know if this is forbidden for this forum, but I'd welcome a loan word or phrase if there's a better one.) I am using PHP with Apache on Linux, with Sendmail. I use the PHP  function. The email is sent, but the envelope has the Apache_user@localhostname in MAIL FROM (example nobody@conniptin.internal) and some remote mail servers reject this because the domain doesn't exist (obviously). Using mail, can I force it to change the envelope MAIL FROM?  EDIT: If I add a header in the fourth field of the mail() function, that changes the From field in the headers of the body of the message, and DOES NOT change the envelope MAIL FROM.  I can force it by spawning sendmail with sendmail -t -odb -oi -frealname@realhost and piping the email contents to it. Is this a better approach?  Is there a better, simpler, more PHP appropriate way of doing this?  EDIT: The bottom line is I should have RTM. Thanks for the answers folks, the fifth parameter works and all is well. What is the need of complex functions in wave analysis? It is commonly known that waves can be express in terms of sine or cosine function. But when I study further, I seen that for analyising the waves, it is common to use complex functions in the form $$y=y_{_0}e^{i(kx-\omega{t})}$$ where $y_{_0}$ is the amplitude, $k$ is the wave number, $\omega$ is the angular velocity and $x$ &amp; $t$ are position an time respectively. Ofcourse, I know that the function $e^{ix}$ can be written in the form $\cos{x}+i\sin{x}$ and so it is a periodic function with period $2\pi$ but my question is for what purpose we define it in terms of complex numbers? It seem to be more convenient to use real functions for real variables such as amplitude, electric and magnetic field of an electro magnetic wave, and also in quantum mechanics. What actually this interpretation means or what is the advantage of such functions? How to render an animation as video in Blender? Yesterday I was working on a simple animation, an animated logo.   Here is an image of the progress:    I already have the animation working and everything is okay with the project, but I can't figure out how I can render the animation and turn it into an AVI format video.  How do I render an animation in Blender? Cannot find Underground Jungle Temple On my 1.2 Terraria Map I have been mining from left to right in my large underground jungle using my rocket launcher. Despite this, I have had no luck on finding the Underground Jungle Lihzahrd Temple. I have been searching the layer above where lava constantly spawns. Have I simply spawned in a world without one or am I searching in the wrong place? I have also considered using the clentimator with Dark Blue ammo to provide light, should I do that? How to determine a matching color code from a physical sample? I need to make a restaurant menu design that matches restaurant wallpapers. For some reason my client cannot get color codes used in wallpaper, but he provided me with a sample. (see below)    How can I get the correct color codes from the wallpaper? (someone mentioned that there are scanners for this purpose, but I could not find any information regarding that)  Let me know if this question should be in another site. How could I retrieve the exact duplicate value from conditionally formatted list that highlight duplicates? I have imported a webpage table in to Google Sheets. It frequently being updated. A series of calculations has been conducted on the sheet named Shawn Of the link spreadsheet.  I have filtered the my desired results into the Calculation sheet of that linked document... which is in columns A5:A. I then applied =ARRAYFORMULA(if(A5:A200=&quot;&quot;,,A5:A200*{12,13,37,101,111})) in columns B5. The Results of the formula extends from B5:F. This results from a5:F was subsequently conditionally formatted to highlighted duplicates in the aforementioned, i.e. a5:f using the lists of values in K5:K and I5:5. In Columns A5:F, is it possible to generate/place values in the range A5:f with matching name of states and aligned values in J5:K and H5:I? We know that the maximum level a dweller can train to on any SPECIAL skill is 10, however this does not consider bonuses given from their outfit.    Is there any additional benefit for going over 10? For example, a dweller with an Intelligence skill of 10 wearing a lab coat that boosts Intelligence by 3?   If it is a hard cap, would it be more useful to use outfits that raise a secondary characteristic instead?