I'm just trying to wrap my mind around the decision to select the 128-bit Rijndael as the AES cipher, even with 192-bit and 256-bit keys. Even with a 256-bit key, you only get 2^128 possible outputs per 128-bit block, thus kind of rendering the larger key size meaningless (not to mention the weaker key schedules).  Was this a NIST oversight when standardizing AES?  (Answering this isn't urgent. I'm using libsodium, which uses Xsalsa20 + Poly1305, in most of my projects these days, but it's something I don't readily know the answer to.)
points out that certain key and block lengths were a requirement for the AES submissions:     The candidate algorithm shall be capable of supporting key-block combinations with sizes of 128-128, 192-128, and 256-128 bits.   My question is this; how can having a key length that is greater than the block size enhance security?  If we look at ECB mode for simplicity, when the key length is equal to the block length we have a permutation relationship between the set of all plaintexts and the set of all ciphertexts.  Once you increase the key length beyond that, you start to introduce collisions. In fact, you only introduce collisions from then on don't you? Collisions in the sense that a key will create the same ciphertext-plantext relationship as another key.  This would lead me to believe that only part of the key-space is unique, and only that part of key-space needs to be brute-forced?  I know that I am clearly incorrect, I just don't understand why.
Should we have a tag for significant points in time? There are many discussions about the current incidence. For example:          Should we have a whole tag for this incidence? In general, if in the future there are more crises and incidences like this, should they have their own tags too? I feel it's fine, as we have specific tags for individual events like . And, should we have a  tag?    Related:        Note that these questions are specifically about the conflict 2019, while this question is simply about creating meta tags for significant events. Reason of existense of the extra space in align environment and removal of it between two align environments This is a follow-up question regarding the extra vertical space in amsmath's align environment. Why when in use align uses so much vertical space in contrast with other environments like for example tabular or itemize?  \documentclass[12pt]{article} \usepackage[top=0.3in, bottom=1.2in, left=0.8in, right=0.8in]{geometry}   \usepackage[fleqn]{amsmath} \usepackage{unicode-math}  \setlength{\mathindent}{0cm} \newcommand{\3}{\vspace{0.3cm}}  \title{} \author{} \date{}  \begin{document}  70  \begin{align*} &amp;e^{jz}=\cos z+j\sin z\\ &amp;\cos z=(1/2)(2\cos z)=\\ &amp;=(1/2)(2\cos z+j\sin z-j\sin z)=\\ &amp;=(1/2)(\cos z+j\sin z+\cos z-j\sin z)=\\ &amp;=(1/2)(e^{jz}+e^{-jz}) \end{align*}  80  \begin{itemize} \item Item 1  \item Item 2  \end{itemize}  90  \begin{tabular}{c|c}  Entry 1&amp; Entry 2  \\  Entry 3&amp; Entry 4 \end{tabular}  \end{document}     Also another image of the huge space between two align environments. Even without the blank lines the space is a lot.    \begin{document}  \begin{multicols*}{2}   \begin{align*} &amp;\text{70}\\ &amp;e^{jz}=\cos z+j\sin z\\ &amp;\cos z=(1/2)(2\cos z)=\\ &amp;=(1/2)(2\cos z+j\sin z-j\sin z)=\\ &amp;=(1/2)(\cos z+j\sin z+\cos z-j\sin z)=\\ &amp;=(1/2)(e^{jz}+e^{-jz}) \end{align*}    \begin{align*} &amp;\text{207}\\ &amp;x(t)=A_{c}\cos \theta(t)\\ &amp;\theta(t)=2\pi f_{c}t+\phi(t)\\ &amp;\phi(t)=K_{p}m(t)\\ &amp;x(t)=A_{c}\cos[2\pi f_{c}t+K_{p}m(t)] \end{align*}   Edit I:  As I mention in a comment I have tried the following code and there is no difference between two align environments, only between text and an align environment. Why doesn't work in the case of the two environments and how can I fix it so to work? Also what is the reason that this space exists?  \setlength{\abovedisplayskip}{0pt} \setlength{\belowdisplayskip}{0pt} \setlength{\abovedisplayshortskip}{0pt} \setlength{\belowdisplayshortskip}{0pt} I have this struct:  struct Map {     public int Size;      public Map ( int size )     {         this.Size = size;     }      public override string ToString ( )     {         return String.Format ( "Size: {0}", this.Size );     } }   When using array, it works:  Map [ ] arr = new Map [ 4 ] {     new Map(10),     new Map(20),     new Map(30),     new Map(40)};  arr [ 2 ].Size = 0;   But when using List, it doesn't compile:  List&lt;Map&gt; list = new List&lt;Map&gt; ( ) {     new Map(10),     new Map(20),     new Map(30),     new Map(40)};  list [ 2 ].Size = 0;   Why? Spring's SecurityContextHolder.getContext().getAuthentication() returns null after RedirectView is used in HTTPS/SSL Disk Utility won't Unmount HD for formatting Finding the missing digits of $23!$ It is given $23!=2585201xy38884976640000$. Now it is required to find the value of $x$ and $y$. I know I could find it by using divisibility rules and solving simultaneous equations. Is there any other way to solve it (without computing it by a calculator)? This question is just out of curiosity. Why can't the Others go around the Wall at sea? As explained in a  earlier , the Wall does not extend all the way to the sea on the East, and the castle there is essentially undefended anyway. Thus, wildlings -- and Stannis' army -- were able to go around it undetected.  We know that the Others and the wights they raise can't cross through the Wall, and I think we can assume that it's built to stand up to any attacks they make trying to bring it down. But there does not appear to be any reason they can't just go around like anyone else.  Possibly related: in the TV Show, we actually see the attempted evacuation of Hardhome, and the Night King allows Jon Snow and his human army and civilians to flee back to their boats to safety, even after raising a massive army of wights. You could interpret this as merely a psychological ploy, but it may be a hint that the dead can't cross the water either.  Has there been any indication (books or show) that the Others/White Walkers and their army of wights are blocked by open water, or are somehow tied to the land of the Frozen North, or that there's any other obstacle keeping them from just sailing/swimming around the Wall? In an ordered field we have $x^2 \ge 0$, hence the equation $-1 = x^2 + y^2$ has no solution. But what about finite fields in general? What is the solutions set $$  -1 = x^2 + y^2 $$ of this equation? How can I install .ipa file to my iPhone simulator? I need to install .ipa file to my iPhone simulator.   I tried to change the extension .ipa to .zip and extracted it.  And I got the Payload folder and moved the application inside to my iPhone simulators applications folder found at: /Library/Application\ Support/iPhone Simulator/6.1/Applications/.   Application appears on iPhone Simulator, But the application did't running. How to solve the problem then how to run the app. Using Virtual Box, how can I install an OS to a secondary, physical disk, and boot it in both (at separate times) Virtual Box, and as a typical secondary OS install? How can you turn on or off the cheats after you make an offline server?My brother did something in settings but I can't find it. In Xubuntu 16.04.3 (and several previous versions aswell) it is not possible to have no power icon in the notification area.  A power icon is displayed even though 'Show system tray icon' is unchecked in Xfce Power Manager.  When 'Show system tray icon' is checked, there are two power icons displayed.  (See screenshots)  I've searched and I can't find any information related to this in Xubuntu/Xfce.  Is there a way to fix or work around this bug? What's the derivative of: $ \sqrt{x+\sqrt{{x}+\sqrt{x+\cdots}}}$? let $ y=\displaystyle \sqrt{x+\sqrt{{x}+\sqrt{x+\cdots}}}$, i'm really interesting to know how do I find :  $\displaystyle \frac{dy}{dx}$ ?.  Note: I have used the definition of derivative of the square root function but i don't succed .  Thank you for any help How to fully backup non-rooted devices? Problem 4.6, I. Martin Isaacs' Character Theory I've seen lots of examples of making an entire regular expression case-insensitive.  What I'm wondering about is having just part of the expression be case-insensitive.  For example, let's say I have a string like this:  fooFOOfOoFoOBARBARbarbarbAr   What if I want to match all occurrences of "foo" regardless of case but I only want to match the upper-case "BAR"s?  The ideal solution would be something that works across regex flavors but I'm interested in hearing language-specific ones as well (Thanks )  Edit  The link Espo provided was very helpful.  There's a good example in there about turning modifiers on and off within the expression.  For my contrived example, I can do something like this:  (?i)foo*(?-i)|BAR   which makes the match case-insensitive for just the foo portion of the match.  That seemed to work in most regex implementations except Javascript, Python, and a few others (as Espo mentioned).    The big ones that I was wondering about (Perl, PHP, .NET) all support inline mode changes. $$y'=x^2+y^2$$ I know, that this is a kind of Riccati equation, but is it possible to solve it with only simple methods? Thank you Why do I get the same result with rand() every time I compile and run? MS word: a macro to turn ON/OFF some proofing settings What macro could turn ON/OFF some proofing settings? (Unfortunately macro recording doesn't record the setting change)  I'm looking for a way to turn ON/OFF 2 proofing settings (at the same time):    check spelling as you type mark grammar errors as you type Adverb sentence query He is arguably the best actor of his generation   In the above sentence the adverb is placed just after "be" Can we use adverb after "be"? If we can use then please explain properly because I have studied that adverb can be used before adjective and adverb .