Assume that a malicious user knows what string is being encrypted (a user_id, for example, which the user can know) and can also see the result of the encryption (the encrypted user_id that is used to authenticate them to another site.)  If the user knows what is going into the encrypt function, as well as what is coming out, in theory it seems it could be possible for them to determine the encryption key as well.  Assuming that this is the case, what could be done to address this problem?  Background: The project I'm working on uses the code found below. I have concerns that the shared encryption key could become compromised   The concern is simple: The key is shared, so if someone knows the key, they can trick the authentication mechanism and log in with whatever user ID they want.
Given a message and DES encrypted form of said message, is it possible to efficiently compute the key used to encrypt the data?
I'm using leaflet to display a map.  I have a control section that I'd like to be open by default, but I can't find a way to do it through the . Is there a way to do this? Let $U_1, \cdots, U_n$ be $n$ i.i.d continuous uniform random variables on $(0,1)$ and their order statistics be $U_{(1)}, \cdots, U_{(n)}$.  Define $D_i=U_{(i)}−U_{(i−1)}$ for $i=1, \cdots, n$ with $U_0=0$.  I am trying to figure out the distribution $\lim_{n\to\infty} \#\{i = 1, \cdots, n \mid nD_i \geq z\}/n$. This must be very well known, but I cannot find a reference. Assume $x$ doesn't occur free in $\alpha$, show that: $$\vdash (\forall x \beta \to \alpha) \leftrightarrow \exists x (\beta \to \alpha)$$   This is an exercise on page 130, A Mathematical Introduction to Logic, Herbert B. Enderton（2ed).   Here's my attempt: For the '$\to$' direction, since $x$ doesn't occur free in $\alpha$, we have $α→∀x α$ and $\forall x \alpha \to \alpha$ as logical axiom(In the second formula, we have$\alpha_x^x = \alpha$). Thus it suffice to show $\vdash (\forall x \beta \to \forall x \alpha) \rightarrow \exists x (\beta \to \alpha)$. By logical axiom $∀ x(α→β)→( ∀ x α→∀x β)$, it would suffice to show $\vdash \forall x (\beta \to   \alpha) \rightarrow (\exists x (\beta \to \alpha))$. It has been shown in a previous exercise that there's a deduction $∀ x ϕ→∃x ϕ$, so we are done for the "$\to$" part.  The problem for me is how to show the "$\leftarrow$" direction.  Added: Here's logical axioms that we can employ:         Tautologies(in the sense of propositional logic);   $∀ x α →α^x_ t $, where $t$ is substitutable for $x$ in $α$ ($α^x_ t$ is the formula derived from $\alpha$ by replacing $x$ by a term $t$);   $∀ x(α→β)→( ∀ x α→∀x β)$;   $α→∀x α$, where $x$ does not occur free in $α$.      Besides, generalization theorem and deduction principle can be utilized:     If $\Gamma \vdash ϕ$ and $x$ do not occur free in any   formula in$\Gamma$, then$\Gamma \vdash ∀ x ϕ$.      If $\Gamma ; γ \vdash ϕ,$ then $\Gamma \vdash  γ \to ϕ$. Answer didn't load temporary Remove HTML tags from a String Is there a good way to remove HTML from a Java string? A simple regex like replaceAll(&quot;\\&lt;.*?&gt;&quot;, &quot;&quot;)   will work, but things like &amp;amp; wont be converted correctly and non-HTML between the two angle brackets will be removed (i.e. the .*? in the regex will disappear). Explain why $\mathbb{Z \times Z}$ and $\mathbb{R \times R}$ is not a field I was able to install Ubuntu 12.04 using the alternative version of the image, (64 bit) but when I start the system it tells me the GPU  locked up, and instead presents a text only screen.  I understand that this site is not for bug reports, but at the same time, I know that there are some versions of the installer than have to be compatible with my graphics card (Nvidia GTS 360M).  I assumed that the mere fact that the alternative installer ran was an indication that I could get some sort of graphical interface running after the install.  Is there some way of getting some type of graphical interface running on my machine? Even better would be is there a way to get the rest of the system running as normal (i.e. GPU up and running)?  If an internet connection is required to download driver support or something similar, directions for how to configure a wireless connection with WPA2-Personal protection from the text-only interface (bash).  Any help would be appreciated.  Note: I was able to find  which tells me that the card is supported.  Note 2: In the install software stage of the install, I was unable to install anything (no internet connection)  Update: The exact error message is [8.591394] [drm] 0000:01:00.0: GPU Lockup - switching to software fbcon  Update 2: If I try to install with the regular version of Ubuntu, the screen goes staticy. This also happens if I install with Wubi (distasteful I know) and then try to use Ubuntu.  Update 3: I've tried xforcevesa, nomodeset and xforcevesa nomodeset as my wubi boot options.  Update 4: Thanks to jokerdino, I can now connect to the internet, so internet tools would now be a possibility. What happens when a moderator clicks 'leave open' in the close-vote queue? It takes  clicking "leave open" in the close-vote queue to remove the question from the queue.  How about diamond mods?  Do they remove it from the queue in one click, or not? How many associative binary operations for a set of two elements? Suppose we have a set  $S=\{a,b\}.$ Obviously, the total number of binary operations on $S$ is the number of all the pairs such that $$*(a,b)=a \, \text{or}  \, b,$$ which gives  $ 2 \cdot 2 \cdot 2 \cdot 2=2^4$ possible ones. Is there a way to find which of these $16$ binary operations are associative without writing all the operation matrices and checking it by hand? My neighbor has asked me help with his laptop, an HP with lost power-on password. I tried inserting an Ubuntu cd to format the partition, but well... it doesn't even get there. Any ideas? Ubuntu 12.04 boots to TTY1 We are experimenting with running an OpenVPN server for our business. One question I can't seem to find the answer to is this:  When we generate keys for one of our users for them to use at home, can their use the same keys on their home laptop as well as their home desktop? Or do we need to generate separate keys for each user's client machine? B2B application: users has its own users B2B Scenario I am trying is that:  The following Roles exists in the system:  Super Admin Super Admin Staff Owner (client) Admin (owner i.e. client and creates admin to define sales counters) Sales Counters  That means there are users who'll create their own sub users e.g.  [FLAG-A] ROLE &quot;SUPER ADMIN&quot; creates a ROLE &quot;Owner&quot; and &quot;OWNER&quot; creates its own sub users ROLES i.e. &quot;ADMN&quot; &amp; &quot;SALES COUNTER&quot;. Each role obviously has its info to login to the system I tried to design database as following:  In this diagram I am assuming that main user creates sub user that in my view many to many relationship so I have to add table between them as &quot;USER_PERSON&quot;. Problem is to set &quot;WHO CREATED USER&quot; in the system. I mean which user has created sub user as described in [FLAG-A]  Please check this diagram What is the use of multiple main methods? A Particular Two-Variable System in a Group Suppose $a$ and $b$ are elements of a group $G$. If $a^{-1}b^{2}a=b^{3}$ and $b^{-1}a^{2}b=a^{3}$, prove $a=e=b$.   I've been trying to prove but still inconclusive. Please prove to me.  Thanks very much for proof. Is there a pronoun I can use as a gender-neutral pronoun when referring back to a singular noun phrase?  Each student should save his questions until the end. Each student should save her questions until the end. Intuitive explanation of why $\dim\operatorname{Im} T + \dim\operatorname{Ker} T = \dim V$ I'm having a hard time truly understanding the meaning of $\dim\operatorname{Im} T + \dim\operatorname{Ker} T = \dim V$ where $V$ is the domain of a linear transformation $T:V\to W$. I've used this equation several times in many problems, and I've gone over the proof and I believe that I fully understand it, but I don't understand the intuitive reasoning behind it. I'd appreciate an intuitive explanation of it.  Just to be clear, I do understand the equation itself, I am able to use it, and I know how to prove it; my question is what is the meaning of this equation from a linear algebra perspective. Why does volatile exist? What does the volatile keyword do? In C++ what problem does it solve?  In my case, I have never knowingly needed it. What is the Big-O of a nested loop, where number of iterations in the inner loop is determined by the current iteration of the outer loop? What is the Big-O time complexity of the following nested loops: for (int i = 0; i &lt; N; i++) {     for (int j = i + 1; j &lt; N; j++) {         System.out.println(&quot;i = &quot; + i + &quot; j = &quot; + j);     } }  Would it be O(N^2) still? Are there any places to leave luggage in Brussels, for short and/or long periods of time?