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Is there a way of maintaining malleability in a homomorphic encryption system while making it infeasible to perform chosen ciphertext attacks?   I have been reading about homomorphic encryption and malleable cryptosystems lately and have found it fascinating. I still have a lot of reading to do, however, I came across a statement in my reading that suggested malleability is inherently counter to security against chosen ciphertext attacks.  While I read up more about this relationship, I am curious to learn if there a way to maintain malleability while making a chosen ciphertext attack computationally infeasible? Why or why not? What are the differences between struct and class in C++? Does adding two linear equations will result in a line which will pass through an intersection of the linear equations? I was wondering why it is almost impossible to find a geometrical explanation of why adding two linear equations helps us to find a solution of a system of linear equations? Am I right that adding two linear equations will result in an equation of a line which will pass through a point where two linear equations intersect?  If it is right then I completely don't understand why such a crucial point in understanding how to solve systems of equations is never properly taught even at a university level. Resolving ambiguous overload on function pointer and std::function for a lambda using + What's the associated matrix of this linear operator? Let $V$ be a complex vector space of dimension $n$ with a scalar product, and let $u$ be an unitary vector in $V$. Let $H_u: V \to V$ be defined as  $$H_u(v) = v - 2 \langle v,u \rangle u$$  for all $v \in V$. I need to find the characteristic polynomial of this linear operator, but the only way to find it that I know of is using the associated matrix of the operator.  I don't know how to find this matrix because I don't know how to deal with the scalar product. Is there some other way to find the characteristic polynomial? If not, how can I find the associated matrix of this linear operator?  Thanks in advance. Is there any UNIX variant on which a child process dies with its parent? Probability Math Question...? Bag A contains 3 white and 2 red balls. Bag B contains 6 white and 3 red balls. One of the two bags will be chosen at random, and then two balls will be drawn from that bag at random without replacement. What is the probability that the two balls drawn will the be the same color? Express your answer as a common fraction. is uniform convergent sequence leads to bounded function? Suppose there is there is uniform convergent sequence $(f_n)$ on the set $A$, and each $f_n$ is bounded on $A$, i.e., there exist $M_n&gt;0$ such that $|f_n(x)|\le M_n$ for all $x\in A$ Is it true that there exist a function $f$ that is bounded on set A? Can I prove it this way:  Since $f_n \to f$ uniformly on A, $\exists n \ge N$ such that $$|f_N(x) - f(x)| \le 1$$ and $$|f_n(x)-f_N(x)| \le 1$$  Therefore, $|f(x)| \le |f_N(x)|+1 \le M_N + 1$ and $|f_n(x)| \le |f_N(x)| + 1 \le M_N + 1$, $x \in A , n \ge N$  Let $M = \max\{M_1, M_2,\dots,M_N\} + 1$ : $|f_n(x)| \le M$, $\forall x\in A$  Therefore, $f$ is a bounded function on A. Does this seemingly elementary question require König's theorem? If  $$\sin A + \cos A + \tan A + \cot A + \sec A + \csc A = 7$$ then prove that  $$\sin 2A \quad\text{ is a root of }\quad x^2 - 44x - 36 = 0$$  I have no idea how to solve it. Plz help. How many combinations are possible in the game tic-tac-toe (Noughts and crosses)?  So for example a game which looked like: (with positions 1-9)  A1   --   B1  A2   --   B2  A3   --   --   [1][3][4][6][7] would be one combination Is it possible to link multiple leaders lines to one piece of annotation?  I'm working in ArcGIS 10.2 Desktop Advanced with non-feature linked geodatabase annotation. I have hundreds of numbers labeling various polygons, but some polygons share a number. Instead of creating multiple numbers/annotations for each polygon I'd like to have one number with multiple lines pointing to each polygon.   So, in the image below, the number 5 corresponds to multiple polygons. Here I've moved 5 from it's ideal location to show that the second leader line is not connected to the number annotation. My workaround has been to create another piece of geodatabase annotation with a blank text string to serve as a placeholder for a leader line. The other option was to use map/graphic annotation to create the second leader line, but with the multiple disadvantages of not being in the same annotation feature class as the number annotation.    My goal would be for each piece of number annotation to be connected to multiple leader lines like appears below. Why is negative times negative = positive? Currently I had built a file upload functionality in Lightning component which accepts the CSV file, read it as text(Each row in CSV is split using \n and each column in the row is split using ,). Then each columns in each row are validated in Javascript and if everything is fine,the data is saved in the backend. While uploading the data, if the file contains , in its data then it is taken as another column. Eg: X-36936,SS-341487,11-WT,414081,"LENDERS, THE HACK",2-Manage,,,,,,,,,,,,12/1/2013,3150,,0,,Dealing,2018,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,  Here "LENDERS, THE HACK" is a single column but it is taken as 2 columns (LENDERS --> 1st column and THE HACK --> 2nd column).Could anyone please help me how to resolve this issue? Proofs involving $ (A\setminus B) \cup (A \cap B)$ Prove that $f$ has a fixed point . For $f:[a,b]\rightarrow [a,b]$ is a continuous . Prove that $f$ has a fixed point . Is that true if we change $[a,b]$ by $[a,b)$ or $(a,b)$. Is it possible to use "negative sound waves" to "cancel out" a sound to create silence? $X$ is a topological space with no special properties.  If a space $X$ has no isolated points, then show the same for any dense subset of   $X$.  Thanks a lot. Vertical placing of wide accents in superscript The following code  $\widetilde{aaa} \quad L^{\widetilde{aaa}}$  $\tilde{aaa} \quad L^{\tilde{aaa}}$  $\widehat{aaa} \quad L^{\widehat{aaa}}$  $\hat{aaa} \quad L^{\hat{aaa}}$  $\overline{aaa} \quad L^{\overline{aaa}}$  $\bar{aaa} \quad L^{\bar{aaa}}$   produces the following output:    What is the reason for additional vertical spacing for \widetidle and \widehat in superscript and what can one do about it? terminator: permission denied for sudo