Are sufficiently large key sizes enough to deter quantum attacks for symmetric key ciphers such as AES?
We know  speedup brute-force attacks two times faster in block ciphers (e.g brute-forcing 128-bit keys take $2^{64}$ operations, not $2^{128}$). That explains why we are using 256-bit keys to encrypt top secrets. But  on AES shows brute-forcing AES-256 take $2^{100}$ operations. Does this attack work with Grover's search to make AES cipher quantum unresistant?
Number of normals from a point to an ellipse From a typical point $P$ inside an ellipse, how many points $Q_i$ on the ellipse have $PQ_i$ normal to the ellipse?  Someone asked me at school many years ago but I don't think I worked it out. Finding Stack Overflow/Exchange users based on geographic area? Fermat primes relation to $2^n+1$ If $2^n+1$ is prime how to show that  $n$ must be a power of $2$  Being at elementary level I am at a loss what to begin with? Node only partially rendered near edge of plot I'm trying to draw a relatively simple chart of a number line, and when one of the nodes is too close to the edge of the plot, it gets cut off.  The code:  \documentclass{article}  \usepackage{natbib} \usepackage{graphicx} \usepackage{pgfplots}  \begin{document}  \begin{tikzpicture} \begin{axis}[   width=\columnwidth,   axis y line=none,   axis lines=left,   axis line style={-},   xmin=0,   xmax=1,   ymin=0,   ymax=1,   xlabel=$\mu$,   scatter/classes={o={mark=*}},   restrict y to domain=0:1,   xtick={0,1} ] \draw[ultra thin] (axis cs:0, 0) -- (axis cs:0,.05); \draw[ultra thin] (axis cs:.4, 0) -- (axis cs:.4,.05); \node[coordinate,label=above:{$B$}] at (axis cs:0.0,0.05) {}; \node[coordinate,label=above:{$A$}] at (axis cs:0.4,0.05) {}; \node[coordinate,label=above:{$b$}] at (axis cs:0.2,0.02) {}; \node[coordinate,label=above:{$a$}] at (axis cs:0.7,0.02) {}; \end{axis}; \end{tikzpicture} \end{document}   The Result:    How do I get the B to fully render? I've got bunch of files with ill-formed numbering:  prefix-#.ext       | for files with number 1-9 prefix-##.ext      | for files with number 10-99 prefix-###.ext     | for files with number 100-999   Due to further processing I need all of their names to be in format: prefix-###.ext. Is there any easy way to do that? I'm looking for one word which describes what a student who missed classes needs to do I tried to create a Windows 10 USB boot medium with WoeUSB. I formatted a USB drive with an NTFS partition, but WoeUSB complains with:  Installation failed! Exit code: 256 Log: WoeUSB v@@WOEUSB_VERSION@@ ============================== Mounting source filesystem... Error: File "/media/woeusb_source_1543626298_6098/sources/install.wim" in source image has exceed the FAT32 Filesystem 4GiB Single File Size Limitation and cannot be installed.  You must specify a different --target-filesystem. Refer: https://github.com/slacka/WoeUSB/wiki/Limitations#fat32-filesystem-4gib-single-file-size-limitation for more info. Unmounting and removing "/media/woeusb_source_1543626298_6098"... You may now safely detach the target device   I've also tried to start WoeUSB via command line, did not work.  sudo woeusb --partition Win10_1809Oct_English_x64.iso /dev/sdb   My iso is located in:     home/sawyer/Downloads/Win10_1809Oct_English_x64.iso  Thanks in advance! I've been trying to get windows installed for three nights now, so any help towards that goal is greatly appreciated. Follow-up to question: Aut(G) for G = Klein 4-group is isomorphic to $S_3$ This is most likely a lack of understanding of wording on my part. I was considerind the Klein 4-group as the set of four permutations: the identity permutation, and three other permutations of four elements, where each of those is made up of two transposes, (i.e., 1 $\rightarrow$ 2, 2 $\rightarrow$ 1 and 3 $\rightarrow$ 4, 4 $\rightarrow$ 3) taken over the three possible such combinations of four elements.  Here, then, is my question. I am assuming (?) that Aut(G) in this case is the set of permutations of the four elements of the Klein 4-group - or the three non-identity ones for the purpose of showing isomorphic to $S_3$. If this is the case, what does it mean to have a permutation of these three permutations that I mentioned above? As always, thanks for your help. Prove that if $\sum{a_n}$ converges absolutely, then $\sum{a_n^2}$ converges absolutely I'm trying to re-learn my undergrad math, and I'm using Stephen Abbot's Understanding Analysis. In section 2.7, he has the following exercise:  Exercise 2.7.5 (a) Show that if $\sum{a_n}$ converges absolutely, then $\sum{a_n^2}$ also converges absolutely. Does this proposition hold without absolute convergence?  I'm posting about this here because my answer to that last question about whether the proposition holds without absolute convergence is "Yes", but my suspicions are raised by him merely asking the question. Usually questions like this are asked to point out that certain conditions are necessary in the statement of propositions, theorems, etc. I just want to see if I'm missing something here.  Anyway, here's how I prove the absolute convergence of $\sum{a_n^2}$, and note that I never use the fact that $\sum{a_n}$ is absolutely convergent:  Proof: Let $s_n = \sum_{i=1}^n{a_n^2}$. I want to show that $(s_n)$ is a Cauchy sequence. So, let $\epsilon &gt; 0$ and $n &gt; m$, and consider, \begin{equation}   \begin{aligned}     |s_n - s_m| &amp;= |(a_1^2 + a_2^2 + \cdots a_n^2) - (a_1^2 + a_2^2 + \cdots a_m^2)|\\                 &amp;= |(a_{m+1})^2 + (a_{m+2})^2 + \cdots + a_n^2|\\                 &amp;= |a_{m+1}|^2 + |a_{m+2}|^2 + \cdots + |a_n|^2\\   \end{aligned} \end{equation} Now, since $\sum{a_m}$ converges, the sequence $(a_m)$ has limit 0. Therefore I can choose an $N$ such that $|a_m| &lt; \sqrt{\epsilon/n}$ for all $m &gt; N$. So for all $n &gt; m&gt; N$,  we have, \begin{equation}   \begin{aligned}     |s_n - s_m| &amp;= |a_{m+1}|^2 + |a_{m+2}|^2 + \cdots + |a_n|^2\\                 &amp;&lt; \left(\sqrt{\frac{\epsilon}{n}}\right)^2 + \left(\sqrt{\frac{\epsilon}{n}}\right)^2 + \cdots + \left(\sqrt{\frac{\epsilon}{n}}\right)^2\\                 &amp;&lt; \left(\sqrt{\frac{\epsilon}{n-m}}\right)^2 + \left(\sqrt{\frac{\epsilon}{n-m}}\right)^2 + \cdots + \left(\sqrt{\frac{\epsilon}{n-m}}\right)^2\\                 &amp;= \epsilon   \end{aligned} \end{equation} Therefore $(s_n)$ is Cauchy and $\sum{a_n^2}$ converges. And since $\sum{a_n^2} = \sum{|a_n^2|}$, the series $\sum{a_n^2}$ is absolutely convergent. &#x220E;  Am I doing something wrong here? Am I right in thinking that $\sum{a_n}$ need not be absolutely convergent for $\sum{a_n^2}$ to be absolutely convergent? How to prove the following expression does not depend on x? I'm not sure how to approach this question, but I know it has something to do with taking the derivative of this. Can anyone please help me out?  Let x > 0. Prove that the value of the following expression does not depend on x: $$\int_{0}^{x}\frac{1}{1+t^4} dt + \frac{1}{3}\int_{0}^\frac{1}{x^3} \frac{1}{1+t^\frac{4}{3}} dt$$ I've bent (again) my derailleur hanger. It's a replaceable hanger but for this summer I can't get an original one and I know that the non-original one I can get is made in a harder material and could possibly damage the frame.  So I'm left with the choice of straightening this light aluminium alloy thing. How do I do that without breaking/weakening it? Am I going to have trouble flying with a reversed name on the ticket? I'm flying to Peru with my girlfriend next week and I realized that her name is incorrect on the reservation.  Instead of Sally Marie Jones it's Jones Marie Sally.  We're flying into Houston, then Lima, and in Lima we switch airlines for our flight to Cajamarca.  I booked the ticket with Orbitz who made the reservation with United. United booked the flight with LAN air, the Peruvian airline.  Both companies say that they are unable to change the name because of TSA restrictions not allowing a name change. I asked if I could just cancel and re-book, but United said they could not do this because there are multiple airlines involved.  A note has been attached to the reservation explaining the issue, and the United rep said that they would be able to print her boarding pass with the correct name. However, he said there are no guarantees that she'll be able to fly because although the boarding pass will be correct, the ticket will still have the reversed name.  I was prepared to just take the chance that it will all work out, seeing how it's really obvious the name is just backwards, but with recent events I'm worried that US airport security is going to be extra strict for the next little while.  Is this something I need to worry about, or are chances good that this will work out fine?  The United rep said there's a chance we could cancel the United flights and get a new ticket with the correct name for no cost, but we'd have to pay for new tickets within Peru ($500 out of the total $1300 ticket cost). I'd rather not do this unless there's a reasonable chance we'll have trouble at the airport. Why is the plural of "basis" "bases" and not "baseis"? Looking at the , it indicates that the plural is either bases or baseis.  It looks like the rare  comes from the Greek, but the common  just refers back to basis and that does not explain the plural etymology.  Is there a standard rule at work here, or is this just an exceptional case that arose over time by convention? Can a massless rope accelerate? What is the difference between an indeterminate and variable? From Wikipedia-     In mathematics, and particularly in formal algebra, an indeterminate is a symbol that is treated as a variable, but does not stand for anything else but itself and is used as a placeholder in objects such as polynomials and formal power series.   So, how it is different from variable which is also used as a placeholder? What is the use of the indeterminate? How to change phone number in Google account? I gave Google my phone number to verify it, not knowing that it would change it, and now my phone number is completely different? What have I done, and how do I unverify it and change my phone number back? Simple past or past perfect with "by" and years What is the difference between      He became a star by 1990's.     He had become a star by 1990's.    Is the first sentence correct? If yes, then please tell me the difference between the two. An element of a group has the same order as its inverse If $a$ is a group element, prove that $a$ and $a^{-1}$ have the same order.   I tried doing this by contradiction.    Assume $|a|\neq|a^{-1}|$  Let $a^n=e$ for some $n\in \mathbb{Z}$ and $(a^{-1})^m=e$ for some $m\in \mathbb{Z}$, and we can assume that $m &lt; n$.  Then $e= e*e = (a^n)((a^{-1})^m) = a^{n-m}$. However, $a^{n-m}=e$ implies that $n$ is not the order of $a$, which is a contradiction and $n=m$.  But I realized this doesn't satisfy the condition if $a$ has infinite order. How do I prove that piece? How do I compare binary files in Linux? I need to compare two binary files and get the output in the form:  &lt;fileoffset-hex> &lt;file1-byte-hex> &lt;file2-byte-hex>  for every different byte. So if file1.bin is    00 90 00 11   in binary form and file2.bin is    00 91 00 10   I want to get something like    00000001 90 91   00000003 11 10   Is there a way to do this in Linux? I know about cmp -l but it uses a decimal system for offsets and octal for bytes which I would like to avoid. What does the TLS 1.2 client finished message contain? I am implementing TLS 1.2 and I'm stuck on the client finished message.   My question is: what is the size and structure of a clients finished message in TLS 1.2 when using the ECDHE_RSA_AES_128_GCM_SHA256 cipher suite.   I searched for this question and someone somewhere stated its size is 48 bytes; more specifically:   12 byte verify data 1 byte handshake type 3 byte verify data length and 32 byte MAC   Is that really correct?   I mean: according to  finished messages have {verify_data[verify_data_length]} and verify_data = PRF(master_secret, finished_label, hash(handshake_messages). Also, according to RFC 5246 section 5 PRF(secret, label, seed) = P_&lt;hash&gt;(secret, label+seed) and P_hash(secret, seed) = HMAC_hash(secret, A(1) + seed). So, when I compute HMAC using SHA256 for verify_data its size is 32 byte.   As a result, I'm a bit confused in relation to the verify_data size and the finished message structure. Can anyone help me to understand this and/or maybe put me on the right track somehow?