Can anyone dumb it down for me on why you would need to format the first and last byte of a random number to properly generate a curve25519 private key as noted in 'Computing secret keys' section of .  Computing secret keys. Inside your program, to generate a 32-byte Curve25519 secret key, start by generating 32 secret random bytes from a cryptographically safe source: mysecret[0], mysecret, ..., mysecret[31]. Then do  mysecret[0] &amp;= 248;  mysecret[31] &amp;= 127;  mysecret[31] |= 64;   mysecret[0] &amp;= 248 = 0b1111 1000...setting three lsb's to 0 to ensure multiple of 8? mysecret[31] &amp;= 127 = 0b0111 1111...setting the msb to 0 for? mysecret[31] |= 64 = 0b0100 0000...setting the second msb to 1 for? I must be missing some important note on this in ?
According to the original paper of , there is no key validation needed when using Curve25519 for Diffie-Hellman Key Exchange. However, where does this property come from? Is there any proof or argumentation available in order to understand this really practical property of Curve25519? Does this mean that each $x$ coordinate could belong to a point $P=(x,y)$ from Curve25519? Is that even possible?
Does Blender have different languages (language as in speech language as english, not computer language as python)? Sometimes it's more convenient for me to use Blender in another language. Does Blender have different languages (language as in speech language as english, not computer language as python)? Find minimum value of $\sum \frac{\sqrt{a}}{\sqrt{b}+\sqrt{c}-\sqrt{a}}$ How to pronounce "Moderators's"? If I want to use the plural of &quot;moderator&quot; and also add the apostrophe plus S, how do I pronounce it? How do native speakers pronounce it?  Moderators = moderatorz Moderators's = moderatorziz or just moderatorz?  A sentence is:  &quot;I always thought that moderators's decisions seemed fairly arbitrary.&quot;   I guess moderatorziz is correct but it sounds weird to me. Do native speakers pronounce it as moderatorziz? How do I convert html page to SharePoint 2013 master page? There is functionality provided in SP2013 for converting html page to SharePoint master page. I have tried this functionality but each time it convert nothing. Is there any specific method that I need to follow? Or is there any specif layouts of html page need to be converted into SP 2013 master page? Search for singleton tags on questions Is there any way to search for questions that have a specific tag and only that lonely tag?  In other words, I'd like to be able to do something like the following to find questions that have a single tag and no other:  [mytag] tagcount:1   This would be very useful for tag cleanup situations to be able to do house-cleaning before nuking a tag. Why $f(x) = \sqrt{x}$ is a function? Schengen visa in US without H1B stamp Alias and functions From the bash manual     The rules concerning the definition and use of aliases are somewhat   confusing. Bash always reads at least one complete line of input   before executing any of the commands on that line. Aliases are   expanded when a command is read, not when it is executed. Therefore,   an alias definition appearing on the same line as another command does   not take effect until the next line of input is read. The commands   following the alias definition on that line are not affected by the   new alias. This behavior is also an issue when functions are executed.   Aliases are expanded when a function definition is read, not when the function is executed, because a function definition is itself a   compound command. As a consequence,   aliases defined in a function are not available until after that function is executed. To be safe, always put alias definitions on a   separate line, and do not use alias in compound commands.   The two sentences "Aliases are expanded when a function definition is read, not when the function is executed" and "aliases defined in a function are not available until after that function is executed" seem to be contrary to each other.  Can you explain what they mean respectively? A set $A \subset l_1$ is compact if and only if closed, bounded, and one other condition A set $A \subset \ell_1$ is compact if and only if $A$ is closed and bounded and given any $\epsilon &gt;0$, there exists $n_0$ such that $\sum_{k=n}^{\infty} |x_k| &lt; \epsilon$ for all $n&gt; n_0$ and $x \in A$.   It's easy to prove the part assuming that $A \subset l_1$ is compact, but I am finding difficulty to prove the other part. Fermat: Last two digits of $7^{355}$ I am doing this problem mentioned above and I know the answer because I know Euler's Theorem that $$a^{\varphi{(m)}}\equiv{1}\pmod{m}.$$  I used 100 as my modulus and got that the last two digits of $7^{355}$ are $43$.  My question is this.  What prime should I pick to solve this problem using Fermat's theorem $$a^{p-1}\equiv{1}\pmod{p}$$  As a precursor problem, the author (Dudley; Elementary Number Theory) asked to find the last digit of the number above; so using a modulus $5$, $7^4\equiv{1}\pmod{5}$ by Fermat.  Since the answer is $7^{355}\equiv{3}\pmod{5}$, the last digit is either $3$ or $8$.  Since $7$ is odd, the answer will clearly be odd, so $3$ is it.  The book is working linearly, building from the previous chapters and Euler's Theorem isn't mentioned for another two chapters (I remembered Euler from a problem solving class in college).    So again, what prime would be best?  How should I procede?    EDIT: I've seen a bunch of problems on the site and none that I looked at did it using Fermat.  If there is one, that could be posted and I would be happy.  EDIT 2:  it seems that the problem of finding of finding the last two digits using is rather difficult because of the implication that we need something mod 100.  Is there a way around this , like adding a step or complexifying, in order to finish the problem with Fermat? Are all eigenvectors, of any matrix, always orthogonal? What is the difference between "var=${var:-word}" and "var=${var:=word}"? Series involving log $\sum_{n=1}^{\infty} \left( n\log \left(\frac{2n+1}{2n-1}\right)-1\right) = \frac{1-\log 2}{2}$ How can I prove the maximum number of edges? On my book it says that the maximum number of edges E, in a simply connected undirected unweighted graph $G(V,E)$ is $\dfrac{|V|(|V|-1)}{2}$.  How can I show that it is true? Thanks! ART has better performance and better battery life on paper at least.  Should I consider switching to it on my moto g? What are the results I can expect? What precautions should I take? Is it easy to turn back to dalvik? Play audio with Python Excuse me if the question is naïve. I am not a physicist.  Let's imagine formation of a black hole from a homogeneous collapsing star. At certain moment when enough of matter is inside of a small enough spherical area the event horizon starts to exist. When does the singularity start to exist and why?  The matter below the event horizon still continues to collapse towards the centre (e.g. in the reference frame of the falling matter). What are the necessary conditions for the singularity to appear?  I have found two similar questions but the answers did not really explain this problem to me: What are the differences between a pointer variable and a reference variable in C++? Show that if $u$ is harmonic in $\mathbb R^n$ and $u=o(|x|)$, then $u$ is a constant.(Hint: use the solid version of the mean value property $u(x)=\frac{1}{\omega R^n} \int _{B_{R(x)}} u(y)dy$, and estimate $|u(x)-u(x')|$.)  Can anyone tell me how to use this hint? Can I mill my opponent into defeat with Mindcrank and Duskmantle Guildmage? Okay the scenario I'm thinking of is as follows:   I control a ,  and 3 untapped lands (2 swamps, 1 Island to be perdantic). In my opponents turn he casts a burn spell to kill my duskmantle.   I activate his first ability in response.   The way I am hoping the following interactions will go is:   Duskmantles ability will hit the stack at the top and resolve The burn spell resolves dealing its damage to Duskmantle The burn spell card hits the graveyard and triggers the infinite loop for duskmantle and mindcrank killing my opponent Duskmantle perishes   Is this the way that the stack would pan out? Do I win in this situation regardless of the stack being correct or not above? (I am not fully familiar with how the stack really works in magic) You can see the cards from my deck .