## Evaluating by real methods $\int_0^{\pi/2} \frac{x^5}{2-\cos^2(x)}\ dx$ November 26    1

$\def\Li{{\rm{Li}}}$I'm sure you guys can briefly get the result by some methods of complex analysis, but nowI'm only interested in real analysis methods of proving the result. What would you proposefor that? \begin{align*} \int_0^{\pi/2} \frac{x^5}{

## How is a singular continuous measure defined November 26    2

On a measurable space, how is a measure being singular continuous relative to another defined? I searched on the internet and in some books to no avail and it mostly appears in a special case - the Lebesgue measure space $\mathbb{R}$. Do you know if

## necessary and sufficient condition for continuous function to be monotonic at certain domain November 26

Lately I found there exists a function which is "continuous but nowhere monotonic".So, now I want to know that (the title).I'm really thank you if you give me a proof of it.

How to find $E_{p^2}$ of an elliptic curve $E_p$ defined over finite field $F_p$ where $p$ is a prime number?Well, so we have $\,y^2=x^3+2x+3\,$ , so what I had in mind is to check particular cases, say:$$y=1\Longrightarrow f(x):=x^3+2x+2=0\Longright ## Why are supersingular elliptic curves useful for cryptography November 26 I don't know very much about cryptography and would like to learn more. I know the basics of RSA alogrithm and how elliptic curves over finite fields can be used to do something similar. But I would like to know why supersingular elliptic curves are ## Elliptic curves (sum and multiply) November 26 4 I was wondering if someone could give me some resources on elliptic curve cryptography. Specifically I need to know how to do something like:y^2=x^3-x+1 compute (0,1)⊕(1,1) ory^2=x^3+x^2-x compute 2*(-1,1)I can't seem to find anything that ex ## Finding all Points on a Edwards curve November 26 1 I need to find all affine points on the Edwards curve:x^2 + y^2 = 1 - 5x^2y^2 over F_{13}I tackle this by transforming the equation to:y^2 = \frac{1-x^2}{1+5x^2}I then go from x = 0 to \frac{p-1}{2} in this case x from 0 to 6.If you can take ## Queston concerning cracking an RSA message November 26 I don't have a clue how to solve this exercise:Let m be an RSA modulus, g an encryption Exponent and N be a space of Messages. You know that k^g is such that k \in S \subset N with an S of cardinality \log_2{(m)} . How do you find m?It seems th ## AES Key Scheduler November 26 1 How do you get the rcon for AES's key scheduler? Where does it come from; is it a constant because it seems to differ?The bytes in AES are considered as elements in a finite field of size 2^8, and we can see them as polynomials over a variable x, ## What is a good book on Cryptography with an emphasis on algebraic aspects November 26 I have heard of the subject "Cryptography" but never looked much into it. But this summer, I thought is the best time to look into the subject and see if it will interest me. In U.G, I did Cryptography chapter in Burton's book on Number theory a ## What books do you recommend on mathematics behind cryptography November 26 1 I am currently reading the Book Understanding Cryptography from Cristof Paar. I am enjoying the book but i don't like to scratch the surface when it comes to cryptography. I would like do dig a little deeper on the mathematics behind it. I read on:ht ## Reversing Rotation + XOR November 26 2 I have this cypher which is as follows :Take 2 numbers : A=1011 and B=1010if the ith bit of X is 1 then shift Y*i times to the left. So in the end you will get something like 1010 1010 1010 So now you Apply XOR on these numbers which results in :0000 ## Elliptic curve cryptography order November 26 How do I compute an order a a point P on an elliptic curve?My question is specifically in reference to the attached photo. I understand how to do part a but I am totally lost in part b. I don't know how to compute the order, and also I am not positiv ## Square roots in modular arithmetic closed November 26 1 Suppose n = pq with p and q both primes.Suppose that \gcd(a, pq) = 1. Prove that if the equation x^2 ≡ a \bmod n has any solutions, then it has four solutions.Suppose you had a machine that could find all four solutions for some given a. ## Why does a key have to be at least as long as a message (cryptography) November 26 3 I am studying cryptography and find it hard to understand. What happens if the key is one bit or 100 bits shorter than the message?In general, this condition is not needed. But it is needed if you demand perfect secrecy.Definition: A cryptosystem has You Might Also Like • Suppose that (X_1,...,X_N) be N iid samples from uniform distribution. Let X_{(n)} be n-th order sta ... • Consider Pell's equation of the form$$x^2-Dy^2=A.$$I am looking for the reference to the following questio ... • I have a vector (x,y) = (x_2 - x_1, y_2 - y_1). I have an arrow pointing to 0 degrees.With vector (x, y) ... • As the title says, why are those two equivalent? I can find a simple derivation (using natural deduction) of ... • (No, I'm not asking if \sqrt{-1} = +i or if \sqrt{-1} = -i. Yes, I know +i is the principal square roo ... • This is a follow-up to an answer on a previous question on PD algorithms: http://math.stackexchange.com/a/11 ... • Given a recursive sequence \,f_n(x) :[0,1] \to \mathbb R, x \in [0,1], where$$\begin{align*} f_1(x) &am ...
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