finding the value of $a$ for minimal solid November 26    1

Given that $y=x^2+ax-0.25$ is bounded by $x=0$ and $y=1$ and spinning around the x-axis.What is the value of $a$ for min volume of that solid?My attempt: $x^2+ax-0.25=1$ so $x=\frac{-a\pm \sqrt{a^2+5}}{2}$.Then, $f(a)=\pi \int_{0}^{\frac{-a+\sqrt{a^2

Differentiability at a point $(0,0)$ November 26    4

Differentiability at a point $(0,0)$
How would i show $$\frac{xy(x^2-y^2)}{(x^2+y^2)^{3/2}}$$ is not differentiable at $(0,0)$I'm assuming you mean to set $f(0,0) = 0$. In that case, the function most definitely is continuous, ...

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 $(0,1)⊕(1,1)$ or$y^2=x^3+x^2-x$ 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 $x$,

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 $a$.

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