Homework Statement
Note: I think there is a typo here but I'm not sure. Is there supposed to be a comma between the delta t/2 and y_n on K2 and K3, and delta t and y_n on K4?
Homework Equations
See above.
The Attempt at a Solution
Substituting dy/t = z gives
\frac{dz}{dt} = 3z - 2ty -...
Homework Statement
Given some ElGamal private key, and an encrypted message, decrypt it.
Homework Equations
Public key (F_q, g, b)
Private key a such that b=g^a
Message m encrypted so that r=g^k, t=mb^k
Decrypt: tr^-a = m
The Attempt at a Solution
My problem is finding r^-a...
Compare it to
\sum \frac{2^n}{3^n}
\frac{2^n}{3^n}\cdot\frac{3^n-1}{2^n}
\frac{3^n}{3^n} - \frac{1}{3^n}
1- \frac{1}{3^n}
With limit n->infinity, this = 1
Homework Statement
Where P_n(x) is the nth legendre polynomial, find f(n) such that
\int_{0}^{1} P_n(x)dx = f(n) {1/2 \choose k} + g(n)
Homework Equations
Legendre generating function:
(1 - 2xh - h^2)^{-1/2} = \sum_{n = 0}^{\infty} P_n(x)h^n
The Attempt at a Solution
I'm not sure if that...
Homework Statement
Given the following key, find two plaintext pairs that encrypt to the same ciphertext.
\begin{pmatrix}
9 & 5 \\
7 & 3 \\
\end{pmatrix} (mod \ 26)
Homework Equations
The Attempt at a Solution
Let the two plaintext pairs be (a, b) and (c, d). Let the...
Here's how I would do it:
First, make one equation. So f(t) - g(t)
Then find the derivative of that equation for both t<3 and t>3. From there you should be able to find the answer to ( a ). Derivatives describe the behavoir of the original equation. They give the slope of the tangent to the...
Homework Statement
Find the horizontal asymptotes for the following equation:
Homework Equations
f(x) = \sqrt{x^2+4x}-\sqrt{x^2+x}
The Attempt at a Solution
First I factored f(x):
f(x) = \sqrt{x}\sqrt{x+4}-\sqrt{x+1}
Then I conjugated it:
f(x) =...