# Analysis Incarnate 2

This is a proof of Euler’s Identity using the Taylor Series.

$\dpi{300}&space;\tiny&space;e^{i\pi}+1=0$

We can write e^iphi as the Taylor Series expansion.

$\dpi{300}&space;\tiny&space;e^{i\phi}=\sum_{n=0}^{\infty}\frac{(i\phi)^{n}}{n!}$

Let’s visualize this sum. It helps to write out all your terms because you know that the powers of i are going to alternate between 1,-1,i,and -i.

# Analysis Incarnate

This is a quick proof of Euler’s formula without the use of the Taylor Series.

$\dpi{300}&space;\tiny&space;e^{i\phi}&space;=&space;cos&space;\phi&space;+&space;i&space;sin\phi$

Even with the imaginary number i, this equation is differentiable, so we can take the derivative of :

$\dpi{300}&space;\tiny&space;f(x)=\frac{e^{i\phi}}{cos\phi+isin\phi}$

# Access=0000

This is a writeup for a crypto challenge in RACTF 2020, where we placed 6th.

### Challenge Description:

Challenge instance ready at 95.216.233.106:57735

We found a strange service, it looks like you can generate an access token for the network service, but you shouldn't be able to read the flag... We think.


### Solving :

We are given access.py. Lets take a look the server file to see what the program does.

From the top, we see that get_flag:

# Really Smart Acronym

### Challenge Description:

Man, oracles are weird.

nc challenges1.hexionteam.com 5000


### Solving :

​Really Smart Acronym, of course, is RSA. Looking at the code, it uses PyCrypto to generate a RSA key to encrypt the flag. You also get one encryption and 1024 decrypts, but you only get the last bit of the decrypts. At first we thought it could be Franklin-Reiter related-message attack, but there is not enough information for that.

# S.S.S.

This is a writeup for HexionCTF 2020, where we placed third.

### Challenge Description:

Math is so beautiful and can always be used for cryptographic
encryption!
nc challenges1.hexionteam.com 5001


### Solving :

We are given an sss.py. See here for source.

We found that SSS stands for Shamir’s Secret Sharing by copy-pasting the loop from eval_at, which brought me to this Wikipedia Page. Shamir Secret Sharing is based on polynomials and lagrange interpolation.