Plaid CTF 2012 – Nuclear Launch Detected

Our spies intercepted communications and a file between 5 of the top 10 robo-generals and their nuclear bomb server. We must recover the final launch code from the 5 robo-general’s secret codes, so we can stop the detonation!
Title: Nuclear Launch Detected (150)
Category: Password Guessing

For this challenge we had to find a a cryptographic secret from a number of shares.

Reading the challenge text: 5 of 10 generals coming together to launch a bomb we were immediately triggered about secret sharing/treshold schemes. The most famous one being Shamir’s secret sharing method.
Looking at the pcap and the provided file confirms that, some very large numbers are exchanged and we are provided with another large number.

We find a nice implementation in python for this scheme at: http://codepad.org/NvYVdZFT

Using that we can very easily decode the challenge by plugging in the numbers.

pairs = [(1,c1),(2,c2),(3,c3),(4,c4),(5,c5)]
a= '%X' % (interp_const(pairs,5,p))
print a.decode('hex')
--> s3cr3t_5h4r1n9_i5_H4RD_!!