Get Into Crypto Capture The Flags (CTFs)

What is one of the best ways to develop an advanced approach to solving cybersecurity problems? Well, CTFs allow you to meet new problems, and work out solutions to them. Some of the best are related to the cracking of cryptography, as they allow you to learn how encryption actually works and how to code for a given solution. This normally involves a bit of maths and then some coding in Python. You thus pick up a bit of problem-solving, a bit of maths, and a bit of Python. But the best bit is where you end up with a solution that works. So, let’s try one that I’ve been working on. For this, we will create a CTF generator and then reveal the solution.

The challenge is:

Bob’s RSA program has used the same prime number (p) for different modulus values (N1=p.q and N2=p.r). He has then lost these modulus values and the prime numbers which generated them. So, given two ciphertext values (Ca and Cb) and decryption exponents for each modulus (da and db), can you decrypt these ciphertexts?

C_A= 53076781476001918980541481586924954661844290230187469413721814208978175578689812434506485756303137373411983183821523499356718941957462796750366565306981279096920001684341033667106062625641623824611746178114499495060920261013868649922549275513310651497559442590121242176702079874889134767706658633548623441729
C_B=…