1. Bob chooses two prime numbers: p = 157 and q = 199. He calculates n = p × q = 31243.
2. With ϕ(n) = n − p − q + 1 = 31243 − 157 − 199 + 1 = 30888, Bob selects e = 163 such that e is relatively prime to ϕ(n); moreover, he selects d = 379, where e × d = 1 mod ϕ(n), i.e., e × d = 163 × 379 = 61777 and 61777 mod 30888 = 1. The public key is (n,e), i.e., (31243,163) and the private key is $(n,d), i.e., (31243,379).
3. Let’s say that the value they want to encrypt is x = 13, then Alice would calculate and send y = xe mod n = 13163 mod 31243 = 16341.
4. Bob will decrypt the received value by calculating x = yd mod n = 16341379 mod 31243 = 13. This way, Bob recovers the value that Alice sent.

You need to know the main variables for RSA in CTFs: p, q, m, n, e, d, and c. As per our numerical example:

• p and q are large prime numbers
• n is the product of p and q
• The public key is n and e
• The private key is n and d
• m is used to represent the original message, i.e., plaintext
• c represents the encrypted text, i.e., ciphertext