I got this question in a local hacking event, but I couldn't solve it.
Problem Statement ----
Continuing their snooping habit, NSA kept bugging Alice's communication. Resorting to the age old RSA encryption, Alice used 128-bit RSA encryption to exchange messages. Alice shares her public key as
0xffffffa95256a837568a41c265f4fe27110814aae19f144762d5cc0bcb931807and her public key exponent $e$ (derived from $\phi(n)$) as
However, NSA, with its enormous resource, cracked this 128 bit encryption super easily. Seeing your work on the previous ciphers, NSA decided to offer you a job in their Cryptography group. As a final test, NSA shared this public key which they intercepted from Alice and Warden's conversation. They also gave away the private key that they computed from their message exchange.
Public Key: 0xffffffa95256a837568a41c265f4fe27110814aae19f144762d5cc0bcb931807 0x11 Private Key: 0xffffffa95256a837568a41c265f4fe27110814aae19f144762d5cc0bcb931807 0xc3c3c3817b3335577e69b9d0e48e2bc1fdf71f1f4f73a38a7d628d39739bbaf1
What are the values of $p$ and $q$? (the prime numbers used in key generation)
How can I find the prime numbers used in RSA?