tldr;

• Okamoto-Uchiyama cryptosystem is being used
• The private information is the factorisation of n; if we have the prime factorisation, we can easily decrypt
• q is generated from p, and we can write q = p^2 + 2^256 + delta
• Bruteforce delta and solve for p by finding roots of the quartic p^2 (p^2 + 2^256 + delta) - n

writeup

Original writeup (https://jsur.in/posts/2020-08-09-poseidonctf-2020-writeups#discrete-log).