One Line Crypto Writeup

Crypto CTF 2020 - Crypto 142 - 30 solves

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Encryption logic

Plain textbook RSA, which prime generation logic is exposed and seems weak. All prime has form x ** (m + 1) - (x + 1) ** m

Exploit

I can assume the public modulus' size is almost same with ciphertext. Bit length of ciphertext: 2047 so I can deduce that prime sizes are bigger than 2 ** 1020.

By iterating x and m for 5 minutes to generate primes using upper filtering condition, I could gather primes which are candidates of primes used in encryption. Try few prime pairs to decrypt ciphertext.

I get flag:

CCTF{0N3_1!nE_CrYp7O_iN_202O}

Exploit code: solve.sage with config.py