Matemith - CryptoCTF - writeup

Wed, 24 Dec 2025 00:00:00 +0000

For this challenge, we are given a matemith.sage and a output.txt. The challenge starts by splitting the flag into 6 parts (the number of parts can be later seen in the code):

l, flag = 14, flag.lstrip(b'CCTF{').rstrip(b'}')
FLAG = [flag[l * i:l * (i + 1)] for i in range(len(flag) // l)]
M = [bytes_to_long(_) for _ in FLAG]

Then, 6 polynomials in $\mathbb{Q}[u, v, w, x, y, z]$ are generated:

p = getPrime(313)
R.<u, v, w, x, y, z> = PolynomialRing(QQ)

COEFS = [getRandomRange(1, p - 1) for _ in range(21)]
f = COEFS[0] * u * v + COEFS[1] * u + COEFS[2] * v
g = COEFS[3] * u * x * y + COEFS[3] * x + COEFS[5] * y + COEFS[6] * v
h = COEFS[7] * u * w + COEFS[8] * w + COEFS[9] * u
i = COEFS[10] * v * y * z + COEFS[11] * y + COEFS[12] * z + COEFS[13] * w
j = COEFS[14] * v * w + COEFS[15] * v + COEFS[16] * w
k = COEFS[17] * w * z * x + COEFS[18] * z + COEFS[19] * x + COEFS[20] * u
f, g, h, i, j, k = R(f), R(g), R(h), R(i), R(j), R(k)

Then, they are evaluated in the flag parts and printed:

Multivariate Polynomials on manbolq's Blog

Matemith - CryptoCTF - writeup