The Ashen Field

CACTF2026

Task: HFE multivariate public-key cryptosystem over GF(2) with N=137 variables; recover a KEY that seeds an AES-ECB flag key. Solution: the central map F^4+F^2+1 is a linearized polynomial and boolean variables (x^2=x) collapse the whole public key to an affine GF(2) map, so Gaussian elimination recovers KEY and decrypts the flag.