Tags: crypto fhe 

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The flag is encrypted with ElGamal and an additional layer of custom fully-homomorphic encryption. We can recover the FHE key under known-message attack by solving a linear system. The group used for ElGamal is weak (its order has small prime factors), so we can compute a discrete logarithm to recover the secret exponent and decrypt the flag.

Original writeup (https://duksctf.github.io/PCTF2017-FHE/).