Cryptographic analysis of the generalized ElGamal's cipher over $\operatorname{GL}(8,\mathbb F_{251})$

A cryptographic analysis is given to the generalized ElGamal's protocol over group $\operatorname{GL}(8,\mathbb F_{251})$ that was introduced by Pedro Hecht. The exchange of a secret key in this protocol is a particular case of the Shpilrain–Ushakov's key exchange protocol. We show that there exists an efficient algorithm for finding this key without computing the secret parameters of the protocol. Thus, the Hecht's protocol is theoretically and practically vulnerable.