A general encryption scheme using two-sided multiplications with its cryptanalysis

We show that many known schemes of the public key exchange protocols in the algebraic cryptography, that use two-sided multiplications, are the specific cases of the general scheme of such type. In most cases, such schemes are built on platforms that are subsets of the linear spaces. They have been repeatedly compromised by the linear decomposition method introduced by the first author. The method allows to compute the exchanged keys without computing the private data and therefore without solving the algorithmic problems on which the assumptions are based. We demonstrate that this method can be successfully applied to the general scheme, thus it is in some sense universal.