  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.
