  We discuss a new attack, termed a dimension or linear decomposition attack,
on several known group-based cryptosystems. This attack gives a polynomial time
deterministic algorithm that recovers the secret shared key from the public
data in all this schemes under consideration. Furthemore, we show that in this
case, contrary to the common opinion, the typical computational security
assumptions are not very relevant to the security of the schemes, i.e., one can
break the schemes without solving the algorithmic problems on which the
assumptions are based. The efficacy of the attack depends on the platform
group, so it requires a more thorough analysis in each particular case.
