  We show that for every effective left conjugacy closed left quasigroup, there
is an induced rack that retains the conjugation structure of the left
translations. This means that cryptographic protocols relying on conjugacy
search can be secure only if conjugacy search of left translations is
infeasible in the induced rack. We note that, in fact, protocols based on
conjugacy search could be simply implemented using a rack. We give an
exposition of the Anshel-Anshel-Goldfeld protocol in such a case.
