A Note on Conjugacy Search and Racks

The authors 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. They note that, in fact, protocols based on conjugacy search could be simply implemented using a rack. They give an exposition of the Anshel-Anshel-Goldfeld protocol in such a case.