An improved version of the AAG cryptographic protocol

Abstract An improved version of the Anshel–Anshel–Goldfeld (AAG) algebraic cryptographic key-exchange scheme, that is in particular resistant against the Tsaban linear span cryptanalysis, is established. Unlike the original version, that is based on the intractability of the simultaneous conjugacy search problem for the platform group, the proposed version is based on harder simultaneous membership-conjugacy search problems, and the membership problem needs to be solved for a subset of the platform group that can be easily and efficiently built to be very complicated and without any good structure. A number of other hard problems need to be solved first before start solving the simultaneous membership-conjugacy search problem to obtain the exchanged key.