An Optimization of Gu Map-1

As a modified version of GGH map, Gu map-1 was successful in constructing multi-party key exchange (MPKE). In this short paper we present a result about the parameter setting of Gu map-1, therefore we can reduce a key parameter τ from original O(n) down to O(λn) (in theoretically secure case, where λ is the security parameter), and even down to O(2n) (in computationally secure case). Such optimization greatly reduces the size of the map.