“…After Staddon’s first self-healing group key distribution (SGKD) scheme, many SGKD schemes were proposed. Up to now, four kinds of SGKD schemes exist: polynomial based SGKD (P-SGKD) schemes [ 2 , 3 , 4 , 5 , 6 ], vector space secret sharing based SGKD schemes [ 7 , 8 , 9 , 10 ], bilinear pairings based SGKD schemes [ 11 , 12 , 13 ] and exponential arithmetic based SGKD (E-SGKD) schemes [ 1 , 2 , 14 , 15 ]. Among them, vector space secret sharing based SGKD schemes and the bilinear pairings based SGKD schemes are inefficient compared with the other two in terms of the storage overhead and the communication cost.…”