Hierarchical Group Based Mutual Authentication and Key Agreement for Machine Type Communication in LTE and Future 5G Networks

Table 3

Probability of authentication failure and success.

Group size	100	200	300	400	500	600	700	800	900	1000
Number of groups	100	50	33	25	20	16	14	12	11	10
	0.6358	0.8687	0.9532	0.9835	0.9942	0.9980	0.9993	0.9998	0.9999	0.9999
	0.3642	0.1313	0.0468	0.0165	0.0058	0.0020	0.0007	0.0002	7.63E−05	2.51E−05