Self-Healing Group Key Distribution Facilitating Source Authentication Using Block Codes

Table 3

The comparisons of the computation/communication overhead of related schemes.

Scheme	Communication overhead of one single session	Communication overhead of self-healing of -sessions	GM’s computations in group key distribution	User’s computations in group key recovery	Storage of private data in a node
[22]	∼=(nm + m+1)Len		For jth session: ∼ =		2
[21]	∼=((n+1)m+2m + 1)
[26]				(1+)
[31]	7 Len	Does not provide self-healing	3 + 1	1+	3 Len
[30]	O() broadcast ∼ = O()Len	O() broadcast for one session of a -member batch join^1∼ = O()Len	Not applicable	O() for a -member leave; O() (+ ) for a -member join	2 Len
[27]	() Len + one generator matrix∼ = O()	∼ = O()	+∼ = O()	+1∼ = O()	1 Len
Ours	() Len	Len ∼ = O () Len	+(s+1)∼ = O()	+(s+1)∼ = O()	1 Len

(1) denotes the number of leaving members in a batch leave; denotes the number of total members. denotes the number of members in one session; m denotes the maximum number of sessions; Len denotes the bit length for one scalar value such as one key and one identity; denotes the number of sessions to recover the keys. (2) t denotes the maximum number of revoked users; denotes the number of sessions in which there are users joining the group ( < j), where j is the index of the current session; denotes the number of members in the jth session. (3) j denotes the jth session (could be replaced with O(m)); J denotes the number of sessions with joining users (could be replaced with O(m)), where m is the maximum number of sessions; Q denotes the number of neighbors around the request node. (4) denotes the computational cost for one hashing; denotes the cost for one modular multiplication; denotes the cost for one modular addition/subtraction; denotes the computational cost for one matrix multiplication, which is O(n^2.3737); denotes the cost for one new matrix generation, which is O(n^3.3737); denotes the cost for one exponentiation operation; denotes the cost for one modulo inversion operation; denotes the cost for one modulo division operation; denotes the cost for one η() which is the group key broadcast message generation [30]; denotes the cost for one asymmetric signature generation; denotes the cost for one asymmetric signature verification; denotes the cost for one asymmetric encryption/decryption; denotes the cost for one symmetric encryption/decryption; denotes the cost for one Greatest Common Divisor operation.