“…In Table 4, we compare the primary operations of communication cost for the proposed scheme and other schemes that were proposed, including those proposed by Yanfeng et al [25], Bhatia and Verma [26], Li et al [27], and Qu and Zeng [28]. As shown in Table 4, NP m represents the message size, which we assume was 2048 bits, NP q represents the parameter size, which belongs to elliptic curve and was equal to 160 bits [30,31], NP ID represents the identity size, which belongs to elliptic curve and was equal to 160 bits, and NP G represents the parameter size, which is part of the bilinear group, and its value was 1024 bits. As detailed in Table 4 and depicted in Figure 3, the proposed scheme had lower communication costs than its counterparts.…”