Keying System Clause Samples

Keying System. In the SGRS scheme, each member independently generates multiple cryptographic keys 𝐾𝑌 based upon the locally known secret set 𝑆𝑖 . A multicasting key 𝐾𝑌 is generated using the function 𝑓 (𝑌) = 𝐻𝑎𝑠ℎ(𝑋��𝑅(𝑌𝑠), 𝐾𝐺). To ensure the secrecy of set 𝑌𝑠, set 𝑌 is used as an index value to retrieve the valid secret nonce 𝑌𝑠 from the state set 𝑆𝑖 of members. Only those members can generate the key 𝐾𝑌, holding the corresponding secret nonce 𝑌𝑠 of the enlisted member IDs in set 𝑌; i.e., 𝐾�� is a valid key for all members 𝑁𝑖 if 𝑌𝑠 ⊆ 𝑆𝑖 and 𝐾𝑌 is a private key of members 𝑁𝑖 if 𝑌𝑠 = 𝑆𝑖 . This infers that the group size of |𝑋𝑁| = 𝑁 has the following number of possible multicasting keys. members of a dynamic group • 𝑋𝑁 = Set of member ids of all members in dynamic group, 𝑊 = { (𝑁−1)! + 𝑁! (𝑁−2)!2! + … 𝑁! (𝑁−(𝑁−2))!(𝑁−2)! 𝑁 is odd corresponding ids of 𝑋𝑠 + 𝑁! (𝑁−2)!2! + … 𝑁! (𝑁−(𝑁−1))!(𝑁−1)! 𝑁 is even • 𝑌𝑠 = A subset of 𝑋𝑠 • 𝑌 = A subset of 𝑋��, which are corresponding ids of 𝑌𝑠 However, each member can participate in and/or start 𝑍 number of secure subgroup communication, where 𝑍 ⊆ 𝑊. • 𝐾𝑌 = A key derived from elements of 𝑌𝑠 • 𝐾𝑃 = Public key • 𝐾 = Group key (𝑁−1)! + 𝑁−1! (𝑁−1)! + 𝑁−1! + … (𝑁−1)! (𝑁−(𝑁−1))!(𝑁−1)! + … (𝑁−1)! 𝐺 (𝑁−2)! (𝑁−3)!2! (𝑁−(𝑁−1))!(𝑁−1)! • 𝐸𝐴(𝐵) = Encryption of B using key 𝐾𝐴, where 𝐾𝐴 is any valid 𝐾𝑌, 𝐾𝑃 or 𝐾𝐺 • || symbol for concatenation of terms • 𝖣 symbol to explicate a portion of the term • 𝑆 ⊢ 𝑚 indicate that 𝑆 can generate 𝑚 A. Characteristics of Group Fig. 2. The logically connected group members share the common resources using the group key. The subsets of group members also create multiple secure subgroups.