Keying System.Β In the SGRS scheme, each member independently generates multiple cryptographic keys πΎπ based upon the locally known secret set ππ . A multicasting key πΎπ is generated using the function π (π) = π»ππ β(ποΏ½οΏ½π
(ππ ), πΎπΊ). To ensure the secrecy of set ππ , set π is used as an index value to retrieve the valid secret nonce ππ from the state set ππ of members. Only those members can generate the key πΎπ, holding the corresponding secret nonce ππ of the enlisted member IDs in set π; i.e., πΎοΏ½οΏ½ is a valid key for all members ππ if ππ β ππ and πΎπ is a private key of members ππ if ππ = ππ . This infers that the group size of |ππ| = π has the following number of possible multicasting keys. members of a dynamic group β’ ππ = Set of member ids of all members in dynamic group, π! π = { (πβ1)! + π! (πβ2)!2! + β¦ π! (πβ(πβ2))!(πβ2)! π is odd corresponding ids of ππ π! (πβ1)! + π! (πβ2)!2! + β¦ π! (πβ(πβ1))!(πβ1)! π is even β’ ππ = A subset of ππ β’ π = A subset of ππ, which are corresponding ids of ππ However, each member can participate in and/or start π number of secure subgroup communication, where π β π. β’ πΎπ = A key derived from elements of ππ β’ πΎπ = Public key β’ πΎ = Group key (πβ1)! + πβ1! π = {(πβ2)! (πβ3)!2! (πβ1)! + πβ1! + β¦ (πβ1)! (πβ(πβ1))!(πβ1)! + β¦ (πβ1)! + 1 π is odd π is even πΊ (πβ2)! (πβ3)!2! (πβ(πβ1))!(οΏ½οΏ½β1)! β’ πΈπ΄(π΅) = Encryption of B using key οΏ½οΏ½π΄, where πΎπ΄ is any valid πΎπ, πΎπ or πΎπΊ β’ || symbol for concatenation of terms β’ π£ symbol to explicate a portion of the term β’ π β’ π indicate that π can generate π
Keying System.Β Provide an extension of the existing keying system. Existing locks were manufactured by Medeco and have interchangeable cores. Provide key cabinet as specified.
Keying System.Β In the SGRS scheme, each member independently generates multiple cryptographic keys based upon the locally known secret set . A multicasting key is generated using the function () = β((), ). To ensure the secrecy of set , set is used as an index value to retrieve the valid secret nonce from the state set of members. Only those members can generate the key , holding the corresponding secret nonce of the enlisted member IDs in set ; i.e., is a valid key for all members if β and is a private key of members if = . This infers that the group size of || = has the following number of possible multicasting keys. members of a dynamic group β’ = Set of member ids of all members in dynamic group, ! = { (β1)! + ! (β2)!2! + β¦ ! (β(β2))!(β2)! is odd corresponding ids of ! (β1)! + ! (β2)!2! + β¦ ! (β(β1))!(β1)! is even β’ = A subset of β’ = A subset of , which are corresponding ids of However, each member can participate in and/or start number of secure subgroup communication, where β . β’ = A key derived from elements of β’ = Public key β’ = Group key (β1)! + β1! = {(β2)! (β3)!2! (β1)! + β1! + β¦ (β1)! (β(β1))!(β1)! + β¦ (β1)! + 1 is odd is even (β2)! (β3)!2! (β(β1))!(β1)! β’ () = Encryption of B using key , where is any valid , or β’ || symbol for concatenation of terms β’ β© symbol to explicate a portion of the term β’ β’ indicate that can generate
