Common use of Key Independence Clause in Contracts

Key Independence. We now give an informal proof that TGDH satisfies forward and backward secrecy, or equivalently key independence. In order to show that TGDH provides key independence, we only need to show that the view of the former (prospective) member to the current tree is exactly same as the view of the passive adversary respectively, since this shows that the advantage of the former (prospective) member is same as the passive adversary and by Xxxxxxx 7. We first consider backward secrecy, which states that a new member who knows the current group key cannot derive any previous group key. Let be the new member. The sponsor for this join event changes its session random and, consequently, previous root key is changed. Therefore, the view of with respect to the prior key tree is exactly same as the view of an outsider. Hence, the new member does not gain any advantage compared to a passive adversary. This argument can be easily extended to the merge of two or more groups. When a merge happens, sponsor in each tree changes its session random. Therefore, each member’s view on other member’s tree is exactly same as the view of a passive adversary. This shows that the newly merged member has exactly same advantage about any of the old key tree as a passive adversary. Now we consider the forward secrecy, meaning that a passive adversary who knows a contiguous subset of old group keys cannot discover subsequent group keys. Here, we consider partition and leave at the same time. Xxxxxxx is a former group member. Whenever subtractive event happens, a sponsor refreshes its session random, and, therefore, all keys known to leaving members will be changed accordingly. Therefore, ’s view is exactly same as the view of the passive adversary. This proves that TGDH provides decisional version of key independence.

Key Independence. We now give an informal proof that TGDH STR satisfies forward and backward secrecy, or equivalently key independence. In order to show that TGDH STR provides key independence, we only need to show that the view of the former (prospective) member to member’s view of the current tree is exactly the same as the view of the passive adversary respectively, since this shows that adversary’s view. This is because the advantage of the former (prospective) member is the same as the passive adversary, and the view of the passive adversary and does not reveal any information about the group key by Xxxxxxx 73. We first consider backward secrecy, which states that a new member who knows the current group key cannot derive any previous group keykeys. Let Mn+1 be the new member. The sponsor for this the join event changes its session random and, consequently, previous root key of the current key tree is changed. Therefore, the view of Mn+1 with respect to the prior key tree trees is exactly the same as the view of an outsider. Hence, the new member does not gain any advantage compared to a passive adversary. This argument can be easily extended to the a merge of two or more groups. When a merge happens, the sponsor in each at the top leaf node of the largest tree changes its session random. Therefore, each member’s view on other member’s tree is exactly the same as the view of a passive adversary. This shows that the newly merged member has exactly the same advantage about any of the old key tree as a passive adversary. Now we consider the forward secrecy, meaning that a passive adversary who knows a contiguous subset of old group keys cannot discover subsequent group keys. Here, we consider partition and leave at the same time. Xxxxxxx Xx is a former group membermember who left the group. Whenever subtractive event happens, a the sponsor located immediately below the deepest leaving leaf node refreshes its session random, and, therefore, all keys known to leaving members will be changed accordingly. Therefore, Md’s view is exactly the same as the view of the passive adversary. This proves that TGDH STR provides decisional version of key independence.

Key Independence. We now give an informal proof that TGDH STR satisfies forward and backward secrecy, or equivalently key independence. In order to show that TGDH STR provides key independence, we only need to show that the view of the former (prospective) member to member’s view of the current tree is exactly the same as the view of the passive adversary respectively, since this shows that adversary’s view. This is because the advantage of the former (prospective) member is the same as the passive adversary, and the view of the passive adversary and does not reveal any information about the group key by Xxxxxxx 73. We first consider backward secrecy, which states that a new member who knows the current group key cannot derive any previous group keykeys. Let be the new member. The sponsor for this the join event changes its session random and, consequently, previous root key of the current key tree is changed. Therefore, the view of with respect to the prior key tree trees is exactly the same as the view of an outsider. Hence, the new member does not gain any advantage compared to a passive adversary. This argument can be easily extended to the a merge of two or more groups. When a merge happens, the sponsor in each at the top leaf node of the largest tree changes its session random. Therefore, each member’s view on other member’s tree is exactly the same as the view of a passive adversary. This shows that the newly merged member has exactly the same advantage about any of the old key tree as a passive adversary. Now we consider the forward secrecy, meaning that a passive adversary who knows a contiguous subset of old group keys cannot discover subsequent group keys. Here, we consider partition and leave at the same time. Xxxxxxx is a former group membermember who left the group. Whenever subtractive event happens, a the sponsor located immediately below the deepest leaving leaf node refreshes its session random, and, therefore, all keys known to leaving members will be changed accordingly. Therefore, ’s view is exactly the same as the view of the passive adversary. This proves that TGDH STR provides decisional version of key independence.

Key Independence. We now give an informal proof that TGDH satisfies forward and backward secrecy, or equivalently key independence. In order to show that TGDH provides key independence, we only need to show that the view of the former (prospective) member to the current tree is exactly same as the view of the passive adversary respectively, since this shows that the advantage of the former (prospective) member is same as the passive adversary and by Xxxxxxx Theorem 7. We first consider backward secrecy, which states that a new member who knows the current group key cannot derive any previous group key. Let Mn+1 be the new member. The sponsor for this join event changes its session random and, consequently, previous root key is changed. Therefore, the view of Mn+1 with respect to the prior key tree is exactly same as the view of an outsider. Hence, the new member does not gain any advantage compared to a passive adversary. This argument can be easily extended to the merge of two or more groups. When a merge happens, sponsor in each tree changes its session random. Therefore, each member’s view on other member’s tree is exactly same as the view of a passive adversary. This shows that the newly merged member has exactly same advantage about any of the old key tree as a passive adversary. Now we consider the forward secrecy, meaning that a passive adversary who knows a contiguous subset of old group keys cannot discover subsequent group keys. Here, we consider partition and leave at the same time. Xxxxxxx Suppose Md is a former group member. Whenever subtractive event happens, a sponsor refreshes its session random, and, therefore, all keys known to leaving members will be changed accordingly. Therefore, Md’s view is exactly same as the view of the passive adversary. This proves that TGDH provides decisional version of key independence.

Key Independence. We now give an informal proof that TGDH satisfies forward and backward secrecy, or equivalently key independence. In order to show that TGDH provides key independence, we only need to show that the view of the former (prospective) member to the current tree is exactly same as the view of the passive adversary respectively, since this shows that the advantage of the former (prospective) member is same as the passive adversary and by Xxxxxxx Theorem 7. We first consider backward secrecy, which states that a new member who knows the current group key cannot derive any previous group key. Let be the new member. The sponsor for this join event changes its session random and, consequently, previous root key is changed. Therefore, the view of with respect to the prior key tree is exactly same as the view of an outsider. Hence, the new member does not gain any advantage compared to a passive adversary. This argument can be easily extended to the merge of two or more groups. When a merge happens, sponsor in each tree changes its session random. Therefore, each member’s view on other member’s tree is exactly same as the view of a passive adversary. This shows that the newly merged member has exactly same advantage about any of the old key tree as a passive adversary. Now we consider the forward secrecy, meaning that a passive adversary who knows a contiguous subset of old group keys cannot discover subsequent group keys. Here, we consider partition and leave at the same time. Xxxxxxx Suppose is a former group member. Whenever subtractive event happens, a sponsor refreshes its session random, and, therefore, all keys known to leaving members will be changed accordingly. Therefore, ’s view is exactly same as the view of the passive adversary. This proves that TGDH provides decisional version of key independence.