Efficient Key Packaging Schemes for Group Key Management

群組金鑰管理是安全的多重傳送訊息架構中不可或缺的要素，在2005年11月，林振群等學者提出了一個稱為「One-Way Key Derivation (OKD)」的有效率之機制，此機制利用了樹狀結構來管理金鑰，我們發現在此機制中，當有成員加入一個樹的高度為x的群組時，新成員必須解密O(x)次而求得群組金鑰，另一方面，當有成員離開群組時，其他成員必須解密O(x)次求得群組金鑰，對於運算能力較差的裝置而言，解密是高花費的運算，在此情況下，當有成員異動時，群組成員不能迅速得知新的群組金鑰，因此他們不能立即加密訊息接著傳送出去或是立即解密而得知收到的訊息，尤其是當傳送很緊急的訊息時，此機制對於群組成員是沒有效率的。 在此我們提出了針對OKD而改進的高效率之金鑰包裝機制，在新的機制中，新加入的成員只需一次的解密運算即可求得群組金鑰，另一方面，當有成員離開群組時，我們的機制把解密運算更換為更快速的雜湊運算；和OKD比起來，我們的機制使得群組成員可以更快速地得到新的群組金鑰。Group key management is an essential component of secure multicast architecture. An efficient group key management protocol called One-Way Key Derivation (OKD), proposed by Lin et al. in 2005, uses a tree to manage keys. We find that in OKD, when a member joins a group with key tree height x, the new member has to decrypt O(x) times to get the new group key. On the other hand, when a member leaves the group, other group members have to decrypt O(x) times to get the new group key. For devices with limited computational capabilities, decryption is a costly operation. In these situations, the group members cannot derive the new group key fast enough when membership changes. Therefore, they can neither encrypt and send messages nor decrypt to get the received messages immediately. It is inefficient for group members, especially when the message is very urgent. In this paper, we propose an efficient key packaging scheme for group key management based on OKD. In our scheme, a new group member only needs one decryption to get the new group key. On the contrary, our scheme replaces decryption operations with faster hash operations when a member leaves the group, so it allows group members to derive the new group key more quickly than OKD.1 Introduction...................................1 2 Related Works..................................4 2.1 Group Key Management Protocol...,,.........4 2.2 Logical Key Hierarchy......,,..............6 2.3 One-Way Key Derivation..,,.................9 3 Key Packaging Scheme..........................12 3.1 Motivation................................12 3.1.1 An Example of OKD.....................13 3.1.2 Inefficiency of OKD...................15 3.1.3 An Example of KPS (Join)..............16 3.1.4 An Example of KPS (Leave).............17 3.1.5 A simple Comparison of OKD and KPS....19 3.2 Methods to Package Keys...................20 3.2.1 When a Member Joins...................20 3.2.2 When a Member Leaves..................20 4 Analysis of KPS...............................22 4.1 Security of KPS...........................22 4.2 Efficiency of KPS.........................23 5 Conclusions...................................24 References 2