| As a hot research field in network communication,multicast communication provides one-to-many service mechanism,that is,a specific sender sends multicast messages to multiple receivers.In multicast communication,the most important is how to encrypt multicast messages to ensure the message security,and the common way is to build a secure and efficient group key management scheme.In addition,the group members will change in multicast communication,so the key generation centre needs to update the group key to satisfy the security requirements under the dynamic environment.Centralized group key management schemes are common types of key management,in which,a trusted third party is relied on to manage the entire group.The basic idea is that legally authorized members can calculate the group key,when a member joins or quits,the group key is updated immediately,so that the newly joining member cannot obtain the old group key,and the member who has left cannot access the new group key.This thesis mainly studies the centralized group key management schemes in secure multicast communication scenarios.The existing schemes mainly have the following problems:(1)The construction of the scheme is complicated with many selected parameters.In addition,the computational and storage costs are high;(2)the scheme has poor security performance,which cannot satisfy the forward/backward secrecy requirements and resist collusion attack.Based on the theory of cryptography,this thesis constructs group key management schemes in different multicast scenarios,and extends the scheme.Details are as follows:(1)The dynamic group key management scheme based on the Chinese Remainder Theorem is constructed,which reduces the computational complexity of the group key update stage to O(1),and any group member can recover the group key by one modular operation.In addition,the scheme can resist differential and collusion attacks,ensuring forward/backward secrecy under the dynamic environment.(2)Inspired by secret sharing,the group key management scheme based on interpolation polynomial is proposed,then extends the scheme.By adjusting the length of the published message,the group key management scheme with variable threshold is constructed,and the threshold t is controlled by the key generation centre.Even if t-1 members collaborate,they cannot recover the group key.Moreover,both two schemes are unconditionally secure and are independent of any mathematical assumptions.(3)The dynamic group key management scheme based on access polynomial is proposed,and the construction of access polynomial does not involve encrypting the private keys.From the perspective of computation overhead,the computational complexity of the group key update stage is O(1);from the perspective of storage overhead,any group member always needs to store only one private key,so this scheme is lightweight.The analysis results show that the long-term private key of another group member cannot be stolen even if n-1 group members conspire together. |
