Abstract: This paper studies the problem of designing a storage efficient secure multicast key management scheme based on
Hybrid One-way Function Tree（HOFT） for a prespecified rekey communication overhead.A hybrid tree scheme divides a group of N members into clusters of M members and assigns each cluster to one leaf node of a key tree.Using this scheme,this paper formulates a constrained optimization problem to minimize the centralized group controller storage in terms of the cluster size M,then converts the constrained optimization into a fixed point equation and derive the optimal cluster siz M that leads to the minimal storage overhead as O（N/logN）,when the key update communication constraint is given as O（logN）.The paper designs a algorithm that achieves minimal centralized group controller storage.

Key words: cryptography, key management, communication constraint, optimization, fixed-point equation

摘要： 在特定的密钥更新通信开销的情况下,研究了基于混合单向函数树的高效安全组播密钥管理方案问题。混合单向函数树方案将含N个成员的组划分为若干个含M个成员的簇,并将每个簇安置在密钥管理树的叶子结点上。根据簇大小,将组控制器的密钥最小存储开销表达为约束优化问题,再将约束优化问题转化为一个关于簇大小M的不动点方程,当密钥更新通信开销约束为O（logN）时,证明不动点方程的最大根为簇大小的最优值,它使得混合树的最小密钥存储开销为O（N/logN）。同时设计了一种构造具有最小存储开销的混合单向函数树的算法。

关键词: 密码学, 密钥管理, 通信约束, 优化, 不动点方程