Key Predistribution Schemes and One-Time Broadcast Encryption Schemes from Algebraic Geometry Codes
Key Predistribution Schemes and One-Time Broadcast Encryption Schemes from Algebraic Geometry Codes
复制标题
代数几何码的密钥预分配方案和一次性广播加密方案
DOI：
10.1007/978-3-642-10868-6_16
复制
发表时间：
2009
期刊：
影响因子：
--
通讯作者：
C. Xing
中科院分区：
文献类型：
--
作者：
Hao Chen;S. Ling;Carles Padró;Huaxiong Wang;C. Xing
密钥预分发方案(KPS)和一次性广播加密方案(OTBES)是用于网络中密钥分发的无条件安全协议。在以前的工作中，这些方案的效率是根据它们的信息率来衡量的，即每个用户必须存储的秘密密钥长度与秘密信息长度之间的比率。已经提出了几种具有最优信息率的结构，但在这些结构中，秘密密钥取自一个有限域，其中的元素至少与网络中的用户数相同。这在节点具有有限计算资源的超大型网络中可能是一个重要的缺点，例如无线传感器网络。实际上，密钥预分发方案已经被应用于此类网络的密钥分发协议的设计中。本文提出了一种由线性码构造密钥预分发方案的方法，该方案为任意数量的用户提供新的KPS和OTBES族，并且具有恒定大小的密钥。作为Gilbert-Varshamov界的结果，我们可以证明我们的KPSS比以前的构造是渐近有效的，特别是当我们考虑KPSS对于由恒定部分用户组成的联盟是安全的。我们还分析了由Gilbert-Varshamov界以上的代数几何线性码族得到的KPS，以及由Garcia和Stichtenoth曲线构造的KPS。最后，我们讨论了如何使用基于代数几何编码的KPSS来提供更高效的OTBES。
Key predistribution schemes (KPSs) and one-time broadcast encryption schemes (OTBESs) are unconditionally secure protocols for key distribution in networks. The efficiency of these schemes has been measured in previous works in terms of their information rate, that is, the ratio between the length of the secret keys and the length of the secret information that must be stored by every user. Several constructions with optimal information rate have been proposed, but in them the secret keys are taken from a finite field with at least as many elements as the number of users in the network. This can be an important drawback in very large networks in which the nodes have limited computational resources as, for instance, wireless sensor networks. Actually, key predistribution schemes have been applied recently in the design of key distribution protocols for such networks.In this paper we present a method to construct key predistribution schemes from linear codes that provide new families of KPSs and OTBESs for an arbitrarily large number of users and with secret keys of constant size. As a consequence of the Gilbert-Varshamov bound, we can prove that our KPSs are asymptotically more efficient than previous constructions, specially if we consider KPSs that are secure against coalitions formed by a constant fraction of the users. We analyze as well the KPSs that are obtained from families of algebraic geometry linear codes that are above the Gilbert-Varshamov bound, as the ones constructed from the curves of Garcia and Stichtenoth. Finally, we discuss how the use of KPSs based on algebraic geometry codes can provide more efficient OTBESs.
影响因子：
22.7
作者：
SHAMIR, A
通讯作者：
SHAMIR, A