Efficient Hierarchical Group-Oriented Key Establishment and Decryption

Abstract

In this paper, we present three related and efficient cryptographic schemes for secure communication for hierarchically composed user groups. In such a group, each user is associated with a hierarchical level, so that the group members are divided into two or more hierarchical security classes. Most existing hierarchical cryptographic schemes provide hierarchical deduction of hierarchically arranged predefined keys. In contrast, the first scheme provides secure establishment of hierarchically ordered session keys. Since it prohibits long-term key deduction for underlying (and overlying) classes, such keys do not need to be updated session-wise. An essential security property is that the users can only obtain hierarchical session keys for their own and underlying levels, while it is prevented that a user can obtain hierarchical session keys of overlying levels.This scheme is extended to a hierarchical public key cryptosystem based on the ElGamal cryptosystem, and furthermore to an ElGamal-based threshold decryption scheme. Due to the threshold security requirement, at least t arbitrary group members are required to carry out decryption. The threshold scheme requires only one round of broadcasting in the decryption phase, and is thus well-suitable for wireless networks.

ElGamal with differentiated decryption on K+1 access levels

“…The messages from the information M, which will be accessed by decryption by a user, will be those for which the user has rights. These rights can be organized with the help of access levels [8] [9]. Between levels there are hierarchical links.…”

“…The central subject of this paper is the description of an encryption system elaborated to ensure the access to an encrypted information in a differentiated way. This system is structured on levels of access [7] [8]. The algorithm is based on the El Gamal encryption system [1][3] [4] and, in this article, it will be further called the ElGamal with differentiated decryption on k+1 access levels (EG(k+1)GA), this taking part of the category encryption systems with a public key which is based on the discrete logarithm problem.…”