Enforcing the security of a time-bound hierarchical key assignment scheme

A time-bound hierarchical key assignment scheme is a method to assign a cryptographic key to each class of users in a system organized as a partially ordered hierarchy, in such a way that key derivation is constrained both by class relationships and by time. Recently, a time-bound hierarchical key assignment scheme based on tamper-resistant devices and requiring low computational load and implementation cost has been proposed. Unfortunately, the scheme is not secure.In this paper we show how three malicious users can handle public and private information to misuse their tamper-resistant devices in order to compute some encryption keys that they should not be able to learn. We also show some countermeasures to withstand the weakness we have exploited.