Many trust management(TM)systems have been proposed

but some issues still remain to be addressed

e.g. there is no consensus on the definition of TM in the literature

and algorithms for proof of compliance are inefficient. To address these problems

a formal definition of TM is proposed in this paper

which is composed of a set of countable principals

a set of trust classes

a set of trust attributes

a set of contexts

a set of trust relationships and a set of rules. The relationship between the formal TM and the descriptive TM is discussed. Based on the formal definition of TM

an efficient TM

called NUMEN

is presented

and the algorithm for PoC is based on the lattice-theoretical fix-point theorem. The time complexity and the space complexity of the algorithm are both O(n)where n is the cardinality of the set of authorization credentials. Experimental results show that NUMEN can effectively protect sensitive resources at the cost of little performance of systems

and the PoC algorithm for NUMEN is more efficient than those for the existing TM systems such as SKPI/SDSI and KeyNote. It is observed that the numbers of authorization brokers and of delegation credentials are crucial factors in determining the runtime.