In wireless sensor networks ( WSNs),nodes are usually powered by batteries.Since the energy consumption directly impacts the network lifespan,energy saving is a vital issue in WSNs,especially in the deigning phase of cryptographic algorithms.As a complementary mechanism,reputation has been applied to WSNs.Different from most reputation schemes that were based on beta distribution,negative multinomial distribution was deduced and its feasibility in the reputation modeling was proved.Through comparison tests with beta distribution based reputation in terms of the update computation,results show that the proposed method in this research is more energy-efficient for the reputation update and thus can better prolong the lifespan of WSNs.