Wireless sensor networks (WSNs) can be used in a wide range of environments. Due to the inherent characteristics of wireless communications, WSNs are more vulnerable to be attacked than conventional networks. Authentication and data confidentiality are critical in these settings. It is necessary to design a useful key management scheme for WSNs. In this paper, we propose a novel key management scheme called MAKM (modular arithmetic based key management). The proposed MAKM scheme is based on the congruence property of modular arithmetic. Each member sensor node only needs to store a key seed. This key seed is used to compute a unique shared key with its cluster head and a group key shared with other nodes in the same cluster. Thus, MAKM minimizes the key storage space. Furthermore, sensor nodes in the network can update their key seeds very quickly. Performance evaluation and simulation results show that the proposed MAKM scheme outperforms other key-pool-based schemes in key storage space and resilience against nodes capture. MAKM scheme can also reduce time delay and energy consumption of key establishment in large-scale WSNs