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In this paper, to study rumor spreading, we propose a novel susceptible-infected-removed (SIR) model by introducing the trust mechanism. We derive mean-field equations that describe the dynamics of the SIR model on homogeneous networks and inhomogeneous networks. Then a steady-state analysis is conducted to investigate the critical threshold and the final size of the rumor spreading. We show that the introduction of trust mechanism reduces the final rumor size and the velocity of rumor spreading, but increases the critical thresholds on both networks. Moreover, the trust mechanism not only greatly reduces the maximum rumor influence, but also postpones the rumor terminal time, which provides us with more time to take measures to control the rumor spreading. The theoretical results are confirmed by sufficient numerical simulations.

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SUMMARYSecure multicast is one of the majority services in the near future. The frameworks for IP multicast cannot be directly applied in wireless networks. To address the natural issues of wireless multicast and enhance the efficiency, an adaptive secure multicast framework based on a new primitive called multi-recipient generalized signcryption and a multi-recipient generalized signcryption scheme based on the gap DiffieHellman problem (MGSC-GDH) are proposed. The key technologies to construct a high-performance adaptive scheme including identification function, randomness reusing are investigated. The framework provides separate or joint encryption and signature functions according to users' identities and requirements transparently, and has the ability to aggregate multiple unicast besides the common multicast service. Therefore, overheads are reduced sharply for multiple functions which are provided with a single primitive. By the precise reduction, the gap-bridge between the security of a base scheme and the corresponding multi-recipient generalized signcryption scheme is built, which is a direct measure to quantify the security. Analysis shows that MGSC-GDH is a semantic secure multi-recipient generalized signcryption scheme and more efficient than other similar schemes in computational and communicational aspects. It is suitable for dynamic environment for rekeying is avoided when membership changes.

The Internet of Things (IoT) is an emerging network paradigm that aims to obtain the interactions among pervasive things through heterogeneous networks. Security is an important task in the IoT. Recently, Li et al. proposed a new COOSC scheme (hereafter called LZZ). However, both LTX and LZZ need a point multiplication operation in the online phase, which is not suitable for resource-constrained devices. To overcome this weakness, we propose a new COOSC scheme and prove its security in the random oracle model. In addition, we analyze the performance of our scheme and show its application in the IoT.

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A new signcryption based on elliptic curve cryptosystems that combines ECDSA and PSCE-1 is presented. The signcryption scheme is a publicly verifiable scheme which can be verified by the third party after the specific recipient removes his key information. Analysis shows that the proposed scheme is secure against the adaptive chosen ciphertext attack. The signcryption saves the communication cost at least 1.25 times and enhances computation cost 1.19 times over ECDSA-then-PSCE-1. Compared with other signcryption schemes, such as Y.Zheng's ECSCS, the new signcryption uses a uniform elliptic curve cryptosystem platform instead of four kinds of cryptosystem components: hash function, keyed hash function, symmetric cipher and elliptic curve. While keeping high security and efficiency, the scheme can be implemented in software and hardware at low price because of above advantages. Based on the presented signcryption, a broadcast scheme for multiple recipients and a threshold scheme with Key Distributed Generation for multiple senders are also proposed.