Fog computing is viewed as an extended technique of cloud computing. In Internet of things–based collaborative fog computing systems, a fog node aggregating lots of data from Internet of things devices has to transmit the information to distributed cloud servers that will collaboratively verify it based on some predefined auditing policy. However, compromised fog nodes controlled by an adversary might inject bogus data to cheat or confuse remote servers. It also causes the waste of communication and computation resources. To further control the lifetime of signing capability for fog nodes, an appropriate mechanism is crucial. In this article, the author proposes a time-constrained strong multi-designated verifier signature scheme to meet the above requirement. In particular, a conventional non-delegatable strong multi-designated verifier signature scheme with low computation is first given. Based on its constructions, we show how to transform it into a time-constrained variant. The unforgeability of the proposed schemes is formally proved based on the famous elliptic curve discrete logarithm assumption. The security requirement of strong signer ambiguity for our substantial constructions is also analyzed by utilizing the intractable assumption of decisional Diffie–Hellman. Moreover, some comparisons in terms of the signature size and computational costs for involved entities among related mechanisms are made.

雾计算被视为云计算的扩展技术。在基于物联网的协同雾计算系统中，聚集来自物联网设备的大量数据的雾节点必须将信息传输到分布式云服务器，该云服务器将基于一些预定义的审核策略进行协同验证。但是，由对手控制的受害雾节点可能会注入虚假数据，以欺骗或混淆远程服务器。这也造成了通信和计算资源的浪费。为了进一步控制雾节点签名能力的寿命，适当的机制至关重要。在本文中，作者提出了一种时间受限的强多指定验证者签名方案，以满足上述要求。特别是，首先给出了一种传统的不可授权的，具有低计算量的强多指定验证者签名方案。基于其构造，我们展示了如何将其转换为时间受限的变体。基于著名的椭圆曲线离散对数假设，正式证明了所提方案的不可伪性。我们还利用决策Diffie-Hellman的棘手假设，分析了我们实质性结构中强签名者歧义性的安全要求。此外，在相关机制之间就所涉及实体的签名大小和计算成本进行了一些比较。基于著名的椭圆曲线离散对数假设，正式证明了所提方案的不可伪性。我们还利用决策Diffie-Hellman的棘手假设，分析了我们实质性结构中强签名者歧义性的安全要求。此外，在相关机制之间就所涉及实体的签名大小和计算成本进行了一些比较。基于著名的椭圆曲线离散对数假设，正式证明了所提方案的不可伪性。我们还利用决策Diffie-Hellman的棘手假设，分析了我们实质性结构中强签名者歧义性的安全要求。此外，在相关机制之间就所涉及实体的签名大小和计算成本进行了一些比较。