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In this paper, we address the problem of secure decision of membership. We present a Zero-Knowledge Dual Membership Proof (ZKDMP) protocol, which can support positive and negative (Pos-and-Neg) membership decisions simultaneously. To do it, two secure aggregation functions are used to compact an arbitrarily-sized subset into an element in a cryptographic space. By using these aggregation functions, a subset can achieve a secure representation, and the representation size of the subsets is reduced to the theoretical lower limit. Moreover, the zeros-based and poles-based secure representation of the subset are used to decide Pos-and-Neg membership, respectively. We further verify the feasibility of combining these two secure representations of the subset, so this result is used to construct our dual membership decision cryptosystem. Specifically, our ZKDMP protocol is proposed for dual membership decisions, which can realize a cryptographic proof of strict Pos-and-Neg membership simultaneously. Furthermore, the zero-knowledge property of our construction ensures that the information of the tested element will not be leaked during the implementation of the protocol. In addition, we provide detailed security proof of our ZKDMP protocol, including positive completeness, negative completeness, soundness and zero-knowledge.

Our world is rapidly changing, and swiftly evolving towards so-called “smart worlds”. The smart worlds starting with smart things such as the smart objects, smart city, smart manufacturing, and smart systems, will eventually encompass all aspects of the cyber, physical, social and mental world. A cyber-enabled completely new digital space featured with ubiquitous interconnections, integrations and interactions of physical, social, mental and other spaces will continuously bring out more and more changes. Cyberspace is actually the combinational outcome of various technologies including computers, communications, materials, intelligence and studies in perception, cognition, biology, sociology, etc., as well as advanced computing like the Internet/Web, pervasive networks, ubiquitous sensing and computing, the internet of things, the cloud, big data and so forth. These smart worlds are set to be the next important stage in human history. We have to be aware of the essential problems and crucial issues affecting in building truly smart worlds that benefit humanity, and simultaneously safeguard the natural environment for sustainable development and evolution. Therefore, this is the time to foresee future trends and identify what the grand challenges for smart worlds are. This Special Section in IEEE ACCESS has ten papers, and a brief summary about each paper is presented as follows.

Smart worlds begin with smart things, such as smart objects, smart cities, smart manufacturing, and smart systems, are overlaid with sensing and actuation, many embedded in things, and eventually encompass all aspects of the cyber, physical, social, and thinking hyperspace. In the future, human beings will live in a smart environment where both life and work are well addressed by technology, whereas humans will be responsible only for providing creativity. For this purpose, we have organized the first 2015 Smart World Congress, including five IEEE International Conferences. Specifically, a variety of challenges are presented in the field of smart world. Therefore, an open forum on the top ten challenges (Top10Cs) for smart worlds was held under the congress to identify the main challenges through collecting the intelligence existing particularly in crowd wisdom. Top10Cs and related works, as a crowdsourcing approach, discuss and analyze the top challenges for smart worlds based on the selective results of the crowd and experts via an online platform. Moreover, we summarize the experiences obtained in organizing the Top10Cs forum.