The advent of artificial intelligence-generated content (AIGC) represents a pivotal moment in the evolution of information technology. With AIGC, it can be effortless to generate high-quality data that is challenging for the public to distinguish. Nevertheless, the proliferation of generative data across cyberspace brings security and privacy issues, including privacy leakages of individuals and media forgery for fraudulent purposes. Consequently, both academia and industry begin to emphasize the trustworthiness of generative data, successively providing a series of countermeasures for security and privacy. In this survey, we systematically review the security and privacy on generative data in AIGC, particularly for the first time analyzing them from the perspective of information security properties. Specifically, we reveal the successful experiences of state-of-the-art countermeasures in terms of the foundational properties of privacy, controllability, authenticity, and compliance, respectively. Finally, we show some representative benchmarks, present a statistical analysis, and summarize the potential exploration directions from each of theses properties.