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Cooperative cyberdefense has been recognized as an essential strategy to fight against cyberattacks. Cybersecurity Information Sharing (CIS), especially about threats and incidents, is a key aspect in this regard. CIS provides members with an improved situational awareness to prepare for and respond to future cyberthreats. Privacy preservation is critical in this context, since organizations can be reluctant to share information otherwise. This is particularly critical when CIS is facilitated through an untrusted infrastructure provided by a third party (e.g., the cloud). Despite this, current data formats and protocols for CIS do not guarantee any form of privacy preservation to participants. In this paper we introduce PRACIS, a scheme for CIS networks that guarantees private data forwarding and aggregation. PRACIS leverages the well-known Structured Threat Information Expression (STIX) standard data format. Remarkably, PRACIS can be seamlessly integrated with existing STIX-based message brokering middleware such as publish-subscribe architectures. PRACIS achieves these goals by combining standard format-preserving and homomorphic encryption primitives. We discuss experimental results obtained with a prototype implementation developed for a subset of STIX. Results show that entities may create up to 689 incidents per minute, far beyond the estimated average of 81. Moreover, aggregation of 104 incidents can be carried out in just 2.1 s, and the transmission overhead is just 13.5 kbps. Overall, these results suggest that the costs incurred by PRACIS are easily affordable in real-world scenarios.