Cyberattacks on computer networks pose growing threats to critical infrastructure, businesses, and personal data across the United States. Computer security systems that monitor network traffic to detect suspicious activity are essential for protecting against these attacks, but they face a significant challenge: detecting sophisticated attacks often requires analyzing data from multiple organizations, devices, or locations simultaneously. However, sharing network data raises serious privacy concerns because this information can reveal sensitive details about individuals, businesses, and government operations. This project addresses this challenge by developing advanced privacy protection methods that allow organizations to work together to detect cyberattacks without exposing sensitive information. This work serves the national interest by strengthening cybersecurity defenses across critical infrastructure, supporting economic competitiveness through improved data protection, advancing national security through enhanced threat detection capabilities, and enabling compliance with privacy regulations while maintaining robust cyber defenses. This project develops privacy-preserving techniques for graph-based intrusion detection systems that model network traffic and device relationships as interconnected graphs. The research activities include developing specialized cryptographic protocols for essential operations such as sparse matrix multiplications that are fundamental to