Which FIPS assigns security controls to a system based on categorization?

The answer is based on how FIPS 199 establishes a framework for categorizing information and information systems in terms of the impact of a potential security breach. This categorization helps determine the appropriate security controls that should be implemented, aligning with the overall goal of protecting the integrity, confidentiality, and availability of data.

FIPS 199 provides a methodology for identifying the level of impact (low, moderate, or high) that a loss of confidentiality, integrity, or availability would have on an organization. Each impact level correlates with specific security requirements and controls that need to be applied to ensure the system's security posture is adequate based on the identified category.

In contrast, the other options have different focuses: FIPS 200 outlines the minimum security requirements necessary to protect information systems; FIPS 140 pertains to cryptographic modules and their security requirements; and FIPS 197 establishes the Advanced Encryption Standard (AES) for encryption purposes. Therefore, FIPS 199 is specifically responsible for categorizing systems to assign security controls, making it the correct choice in this context.