1. Gain access to information where that would be in US interests.
2. Protect US information from being accessed by others.
From their web site ( https://www.nsa.gov/about/faqs/about-nsa-faqs.shtml ):
> NSA/CSS has two interconnected missions: Signals Intelligence (SIGINT) and Information Assurance (IA). Through SIGINT, we respond to customer requirements for information relating to the plans, intentions, capabilities, and locations of foreign powers, organizations, terrorist groups, or persons, or their agents, who threaten America’s national security. Under Information Assurance, we protect our nation’s vital national security systems and information from theft or damage by others.
Whether you trust them is another question. Many argue that this dual mission creates an inherent conflict of interest. But if you believe they take both halves of it seriously, you might see them as having a legitimate interest in ensuring good crypto is available. (I'm not advocating for that position, but it doesn't seem totally irrational to me either.)