There's nothing at all opposing about those goals. They're both natural by products of expertise in signals intelligence and cryptanalysis, and skill breaking security helps provide more secure systems by subjecting them to more sophisticated attacks.
Just as a clarification, NSA doesn't set those standards. Agencies like NIST set AES and SHA3 through open worldwide competitions. These standards then become parts of larger compliance guidelines like FIPS (Federal Information Protection Standard I think) that govern how the USG should protect its data.
NIST has like 2 cryptographers, doesn't it? The real guidance at NIST comes from NSA. If you think NSA is backdooring Suite B crypto, you can't trust NIST.
- To eavesdrop on the communications of foreign entities.
- To protect our own government from foreign entities that are doing the same.
It is the latter directive that has provided SELinux and AES.