The NSA had the option to do something like that when they (via NIST) standardized DES. They chose to standardize a version that's secure against attacks that

The NSA had the option to do something like that when they (via NIST) standardized DES. They chose to standardize a version that's secure against attacks that only they knew at the time, shorten the key length so they can still brute-force it if they really need to, and successfully kept the attack secret until researchers at a foreign university independently discovered it decades later.