Well, simply storing and hashed version of the pass would be ok. Even an MD5 or a SHA1 would be enough to guarantee at least a "Very Few plus Us" security.

Hiding that in the could would be much more difficult. And using PKs would make the attack even easier to spot.

And then you have to consider that a "Nobody but Us" backdoor exist only on paper, not in reality. If a key exists and someone knows it, well sooner or later it will be discovered (disgruntled employees, hackers etc). The only safe backdoor is the none backdoor. Now, consider this problem from an attacker that doesn't give a st of your security. He knows that as soon as the backdoor is known (because someone find it in the code, because someone leak the password, because whatever...) the backdoor will be useless most systems. What you do, you design a safe backdoor or you design a backdoor with as little footprint as possible?

Obviously, legally sanctioned backdoor have a different set or constraint and making them safe is a requirement. The fact that it is impossible to prove them safe unless some assumptions (that always prove to be wrong, but...) are made, it's a totally different problem.