In "Let That Be Your Last Battlefield," Kirk decided that when push comes to shove, he's not going to let anyone gain control of his ship. In the name of Starfleet integrity. For queen and country. Because it's sure to impress all the attractive females in the galaxy.

Blowing a ship up in the 23rd century requires three people. For the Enterprise, the following were the sequences necessary for the computer to press The Big Red Button:

1. Destruct sequence 1, code 1, 1A
2. Destruct sequence 2, code 1, 1A, 2B
3. Destruct sequence 3, code 1B, 2B, 3
4. Code 000, destruct 0

Assuming contemporary cryptographic analogies here, isn't this a pretty lame encryption key? I'm sure voice-pattern recognition is part of the mix somewhere for that two-factor authentication, but for a Starfleet command vessel of high visibility, you'd figure the sequence of characters would be a little more random. These numbers might as well be the combination for my luggage.

And to top it off, they didn't even bother changing it after Bele and Lokai heard it. Not as if they had the chance to leak it out anywhere, but you figure Starfleet regulations for rotating these values at regular intervals would dictate immediate change after first attempt.

Here's Chekov in "The Search For Spock" thinking to himself why the hell the destruct code is still the same after all these years:

Picard was smart enough to change his authorization code every episode, and in TNG "Brothers," Data gave a good shot at a longer string when locking the computer, although using limited character sets isn't necessarily good practice:

These über-Starfleet folks should be able to use highly-secure access codes. Otherwise, I'm not impressed.