"Insecure" or "unsecure" when dealing with security?

I agree with Wayne Johnston, but will add some examples. Insecurity has always meant to me a lack or deficiency of security (in whatever context it is used), as opposed to a potentially secure system not being secure at this present time.

Though, I don't think it's black and white. Here are some examples of how I might use in/un-secure.

He was insecure and felt anxious when he went out with his friends.

The system is insecure and needs work before we can roll it out to production.

On the other hand:

Your bike is unsecured. Don't you have a lock for it?

The rope was unsecured. If he didn't find a hook or tree to secure it soon, the truck would fall into the ravine.

Insecure means lacking in security. Unsecured means not secured, not fastened, or not guaranteed. *Unsecure is not a word as far as I can tell.

In your example the correct usage is insecure, meaning that the security of the system was found to be lacking.

The statement, "The system we were testing was determined to be unsecured," would mean that the security was disabled, not that it was deficient.

You will find both insecure and unsecure in most dictionaries. Unsecure is generally used for assets, commodities and systems and refers entirely to safety. Insecure is used predominantly for emotional stability but also for safety, particularly in American English. Corpus searches on both words will show you this usage distribution more clearly. You can use either word, although different audiences will find it more or less strange.

Wikipedia offers a fairly lengthy article on computer insecurity, while unsecurity returns results mostly about the United Nations Security Council. Good enough for me.

In the context of computer security, I would actually recommend "nonsecure"; a system is secure if it is reasonably well protected against intrusion, and nonsecure if it lacks some or all reasonable measures of protection. (Note that "secure" does not guarantee that a successful intrusion is impossible, only unlikely.)

Dictionaries haven't entirely caught up to this usage yet (dictionary.com doesn't have 'nonsecure' but m-w.com does, for example) but it's fairly standard in the computer security field.