Which is the appropriate word to be used in the sentence:
The system we were testing was determined to be insecure/unsecure.
The usage is in the context of security, specifically a lack thereof.
I've always said insecure, because I didn't believe unsecure was a word (although unsecured is). Even as I type this, I'm getting a spell check complaint about it. However, I was laughed at once when I called a particular device "insecure."
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.
As a system never really is totally secure, you might want to use sufficient/insufficient security instead, which would circumvent the unusual unsecure/insecure phrase:
The system we were testing was determined to have sufficient security.
The system we were testing was determined to have insufficient secturity.
Sufficient security would mean that the system has reasonable security measures given it's specific situation.
As other answers have indicated, "insecure" is a much more common word than "unsecure". (The word "unsecured" has an intermediate frequency, but its meaning doesn't seem consistent with what you want.)
The most common nouns that occur after "unsecure" do seem relevant to your desired usage, however: the Ngram Viewer indicates that they are things like "unsecure network(s)", "unsecure line", "unsecure environment", "unsecure connection", and "unsecure channel".
The word "insecure", when used attributively before a noun, is actually often used with non-human nouns, but the top ones shown by Google are abstract like "insecure position", "insecure footing", "insecure basis", "insecure foundation(s)". So if we chose a random occurence of the word "insecure", it probably won't be related to information security. But this by no means indicates that it would be incorrect to speak of insecure devices.
In fact, because "insecure" is so much more frequent than "unsecure", the phrase "insecure network(s)" still seems to be much more common than "unsecure network"; likewise, "insecure channel" and "insecure connection" appear to be more common than "unsecure network" and "unsecure connection".
I would say it looks like you could use either word with this meaning.
Insecure has neurotic connotations. I've always avoided applying it to things that can't suffer from that affliction unless I'm trying to be humorous.
Unsecure is more properly jargon with different specific meanings depending on context; eg. loans, physical protection (unsecured window, unsecured loan, etc). It's always unsecured rather than unsecure, but it also always has a physical and sometimes protective component.
Due to the distinct difference between the emotional and physical, I use unsecure for computing. Besides, I dislike anthropomorphizing an appliance.
IMHO, the propagation of insecure in the context of computing is a result of users whose primary source for proper English is their word processor's spell-checker. Spell-checkers typically don't support jargon.
I am not native speaker, but I found next.
The in prefix is used for situations when property is constantly exists for an object: innocent, insecure, incomplete
The un prefix is used for situation when you apply some property to an object: unsecure (remove the security); undo (make finished task incomplete); unclean (make it dirty, but it was clean before)
Thus if you are going to use unsecure:
I unsecure your network and now it is insecure
You network was unsecured by me, it is insecure now
Examples above looks reasonable to me.
I would suggest using the phrase "not secure". For example, this is what is shown in Chrome if a website is determined not to be secure.
