Trust is next to impossible to regain, regardless of your age.
It's also unclear what it is you've done to violate that trust, were you caught hacking? Browsing porn? Downloading (perhaps specific) apps and games after you were told not to? While it's not relevant to the Q&A "what" has been done, it does affect how much freedom you may be able to negotiate.
For example, if you were caught hacking your parent's bank info it's unlikely there is any conversation you can have with your parents to convince them to give you your space.
However, if the offense was "i got caught browsing porn" then it's ideal to have a one-off adult conversation with your mother or father, whichever is easiest to talk to, about how you understand the danger of what you did (as your parents are responsible for your actions, their complacency can be misconstrued as negligence by the law -- and this has serious implications for your parents, you, AND your siblings -- for parents this can be very scary, and their kids don't really understand the half of it until they become parents, too.)
What am I saying? It's not enough to acknowledge your mistake. This is great textbook advice, but, what is really necessary is for you to acknowledge the ramifications of your actions (and in doing so, you also recognize that your actions were a mistake without needing to say as much.) This will prove to your parents that you've developed to a point that, perhaps, you can be trusted to make good decisions moving forward. This is why "mom, dad, I am sorry I did that one thing. I know it wasn't right, and I know not to do it now, and I will never do anything like that again. I am a different person today" is itself insufficient justification -- as a parent this comes off as begging, grovelling, possibly even penance ... but it is not a sign of maturity, it is the exact opposite (to an educated parent, anyway) and only serves to dissuade them.
Without recognition of cause/effect it is very hard for a parent to trust where trust has been violated once before, as the violation demonstrates that you are willing to make a bad decision (regardless of the circumstances, the violation applies cleanly over ALL concerns.) This is what you are dealing with now, and breaking trust is not something anyone forgets, ever. Time and trust are not really related as we might like to think. Think of trust as an absolute: it is today what it was 2 years ago, and what it will be 2 years from now.
Consider that the prefrontal cortex is the portion of the human brain responsible for rationalizing right and wrong, it is the part of the brain responsible for rationalizing cause and effect. This portion of the brain begins development as early as 5-8 years old, and continues development as late as 22-25 years old (I believe academic studies put the range 7-21?) Parents reading this can confirm that up until this development begins children are very malleable and compliant, if you tell them something is right or wrong they take that knowledge at face value, and this sort of interaction directs a childs actions before they're able to understand on their own what to do or why. As such, your parents learn your personality long before you do as part of raising you, answering your questions and dictating your behavior. They get an idea of how you think as early as 2-3 years old, and they watch that mental development continue for the rest of your life.
This is also why we make the mistakes we do as children. It is why our parents are held legally responsible for our actions. It is what you are battling with, whether you realize it or not.
So with that knowledge, to circle back around:
You need to have a mature conversation to make it clear you understand the ramification of your actions. This will hold more weight with your parents than anything else you can say or do.
This conversation should NOT be attached to your request for freedom/privacy/ownership. DO NOT MIX THESE CONVERSATIONS. Heck, space them out two weeks or so for maximum effect. Not doing so detracts from the credibility of your acknowledgement instead causing it to be viewed as mere "bargaining" (ie. not "acknowledgement.")
Also consider that if this sort of introspection was not possible before reading these answers then it's entirely possible that you're not ready for this conversation (yet), and your attempt will instead be viewed as a negotiation/manipulation attempt and not recognition/comprehension of your actions. (or put another way, consider that a conversation about ones rational capability and maturity is a battle of wits, yours vs. theirs, and you may still fail even if you have prepared a bullet-proof argument.)
All else aside, I was a child "technology enthusiast and savant" at the age of 6 (mmhmm, my poor parents, lulz) and while I won't enumerate all the "mistakes" I made I do remember when my parents confiscated technology, shut off the phone, canceled credit cards, restricted the hours I could be out, restricted who I could associate with, etc. As a result they kept me on the straight and narrow -- not by restriction, but by forcing me to be extremely careful with my actions until I could realize the ramifications of those actions. I, of course, didn't see it this way until my mid 20s (yep. prefrontal know-it-all right here) and so ultimately nothing they did stopped me.. I used friend's computers, got my own laptop and kept it at my friend's house, learned to phreak public lines, at one point I even had a phone line installed without them knowing (later added to the top of the list of "worst ideas ever" the day the mail/bill for the line came in. oops!)
The hardest part for me as a teen was that not having a phone meant I couldn't talk to my girlfriend(s). I eventually got them to turn the phone back on after talking to my mom about this, but, the trade-off was that she got to keep the phone off the hook unless I got pre-approved permission to make a call, and even then she would listen to make sure I wasn't using the line for "other things." This was awkward for me for a while, but, I got used to it and after a while she stopped snooping my calls, gave me some space, and my parents ultimately learned to trust my ability to make sound decisions (although my dad still watches me skeptically when I touch one of his computers, and I am over 40 years old now.)
Trust is next to impossible to regain, regardless of your age.
HTH, best of luck. Parents only ever want the very best for their children and as messed up as it sounds; this is how they show it.