Does bitcoin provide non-repudiation? Bitcoin defines you need to sign the previous hash and the destination public key. By doing so, you assume that you transferred the money. That provides non-repudiation of the transaction to a given key pair.

If you used bitcoin to buy "guns", how can the court legally prove that you, a person, are the owner of the key that made the transaction? 

Since the key is not certified by a trustable third-party, you can't prove the association between the key and its owner. Am I correct?
If you used bitcoin to buy "guns", how can the court legally prove that you, a person, are the owner of the key that made the transaction?


The Ross Ulbricht/DPR trial provides several examples of how you might prove that someone made a transaction:


Being the person who sells the product or service to them. For example, the "hitman" Ross hired to kill Curtis Green was actually an undercover agent.
Grabbing the laptop used to make the transaction out of the hands of the guy who made it, and forensically analyzing it.
Other ways, like having a confidential informant, (like Curtis Green) or getting them to plead guilty (like Carl Mark Force.)