One question, are you encrypting the packets with TLS? It still needs to work on Layer 3 in OSI model, e.g. routing. So you cant encrypt IP-adresses? So encrypting IP-packets with TLS does not hide you IP, right? Therefore its not anonymous who is broadcasting what traffic.. only the content of the packets
IP address is not hidden but things have been arranged such that it's not needed be cause --
Connections made by the BIGcoin wallet is encrypted using TLS v1.2; thus your IPS or network administrator or the government has no idea what you're doing making the BIGcoin protocol completely anonymous.
To make protocol detection more difficult --
Current status: pending
BIGcoin's default port has been changed to 443, the default SSL port for HTTP traffic; in case it's not able to bind to this port, it's going to choose a random port.
This along with protocol encryption makes blocking or detecting BIGcoin protocol next to impossible.
So they wont know that you are using BIGcoin in the first place.
It's to be realized that the wallet does not do anything private except broadcasting the user's transactions (downloading the block chain, uploading it is not private activity and it's not private data). But just in case, If the connected node is someone who's spying on your activity (or recording the transactions exclusively broadcasted by you), then it's not possible to determine if the transaction is exclusively broadcasted by you, since it might have happened that your node is just broadcasting someone else's transaction.
Since the protocol is encrypted and the spy does not know what transactions you received from other BIGcoin clients, it's not possible to tell if the transaction is exclusive to you.
Effectively, the BIGcoin network is itself like tor, but optimized just for the purpose.
More development is under progress to improve this anonymity. This involves a new a protocol message ("Transaction broadcast uncertainty") and changes to the way the client broadcasts the transaction.
