As I said, conceptually the bridge may run serverside. And yes, you’d have to give it your login or e2e keys etc to work, and it ‘breaks’ the E2E of services like telegram by decrypting/reencrypting for Matrix on the bridge. However, you could run a bridge yourself (as @Handle said), or in future we’re looking at ways to run a bridge (and homeserver for that matter) locally on the client. So you’d have the option to either have a lightweight thin-client or a much heavier one which actually federates directly with Matrix (effectively acting as a server), which could likewise run bridging locally. Finally there may also be a halfway house in future where you can run a local bridge which puppets your local client to synchronise it with the remote protocol. We do this today in some places with SMS, where the local client effectively acts to bridge SMS in/out of Matrix.