Client side hash key for bitcoin transactions?

[Sargasm]

So... I was thinking about the problem with theft with bitcoins and its effect on price.

It's bad.

So... as a solution, I was thinking it would be cool if a RSA client key could be implemented with bitcoins as a new option moving forward.

How it would work:

When you create a bitcoin account or with a current one... probably through the current wallet software... create an option for an RSA client key.  You would submit something like a RSA 4096 client key that would be processed against some random number and associated with your address.  For a transaction to be verified, the key would have to be submitted with the transaction.

You would then have a couple options.  Creating a key file which could then be stored elsewhere, in the cloud or on a flash drive.  That way in order to transact a theft, the thief would then have to obtain both an unrelated key file AND access to the bitcoin wallet data OR would have to crack an RSA4096 key which would require the use of every computer in the world for thousands of years.

This would require that the initial key would be randomized for best security (making the loss of such a key tantamount to the loss of all BTC at that address) or could be an interpretive key that would be more prone to brute force cracking.

Regardless you'd virtually eliminate unauthorized transactions from the bitcoin universe thus making the currency FAR more attractive to hold, use or trade.

Thoughts?