No. I was under the impression that the same wallet can have an arbitrary number of addresses. https://en.bitcoin.it/wiki/Address seems to support this idea.
You can have multiple addresses per wallet but BTC is still stored in addresses, not wallets. So if you have some BTC in address A and none in address B then you can't use B to buy anything. If you transfer money from A to B that leaves a record.
But you have no idea if address A and B belong to the same wallet, right? As in, I can create address A, get coins into it, then create addresses B-Z, disburse coins into them, then collect them again? Could I reasonably create enough addresses to create plausible deniability that I actually owned all the coins at all times?
Alternatively, could I use a web wallet to bounce coins around to obfuscate ownership?
Researchers can easily track such trivial ways of "attempted anonymization".
>>> We found out that there is a huge
number of tiny transactions which move only a small fraction of a single bit-
coin, but there are also hundreds of transactions which move more than 50,000
bitcoins. We analyzed all these large transactions by following in detail the way
these sums were accumulated and the way they were dispersed, and realized
that almost all these large transactions were descendants of a single transaction
which was carried out in November 2010. Finally, we noted that the subgraph
which contains these large transactions along with their neighborhood has many
strange looking structures which could be an attempt to conceal the existence
and relationship between these transactions, but such an attempt can be foiled
by following the money trail in a suciently persistent way
--------
ALL BTC transactions are FOREVER archived in the bitcoin ledger. Its how it works.
Unfortunately, the authors of the paper did not understand the relationship between wallets and addresses very well either.
The recommend use of Bitcoin is that every payment you receive should be to a new address. This maximizes privacy and its necessary when you may have multiple concurrent payment in order to sort out which one you've received. Common wallet software (including the reference client) also always pays change to a new address.
... so it's a bummer that the authors of the paper went on to describe every coin assigned to an address which has never spent as in savings (roughly 60% of them), if not for a couple things engaging in the bad practice of address reuse they would have found 100% in "savings".
The real problem occurs when you want to buy something that costs X, and all the addresses you control have fewer than X coins. You have to join the coins from multiple addresses within the wallet, and this joining provides very strong evidence that the same user controls all these addresses. So if one address is known to belong to a particular user, we now know (more or less) that all addresses belong to that user.
This joining means that even if you've been super careful to never link address A to you because you've done sketchy things with A, if at some point in the future (even distant future) you join A with another address that the someone CAN track, they now know you own A.
> this joining provides very strong evidence that the same user controls all these addresses. So if one address is known to belong to a particular user, we now know
