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Digital Cash, Privacy, Anonymity, Double spending protection and Cheating protection

Let's think out loud here for a minute...  I am sending this to Cypherpunks to 
see if someone out there has already thought of a solution to this.

Alice wants to get a file from Bob and wants to pay him $1 using some Digital 
Cash scheme.

- Do we want Alice's identity to remain Anonymous (and Bob's too)? (Note that 
  this means that neither party knows who the other really is.  They could be 
  using aliases to conceal their real identity.)

- Do we want both Alice's & Bob's Privacy maintained in the interactions. (Note 
  the seperation of Privacy and Anonymity with the former referring to the fact
  that the transaction detail is only known between the parties involved.  The 
  transaction detail includes, knowledge of what was purchased, how many, and 
  in the ideal case between which parties!  Those parties could have used an 
  alias and therefore have remained Anonymous independent of whether their 
  Privacy was maintained.  Privacy also means more than simple confidentiality 
  because it may involve having a merchant, for example, not maintain a database
  of purchasing habbits, or if it does maintain such a database, keep it to 

- Do we want to prevent Alice from double spending (and Bob too)?

- Do we want to protect either party from cheating each other?

- Do we want a self-enforcing protocol?  (e.g. No need for Bob to verify the 
  e-coins with a Bank every time.)

- Do we want minimum book-keeping by each party for practical implementations?

- Have I missed more?  Tax, Export, etc (beyond the scope of this email ;-)

The question is can all of the above requirements be achieved?  AND Are they 
all required/desired? 

I know cryptography does wonders, but I ponder upon 1) the need to satisfy
all the above requirements, as well as 2) the feasability of such a solution.

At first glance, it appears that Anonymity and Double spending prevention are
contradictory.  You want to punish a double spender and you need to know their
identity to do that.  Also, Privacy covers a broader scope than cryptographic 
protocols can address (e.g. the merchant database.)  Finally, to prevent/punish cheating using a third party requires the loss of both Privacy and Anonymity as
the third party/judge is presented with the transaction details and asked to 
arbitrate.  Nevermind the other requirements for now... :-)

Please include me in all responses.  Thanks.