Re: Chaumian ecash without RSA

[jamesd@echeque.com]

At 08:10 AM 3/31/96 -0800, David Wagner wrote:
> The bank picks a secret value k, and publishes g^k.
>
> To withdraw a coin, Alice picks an x, sets
>	y = x | hash(x),                [  | is concatenation  ]
> chosen so that y is in G.  Alice chooses a random secret blinding factor b,
> sends to the bank
>	A->B: y g^b,
> and the bank returns
>	B->A: (y g^b)^k,
> debiting Alice's account.
>
> Note that this is a (blinded) Diffie-Hellman key exchange with public
> exponentials g^k and y g^b; the bank returns the exchanged "secret".
>
> Alice unblinds this value, computing
>	z = (y g^b)^k (g^k)^{-b}
> and now c = (x,z) is a coin in the digital cash system.  Note z = y^k.
>
> We use the traditional online clearing protocol; to deposit the coin, a
> shop S sends
>	S->B: x, z.
> The bank checks to make sure the coin hasn't already been spent, and then
> computes
>	y = x | MD5(x),
> checking whether y^k = z. 

Two irritations with this protocol:

1:  A coin is almost twice the size of a coin in the RSA protocol

2:  Nobody except the bank can verify that a coin has face validity.

The second point is more serious than you might think, as most of 
us want to see a world where everyone is his own bank and his own 
credit rating agency, as well as his own publisher.

It will obstruct contracts of the form "Anne promises to provide 
numbers with certain cryptographic properties, provided Bob provides
numbers with certain cryptographic properties."

With RSA crypto cash, Anne can construct a blinded unsigned coin, 
and ask Bob to have it signed.  For this to be reasonably convenient
and practical, we need to have locally verifiable signatures.

For computer mediated management of contracts, transactions, and 
credit ratings, we need contracts such that all intermediate 
transactions can be reduced to locally verifiable cryptographic 
protocols.
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