Commerce

There are a number of ways to do private electronic cash.
Brands' way:
In principle, an electronic coin is just a credential, authorized by the bank, which contains the following private information:
Your bank account number
The value of the coin (say $1)
When you get one from the bank, they deduct $1 from your account.
When you show the credential, you only show the value, not your account number.
So it's private.  Not even the merchant and bank working together can figure out who withdrew the coins that were used in a given payment.
When the merchant shows the bank what you showed him, the bank credits him with $1.