Properties of Bitcoin as an Electronic Cash System I am studying the concept of Electronic Cash, and in several reference I found that the criteria describing the ideal electronic cash system are as follows:


Independence: The security of electronic cash cannot depend on
any physical condition. Then the cash can be transferred through
networks.
Security: The ability to copy (reuse) and forge the cash must be
prevented.
Privacy (Untraceability): The privacy of the user should be
protected. That is, the relationship between the user and his
purchases must be untraceable by anyone.
Off-line payment: When a user pay the electronic cash to a shop,
the procedure between the user and the shop should be executed in an
off-line manner. That is, the shop does not need to be linked to the
host in user’s payment procedure.
Transferability: The cash can be transfered to other users.
Dividability: One issued piece of cash worth value C (dollars)
can be subdivided into many pieces such that each subdivided piece
is worth any desired value less than C and the total value of all
pieces is equivalent to C.


Now, what of the above properties are achieved by the Bitcoin system? I guess 1, 2 and 5 are trivially achieved, and I think 3 and 6 are not fully achieved. I wonder if 4 is achieved, and I'm particularly interested in this off-line property.
When a user pay the electronic cash to a shop, the procedure between the user and the shop should be executed in an off-line manner. That is, the shop does not need to be linked to the host in user’s payment procedure.


Neither merchant nor customer need to be connected directly.

A customer can hand a merchant a previously-signed transaction without using a network connection. However, the merchant can only prove the validity of the coin(s) being spent by contacting the network.