A general definition for cryptocurrencies I am trying to find the definitions to several terms related to digital currencies. Unfortunately, I am always ending up on Bitcoin-oriented pages and websites which only take Bitcoin itself into consideration. So far, I managed to understand (actually, “guess” would be more appropriate) the following:


Digital currencies is the generic term for a currency which exists only as a sequence of zeros and ones on a digital support. 
Electronic money is a way to realize a digital currency, it introduces a system where there is a central authority of trust in charge of managing the wallets of users and certifying all the transactions. Cryptography is only used to secure the communications between the users (buyers/sellers) and the central authority.
Cryptocurrency is another way to implement a digital currency, it defines a way to perform secured transactions and to control the creation of new units with the help of cryptographic schemes and protocols.


Now, lets venture a bit further and try to list the security properties that must (or may) be implemented by a cryptocurrency:


Unfalsifiability: The creation of new legitimate (or not) cryptocoins must be under strict control of the system.
No double spending: Once cryptocoins have been spent for a transaction, they must not be reusable by the original owner in another transaction.
Centralized/Distributed: The transactions using the cryptocurrency is done in centralized/distributed manner.
Anonymity (Optional): A transaction may be anonymous, meaning that the previous owner of a cryptocoin should not be easy to find.
Fraud tracing (Optional): A fraudulent transaction may lead to the unveiling of the original fraudster.


I guess that there might be dozens of optional properties to add… but, lets stop here.

So, my question is: are my definitions valid, or did I forget something (maybe some properties)?
I write here a partial answer to my own question (but it is only partial, feel free to write an answer of your own).

In the book "Introduction to Cryptography with Coding Theory" (2nd edition), by Wadde Trappe and Lawrence C. Washington, chapter 11, Digital Cash, p.288, we can find the following list of properties coined by T. Okamoto and K. Ohta:


  
  The cash can be sent securely through computer networks.
  The cash cannot be copied and reused.
  The spender of the cash can remain anonymous. If the coin is spent legitimately, neither of the recipient nor the bank can identify the spender.
  The transaction can be done offline, meaning no communication with the central bank is needed during the transaction.
  The cash can be transferred to others.
  A piece of cash can be divided into smaller amounts.
  


In the article "Blind Signatures for Untraceable Payments", by David Chaum, the digital cash holds the following properties:


  
  Inability of third parties to determine payee, time or amount of payments made by an individual.
  Ability of individuals to provide a proof of payment, or to determine the identity of the payee under exceptional circumstances.
  Ability to stop use of payments media reported stolen.
  


From all theses definitions, the definition I would find the most suitable is the following (I obviously forgot to speak about the security of each transaction):


Security of Transactions: Transactions between several participants must
be secured and non-repudiable. It must not be possible to pretend to
be someone else during or after a transaction or to spend more
cryptocoins that we really have.
Unfalsifiability: The creation of new legitimate (or not)
cryptocoins must be under strict control of the system.
No double spending: Once cryptocoins have been spent for a
transaction, they must not be reusable by the original owner in
another transaction.
Centralized/Distributed (Altnerative): The transactions using
the cryptocurrency is done in a centralized/distributed manner.


Then, comes optional properties:


Anonymity (Optional): A transaction may be anonymous, meaning
that the previous owner of a cryptocoin should not be easy to find.
Fraud tracing (Optional): A fraudulent transaction may lead
to the unveiling of the original fraudster.