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I read some article about the definition of cryptocurrency and digital currency. Still I can not understand their differences. Can a digital currency omits cryptography? Does that make sense? Is cryptocurrency related to mathematical aspects to define secure organization for a digital currency?

Any thought?

UPDATE:

From wikipedia I see Cryptocurrency is a kind of digital currency, virtual currency or alternative currency. and Digital currency (digital money or electronic money or electronic currency) is a type of currency available only in digital form, not in physical (such as banknotes and coins). There is also a figure at https://en.m.wikipedia.org/wiki/Digital_currency which is not meaningful. What is the relation between cryptocurrency and digital currency?

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    Please post a link to the article, so we can see what it is you read and what you are confused about. – Ben Miller Jul 22 '18 at 12:56
  • I have updated the post. This is just an example. I didn't dig further to read technical documents as I think I haven't understand the basics yet! – mahmood Jul 22 '18 at 16:58
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Can a digital currency omits cryptography?

Yes. A digital currency could be a "bank" with an electronic ledger of who owns how much of the digital currency.

With a purely digital currency, the bank would want some way of authenticating it's customers but this need not be an intrinsic part of the digital currency itself.

The customers might want their communications with the bank kept private, but again, this privacy of communications need not be part of the digital currency definition but something external to it.

With most fiat currencies in advanced countries we are not really that far from this. For a large part of my expenditure I can use digital methods of payment - online bank transfers, debit-card and credit-card readers, contactless payment and so on. If paper banknotes dissapeared sometime in the near future, I could certainly survive.

Is cryptocurrency related to mathematical aspects to define secure organization for a digital currency?

Not really. In major crypto-currencies currently, the key innovation and main purpose of crytography is to eliminate any need to trust third parties while preventing double-spending.

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