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I am looking for the most basic blockchain technology implementation. What is the simplest crypto-currency?

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Crypto-currencies are not simple things. They are a combination of various cryptographic primitives constructed in such a way as to create decentralized trust in a shared ledger. The trust in the system depends on aligning the incentives of the participants so that game theory can predict their actions as rational actors. If you are looking for simplicity...look elsewhere.

Most crytpo-currencies out there have been forked from Bitcoin. From a technical perspective, it's probably best to think "Bitcoin" whenever you hear "blockchain technology", at least so far as the source code is concerned. Most likely, you are dealing with a codebase that was originally forked from Bitcoin, but with changes made on top of it. With that in mind, you could argue that Bitcoin is the simplest.

There are exceptions (like Ripple and CryptoNote) which have not been forked from Bitcoin, but I find it hard to say that any of these systems are simpler than Bitcoin. They are different, less used, and therefore often considered less trustworthy. There are probably some university projects out there which re-implement a blockchain with the minimal required complexity (such as with transaction scripts stripped out, which contribute a great deal to the complexity), but I am unaware of any.

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