Important Projects

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Ethereum

https://ethereum.org/
Second large public blockchain and the largest consortium of projects.

Consensus algorithm:
POW
future plans:
POS casper (decided)
Sharding

Related projects.

EEA
https://entethalliance.org/

Plasma
Lightning Network of Ethereum. Second layer off-chain solution.

Zcash on Ethereum
Zero-knowledge Ethereum cooperated with Zcash.

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R3 Corda

https://www.corda.net/

Largest blockchain consortium for finance. Similar to Hyperledger consortium, it provides platform for blockchain-based solutions instead of blockchain. It is basically a centralised system with BFT for authorised nodes. Individual transactions are validated instead of a block or chain. Hence, they sometimes claim that they are not "blockchain".

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Hyperledger

One of the biggest blockchain consortium in industry by Linux Foundation. There are many projects in Hyperledger, which are once again some generalised schemes instead of a specific blockchain.

Hyperledger-fabric

A consortium blockchain scheme by IBM. Version 1.0 supports many functionalities like smart contract, private channels, total order, endorsement, etc. On core, it is simply a blockchain using PBFT (or slightly variant BFT algorithm).

Hyperledger-Sawtooth

Project of intel, using a secure-hardware (developed by Intel) based consensus algorithm. Public ledger with no support on smart contract.

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Dfinity

https://dfinity.org/

A newcomer in this area with high intelligent level and solid technical background. It aims to compete with Ethereum, hence with many novel techniques in almost every aspects. However, it is still at an early stage.

Consensus algorithm: a combination of Algorand and Omniledger.
https://arxiv.org/abs/1607.01341
https://eprint.iacr.org/2017/406.pdf
It combines POS leader election, collective signing, and sharding. It is the first public blockchain that truly secure without mining.

It's ambition also includes a second layer for transactions and a whole ecosystem.

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Ripple

It is a private blockchain which provides a ledger for international transaction settlement. It use a very simple BFT algorithm for a group of trusted nodes.

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RSCoin

Digital currency from the bank of England, the first digital currency generated by national bank. It is not strictly a blockchain, rather a distributed database for ledger. It does not consider BFT and the management of the ledger is distributed over trusted parties. Hence, it is essentially a centralised currency with ledger managed and validated in a distributed fashion.

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Zcash

The first and one of the only blockchain that uses Zero-knowledge Proof to achieve privacy. It is a distributed ledger using Zk-SNARKS to hide the identity as well as the transactions itself. It provides private transactions and non-private transactions since the communication and computation load for a private transaction is really heavy.

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IOTA

It is a blockchain system use consensus algorithm "tangle", which has a DAG structure. In that sense, it achieves a very high throughput with dependent validity, which limits its application in some areas that requires full uncompromised validity, e.g., finance. This is also the reason that they choose to focus on the area of IOT.

DAG is another hot topic in blockchain, similar systems includes Byteball, a cryptocurrency based on DAG. However, Byteball requires trusted parties since dependent validity is not suitable for cryptocurrency.

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IOHK

https://iohk.io/

Another group combined resources from industry and academia (University of Edinburgh and some other universities in Japan, Germany, and Russia). There are many teams in this group focusing on different project, some of them are side-projects like wallet, ETC projects, etc. The main blockchain team focused on finance, yielding a consensus algorithm called "Ouroboros", which is a POS type of algorithm that based on the assumption of strong synchrony.

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Here is a summary article which includes most of the projects publicly out there in the industry.

https://medium.com/@josh_nussbaum/blockchain-project-ecosystem-8940ababaf27

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Skycoin

https://www.skycoin.net/whitepapers/

Skycoin is a project that explores a new blockchain solution since 2013. Their consensus mechanism is based on gossip dynamics instead of traditional BFT consensus. Their algorithm is compatible with existing BFT solutions while still providing resistance against Sybil attacks.