Private blockchains are valuable for solving efficiency, security and fraud problems within traditional financial institutions, but only incrementally. It’s not very likely that private blockchains will revolutionize the financial system. Public blockchains, however, hold the potential to replace most functions of traditional financial institutions with software, fundamentally reshaping the way the financial system works.
Public blockchains are open, and therefore are likely to be used by very many entities and gain some network effects. To give a particular example, consider the case of domain name escrow. Currently, if A wants to sell a domain to B, there is the standard counterparty risk problem that needs to be resolved: if A sends first, B may not send the money, and if B sends first then A might not send the domain. To solve this problem, we have centralized escrow intermediaries, but these charge fees of three to six percent. However, if we have a domain name system on a blockchain, and a currency on the same blockchain, then we can cut costs to near-zero with a smart contract: A can send the domain to a program which immediately sends it to the first person to send the program money, and the program is trusted because it runs on a public blockchain. Note that in order for this to work efficiently, two completely heterogeneous asset classes from completely different industries must be on the same database - not a situation which can easily happen with private ledgers. Another similar example in this category is land registries and title insurance, although it is important to note that another route to interoperability is to have a private chain that the public chain can verify, btcrelay-style, and perform transactions cross-chain.

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Similarly, a side chain is a separate blockchain that runs in parallel to the main chain. The term is usually used in relation to another currency that’s pegged to the currency of the main chain. For example, staying with the Starcraft motif, say we had an in-game currency called Minerals (oh wait, we do!). We could allow players to peg their Ether (or ETH) to purchase more Minerals in-game. So we reserve some ETH on the main chain, and peg, say 500 Minerals to 1 ETH.
That is however not all. Sidechains also have some specific use cases, unique to a certain blockchain. One example is the usage of sidechains in EOS. EOS is currently facing a RAM problem. RAM is too expensive and developers are complaining. Sidechains could compete with the EOS mainchain by having lower RAM prices, this would lead to competition, incentivizing both the EOS mainchain block producers and sidechain block producers (mainchain and sidechains of EOS are maintained by the same group of block producers) to keep the RAM price as low as possible. This also means there is more RAM available, so the RAM price will go down as a result.
Instead, what if the game was played in its own “channel”? Each time a player made a move, the state of the game is signed by each player. After an epic battle where the Protoss player takes out the remaining Zerg forces and forces a gg, the final state of the game (Protoss wins) is sent to a smart contract on the main chain. This neutral smart contract, known as a Judge, waits a while to see if the Zerg player disputes the outcome. If the Zerg player doesn’t, the Protoss player is paid the 1 ETH.
Blockstream is collaborating with industry leaders to create a Bitcoin micropayment system that supports high volumes of instant tiny payments using proportional transaction fees and that operates at the speed of light. We are now developing Bitcoin Lightning prototypes and creating consensus on interoperability. Our c-lightning implementation is the go-to code and specification for enterprise Lightning Network deployments on Bitcoin, and is what powers our easy-to-use Lightning Charge HTTP Rest API.
The sole distinction between public and private blockchain is related to who is allowed to participate in the network, execute the consensus protocol and maintain the shared ledger. A public blockchain network is completely open and anyone can join and participate in the network. The network typically has an incentivizing mechanism to encourage more participants to join the network. Bitcoin is one of the largest public blockchain networks in production today.
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