The differences between these types of blockchains are based on the levels of trust existing among the members of the network and the resulting level of security. Indeed, the higher the level of trust between the members of the network, the lighter the consensus mechanism (which aims to add the blocks to the blockchain securely). As we will see, there is no trust between the members of a public blockchain since it is open to everyone and inversely the confidence is much stronger on the private blockchain since members are pre-selected. In networks based on a blockchain, the level of trust among the members therefore directly impacts the structure and mechanisms of the network.
For example, Banks A and B often settle thousands of transactions per day. It would be extremely expensive for all of those transactions to be committed to the main blockchain, so A and B set up a side-chain. At the end of each day, at most one transaction is committed to the main blockchain (the only possible outcomes are A and B's balances remain the same, or one of their balances decreases and the other's increases).
To scale Blockchain, sidechain or childchain solutions cannot be undermined. Sidechains are separate Blockchains that are linked to the main Blockchain using a two-way peg. They are an auxiliary network that executes the complementary function of: faster transactions, lower transaction costs and greater scalability in terms of the number of transactions that can be supported in a network at a given time.
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Third option is to write your own blockchain protocol according to your needs. You will be able to answer all your what if questions if you design it by yourself. Ripple, Hyperledger projects (Fabric, Burrow, Indy), Corda, Multichain and most flexible and popular one Ethereum can be examples of that option. That option is the most costly and risky one. You have to invest a lot, and after you create your blockchain, you have to find people & companies to use it. Also you need to attract community of developers to upgrade, enhance your blockchain for coming requirements in the future. Above blockchains are the ones I remember immediately, also there are others.
This list is not exhaustive. There are plenty of public blockchains, and they are actively adopted by such industries as FinTech, gaming, logistics, and beyond. However, it not always makes sense to move certain processes and businesses to the public network as the latter are characterized by comparatively low speed of transactions execution and high costs. Indeed, every transaction requires a consensus of the entire network. Unfortunately, it takes time and resources.
Bitcoin blockchain design has been done for a specific purpose, and this is a money (crypto currency) transfer. But what will we do, if we want to change or add some functions of the bitcoin blockchain? What if we want to transfer other assets rather than money, what if we want to do transactions automatically when pre-determined events occurred. Or what if we don't want other people see our transactions, or track our transactions' history. You can ask countless of what if questions and every answer to these questions drive you to a different blockchain or configurations
It’s the IBM “blockchain”. Basically Apache Kafka queue service, where they have modified the partitions. Each partition is an ordered, immutable sequence of messages which are continuously appended. They added some “nodes” to clean the inputs and voila; blockchain! We should add that there are no blocks, but batches of transactions are renamed to fit the hype better. Since everything gets written in one queue at the end of the day, IBM offers the bluemix cloud server (priced at 120.000$ per year) to host the service. Smaller test packages with a couple of input cleaning nodes go reportedly for 30.000$.
By contrast, the Bitcoin blockchain is not Turing complete since it has little to no ability for data manipulation. It has no ability for a user to deploy if else or goto statements. This is a bit of a simplification but anytime you hear someone say something is “Turing complete” you can do a quick check to see if there is functionality for data changes, memory changes and if/else statements. If there is, that’s usually what they mean.
External Account, which stores ETH balance – This contains the address of the User that was created using the Web3.js API, e,g, personal.newAccount(…). These accounts are used for executing smart contract transactions. ETH is your incentive received for using your account to mine transactions. The address of the account is the public key, and the password of the account is the private key.
Liquid is the world's first federated sidechain that enables rapid, confidential, and secure bitcoin transfers. Participating exchanges and Bitcoin businesses deploy the software and hardware that make up the Liquid network, so that they can peg in and out of the Bitcoin blockchain and offer Liquid’s features to their traders. Liquid provides a more secure and efficient system for exchange-side bitcoin to move across the network.
The creation of sidechains have been a direct result of scalability issues associated with the main blockchain for projects such as Ethereum. Making sidechains increasingly popular way to speed up transactions. Lisk was the first decentralized application (dapp) to implement sidechains. With Lisk, each dapp created exists on its own sidechain without interfering with the mainchain.
“Such brazen theft would indicate  that Bitcoin would be (in the near future) without sidechains of any kind, and  that Bitcoin itself may be in danger from the miners (and we may need to consider using an alternate proof-of-work hash function),” he explained the impact of this setup in his original post on the topic. Like SPV sidechains, drivechains require a soft-forking change to Bitcoin.
The distributed Bitcoin mining network performs quadrillions of calculations every second that maintain the integrity of its blockchain. Other blockchains aren’t remotely as secure, but they innovate much faster. Sidechains, an innovation proposed and developed by the startup Blockstream, allow for the best of both worlds; the creation of new blockchains “pegged” to Bitcoin, so that value can be transferred between them, which can conceivably be automatically secured by Bitcoin miners via “merged mining.”
“Given all of this, it may seem like private blockchains are unquestionably a better choice for institutions. However, even in an institutional context, public blockchains still have a lot of value, and, in fact, this value lies to a substantial degree in the philosophical virtues that advocates of public blockchains have been promoting all along, among the chief of which are freedom, neutrality and openness.”
So, there is a kind of centralized authority that decides who has a right to contribute to and to audit the network. What is more – it’s possible to restrict viewing information stored on private blockchains. It might seem that in such conditions, a blockchain is no longer the blockchain as it lacks transparency and decentralization. Well, these remarks are fair, but only when the network is estimated from the outside. Within it, the rules remain the same as for public networks: it is still transparent for all the members.
A public blockchain is a platform where anyone on the platform would be able to read or write to the platform, provided they are able to show the proof of work for the same. There has been a lot of activity in this space as the number of potential users that any technology in this space could generate is high. Also, a public blockchain is considered to be a fully decentralized blockchain. Some of the examples are:
Mastercoin and Counterparty are embedded consensus protocols (or meta-protocols) that use the blockchain to store their transactional data. Bitcoin devs, except Peter Todd who was hired by both teams to help them find a proper solution, are very unhappy, to say mildly, about storing the data on the blockchain. Heated discussions on this topic go on for hundreds of pages on bitcointalk and Mastercoin github issue. Mining pools like Eligius started censoring Mastercoin transactions (not sure if they are continuing with this practice right now, but the operators of this pool are adamant that data do not belong to the blockchain).
Note: Some would argue that such a system cannot be defined as a blockchain. Also, Blockchain is still in it’s early stages. It is unclear how the technology will pan out and will be adopted. Many argue that private or federated Blockchains might suffer the fate of Intranets in the 1990’s, when private companies built their own private LANs or WANs instead of using the public Internet and all the services, but has more or less become obsolete especially with the advent of SAAS in the Web2.
They rely on a technology called SPV (simplified payment verification) proofs, which work like this: in order to send money to a sidechain and back to the main bitcoin network again, users need to attach a proof that they really have the funds. Without these proofs, when users or miners move their money back to the main chain, under certain conditions, they could take more money than they really have.
"Proof of Work" used by Bitcoin is a competitive consensus algorithm. Each node races to solve a difficult puzzle first. Doing so earns the right to produce a block and you are rewarded in Bitcoin. The block is where the transaction (value of data) is written and confirmed. However, this race is a waste of time and money for those that don’t win. You get nothing unless you are the first to solve the puzzle. Since no one wants to lose, nodes started working together to solve the puzzle and share the reward based on your computational power (the hash rate).
Frankly, secure implementation of Bitcoin is already a pain in the ass .. adding more complexity just seems like the wrong move at this point. It’s already trying to be a currency, a networking protocol and a client in the same codebase. Adding turing complete (or not) scripts with arbitrary outcomes, multiple versions of the official client cooperating, multiple clients, and now multiple blockchains is basically the nail in the coffin in terms of widespread implementation.
State of the art public Blockchain protocols based on Proof of Work (PoW) consensus algorithms are open source and not permissioned. Anyone can participate, without permission. (1) Anyone can download the code and start running a public node on their local device, validating transactions in the network, thus participating in the consensus process – the process for determining what blocks get added to the chain and what the current state is. (2) Anyone in the world can send transactions through the network and expect to see them included in the blockchain if they are valid. (3) Anyone can read transaction on the public block explorer. Transactions are transparent, but anonymous/pseudonumous.