Decentralization and distribution are seen by many to be a major benefit of public blockchains, but not everybody shares this ethos. But this is not the only benefit of public blockchains, of course. Perhaps most importantly, their transparency makes them very secure: because they can be audited by anybody, it is easy to detect fraud on the chain. Security-via-openness is a principle well known in the open source world, and this strategy is also popular among some in the digital currency community. For example, all of the tools and content produced by the Ethereum team is open source. This helps to make Ethereum widely accessible and more secure.
Permissioned blockchains use an access control layer to govern who has access to the network.[46] In contrast to public blockchain networks, validators on private blockchain networks are vetted by the network owner. They do not rely on anonymous nodes to validate transactions nor do they benefit from the network effect.[47][better source needed] Permissioned blockchains can also go by the name of 'consortium' or 'hybrid' blockchains.[48]

A user on the parent chain first has to send their coins to an output address, where the coins become locked so the user is unable to spend them elsewhere. Once the transaction has been completed, a confirmation is communicated across the chains followed by a waiting period for extra security. After the waiting period, the equivalent number of coins is released on the sidechain, allowing the user to access and spend them there. The reverse happens when moving back from a sidechain to the main chain.
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.

“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.” 

The words block and chain were used separately in Satoshi Nakamoto's original paper, but were eventually popularized as a single word, blockchain, by 2016. The term blockchain 2.0 refers to new applications of the distributed blockchain database, first emerging in 2014.[13] The Economist described one implementation of this second-generation programmable blockchain as coming with "a programming language that allows users to write more sophisticated smart contracts, thus creating invoices that pay themselves when a shipment arrives or share certificates which automatically send their owners dividends if profits reach a certain level."[1]
Using Rootstock as an example, in order to transfer assets from one chain to the other a user on the parent first has to send their coins to a special output address where they will consequently become locked and un-spendable. Once the transaction is completed, SPV then confirms it across the chains and after waiting out a contest period, which is just a secondary method to help prevent double spending, the equivalent amount will be credited and spendable on the Sidechain and vice versa.
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Private institutions like banks realized that they could use the core idea of blockchain as a distributed ledger technology (DLT), and create a permissioned blockchain (private or federated), where the validator is a member of a consortium or separate legal entities of the same organization. The term blockchain in the context of permissioned private ledger is highly controversial and disputed. This is why the term distributed ledger technologies emerged as a more general term.
This type of blockchains can be considered a middle-ground for companies that are interested in the blockchain technology in general but are not comfortable with a level of control offered by public networks. Typically, they seek to incorporate blockchain into their accounting and record-keeping procedures without sacrificing autonomy and running the risk of exposing sensitive data to the public internet.

Public blockchains are also expensive, and not just in terms of money. The time and energy required to process transactions on public chains is more intensive than that of non-public chains. This is because every single node on the chain must authorize each new transaction before it is added to the chain, which requires a large amount of electricity and time (not to mention money).
@tradles – thanks for taking the time to explain this. OK – so I get the debate around blockchain bloat and the (grudging) inclusion of OP_RETURN, etc., but what I’m missing is that I can only really see one scenario where embedding any identity data into the blockchain makes sense…. and that’s when I want to *associate* an identity with a transaction I’m performing.

Nodes can be trusted to be very well-connected, and faults can quickly be fixed by manual intervention, allowing the use of consensus algorithms which offer finality after much shorter block times. Improvements in public blockchain technology, such as Ethereum 1.0's uncle concept and later proof of stake, can bring public blockchains much closer to the "instant confirmation" ideal (eg. offering total finality after 15 seconds, rather than 99.9999% finality after two hours as does Bitcoin), but even still private blockchains will always be faster and the latency difference will never disappear as unfortunately the speed of light does not increase by 2x every two years by Moore's law.
By design, a blockchain is resistant to modification of the data. It is "an open, distributed ledger that can record transactions between two parties efficiently and in a verifiable and permanent way".[7] For use as a distributed ledger, a blockchain is typically managed by a peer-to-peer network collectively adhering to a protocol for inter-node communication and validating new blocks. Once recorded, the data in any given block cannot be altered retroactively without alteration of all subsequent blocks, which requires consensus of the network majority. Although blockchain records are not unalterable, blockchains may be considered secure by design and exemplify a distributed computing system with high Byzantine fault tolerance. Decentralized consensus has therefore been claimed with a blockchain.[8]
A typical use case for a private blockchain is intra-business: when a company decides to implement blockchain as a business solution, they may opt for a chain to which only company members have access. This is useful if there’s no need for anybody outside of the company to become part of the chain, because private blockchains are more efficient than public and consortium chains. Also, because they are smaller and contained, it is easier for a consensus process or other technical stipulation to be altered on a blockchain. So, for example, if the developers or proprietors want to change the cryptographic method which runs its consensus process, it is much easier to do this on a private blockchain than a public or consortium chain.
Por lo tanto, y gracias a estas sidechains, se podrían conectar a Bitcoin soluciones con objetivos concretos, complementándole y aprovechando sus ventajas pero con la suficiente independencia. Para ello se usan unas piezas llamadas ‘two-way peg’, que son las encargadas de sincronizar las transferncias (validan y inmovilizan las monedas) entre ambas cadenas: la sidechain cuenta con unas monedas ya minadas pero sin dueño a la espera que, tras el intercambio, queden bajo el control del usuario que llega a esta cadena.
“We believe that public blockchains with censorship resistance have the potential to disrupt society, when private blockchains are merely a cost-efficiency tool for banking back offices. One can measure its potential in trillions of dollars, the other in billions. But as they are totally orthogonal, both can coexist in the same time, and therefore there is no need to oppose them as we can often see it.” 
“The only reason the banks have gotten to the point of thinking about permissioned ledger is because they finally reached the stage of bargaining, third stage in five stages of grief, for industry they’re about to lose. They start with denial, and the basis of denial is, well, this thing isn’t gonna work, it’s gonna die any day soon, and it doesn’t. And then they say, it’s just silly money and it doesn’t have any value, until it does; and no one else is gonna play with it, except they are; serious investors won’t put money into this, except they did; and it still refuses to die. We go from denial to bargaining. Somewhere in between might be anger, some depression, and eventually they’re going to reach acceptance, but it’s gonna take a long time. 
As you can see, several of these real-world demands for the evolution of the initial Bitcoin implementation are still highly relevant. Trade-offs between scalability and decentralization are demonstrated with Ethereum’s focus on decentralization first and resulting complexities in developing scalable solutions. The increased emphasis on smart contract functionality, pegging real-world assets to blockchains, and experimentation of altcoins that are currently ongoing also represent the forward-thinking ideas outlined in the paper.
A consortium blockchain is often said to be semi-decentralized. It, too, is permissioned but instead of a single organization controlling it, a number of companies might each operate a node on such a network. The administrators of a consortium chain restrict users' reading rights as they see fit and only allow a limited set of trusted nodes to execute a consensus protocol.
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The immense promise and accelerated development of permissioned blockchain technology, combined with intense business interest from a wide range of industries, is acting as a perfect stimulant for more and more enterprises to start rolling out blockchain networks into production. I envision these permissioned networks will soon directly or indirectly influence every facet of human enterprise.