A sidechain is a separate blockchain that is attached to its parent blockchain using a two-way peg. The two-way peg enables interchangeability of assets at a predetermined rate between the parent blockchain and the sidechain. The original blockchain is usually referred to as the ‘main chain’ and all additional blockchains are referred to as ‘sidechains’. The blockchain platform Ardor refers to its sidechains as ‘childchains’.
This construction is achieved by composing smart contracts on the main blockchain using fraud proofs whereby state transitions can be enforced on a parent blockchain. We compose blockchains into a tree hierarchy, and treat each as an individual branch blockchain with enforced blockchain history and MapReducable computation committed into merkle proofs. By framing one’s ledger entry into a child blockchain which is enforced by the parent chain, one can enable incredible scale with minimized trust (presuming root blockchain availability and correctness).

Walmart recently filed patents that could allow the retailer to store vendor and consumer e-commerce payment data using blockchain technology to improve security. This application would encrypt payment information in digital shopping systems and create a network able to automatically conduct transactions on behalf of a customer. The payments would be received by one vendor or more, depending on the services and who provided them.
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.

Sidechains are an essential innovation in the blockchain field with some interesting long-term implications and effects on the broader interoperability and scalability of blockchain networks. They are effectively extensions of existing blockchains that increase their functionality and allow for validation of data from other blockchains and for assets to be seamlessly transferred between them.
In order to trade assets from the mainchain for assets from the sidechain, one would first need to send their assets on the mainchain to a certain address, effectively locking the assets up. After the transaction has been completed, a confirmation will be communicated to the sidechain. The sidechain will then release a certain amount of the assets on the sidechain to the user, equivalent to the amount of assets ‘locked up’ on the mainchain times the exchange rate. To trade the assets from the sidechain for assets of the mainchain, one would need to do the same, just the other way around.

Of course, the drawbacks of public and private blockchains are still very much present in the case consortium chains. This all depends on the way each consortium is constructed: a more public consortium chain will bear the burdens of public chains, while a more private one might suffer from the relative lack of openness and disintermediation. The right configuration depends on the needs and vision for each specific chain. Strategy and tailoring are always necessary to get the best solution.

In private blockchains, only specific, pre-chosen entities have the ability to create new transactions on the chain (this is known as “write permissions”). Thus, a private blockchain is a closed network that offers constituents the benefits of the technology, but is not necessarily decentralized or distributed, even among its members. The extent to which each constituent can view (“read”) and create and validate transactions (“write”) is up to the developers of the chain.

The two-way peg is the mechanism for transferring assets between sidechains and is set at a fixed or predefined rate. Bitcoin’s Dynamic Membership Multi-Party Signature (DMMS) plays a vital role in the functionality of the two-way peg. The DMMS is one of Bitcoin’s lesser known but incredibly important components. It is a group digital signature — composed of the block headers in Bitcoin — that has no fixed size due to the computationally powered PoW nature of its blockchain. The Pegged Sidechain paper further describes it as:

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Many people believe this is the future of the blockchain. It maintains network security and allows for scalability. The biggest criticism is that it heavily favors those with more funds as smaller holders have no chance of becoming witnesses. But the reality is, smaller players have no hope of participating in Proof of Work either, as mining from your own laptop at home is no longer a reality. Smaller players get outcompeted by bigger players who have massive mining rigs. STEEM and EOS are examples of DPOS blockchains. Even Ethereum is moving to POS with its Casper project.
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$.

Always there is a balance in nature, even in blockchains. If you want to have extra features, you need to make a sacrifice from your current features. For example to have high speed and volume; you need to give some from your security & immutability by doing consensus with smaller groups or you need to use different methods in consensus like POS / PBFT. (Proof of Stake / Practical Byzantine Fault Tolerance)
Congratulations! You’ve just educated yourself on the most common advanced topics in blockchain that you’ll hear about. By understanding these concepts, you have a firmer grasp on the fundamental tradeoffs and latest research on the blockchain than most industry “experts”! Better yet, next time you hear your colleagues around the water cooler talking about state channels, the Lightning Network and Byzantine fault tolerance, not only will you know what they’re talking about but you might be able to teach them a thing or two!
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.
Blockchains that are private or permissioned work similarly to public blockchains but with access controls that restrict those that can join the network, meaning it operates like a centralised database system of today that limits access to certain users. Private Blockchains have one or multiple entities that control the network, leading to the reliance on third-parties to transact. A well-known example would be Hyperledger.