Blockchains
Blockchains introduced the first successful digital money system.
bitcoin
Bitcoin was the result of Satoshi Nakamoto, the mythical creator of Bitcoin, publishing a whitepaper and then a working implementation of the Bitcoin protocol. Satoshi solved the double spend problem that prevented prior attempts at digial money from working. Byzantine consensus is the fancy name for it, but the challenges of a decentralized network of money are obvious. Centralized monetary systems are more efficient and never have trouble with consensus since there is a single source of truth.
Plenty has been said online about the famous whitepaper they published in 2009, how they solved the double spend problem, and the basic mechanics of how it works. The power of Bitcoin comes from its widespread adoption, its stability, its "proof of work" mechanism, its reliance on cryptography, and because it was the original.
I am that heretic who claims Bitcoin has a fatal flaw that will not be fixed. That flaw is the lack of privacy baked into the protocol. With widespread adoption we set the stage for financial dystopia in my somewhat controversial opinion. Allow me to elaborate.
Imagine that your landlord, who has been eager to raise the rent, can easily know when you get a raise at work. Imagine that your healthcare provider can easily track how much you spent on drinks this weekend and the possible consequences for your insurance premium. Your spending tells a detailed story of how you live your life, who you interact with, when and where.
Now put yourself in the shoes of a business owner. Would you want your competitors to be able to see your payroll numbers? How about your vendor pricing and your costs for suppliers and contractors? Much of the financial records of a private business needs to be hidden from all but the accountants, and when paying taxes, the government.
For this reason (financial privacy) I believe Bitcoin to be fatally flawed. This follows from my belief that privacy, like security, cannot simply be bolted on, but must be an inherent part of the protcol design to be effective. Bitcoin has been more successful than others, and hs become ossified. With no centralized ledership, and core devs who value stabolity over improvement, it's hard to imagine the substantial changes that would change the situation.
monero
Monero is one of the many blockchains that aim to address this concern. Monero was designed from the outset to provide financial provacy, and actively makes protocol changes toward that end.
Monero has many features that provide privacy to users. It is a feature, not a bug, that Monero is preferred by darknet vendors. They don't prefer broken privacy coins that get them caught! Let's briefly mention some of those privacy features that distinguish Monero.
Ring signatures make it difficult to determine which output in a group is associated with the originator of a transaction.
Stealth addresses avoid exposing the recipient’s public address across multiple transactions. Users can create essentially unlimited unique payment addresses as needed.
Ring CT hides the amount being transferred while still allowing the network to verify that the transaction is valid. The original idea is credited to Greg Maxwell, one of the original Bitcoin core devs.
A transparent blockchain creates a powerful and persistent threat - a permanent financial record that can be analyzed years later.
other privacy coins
Plenty of other privacy coins exist, but few are noteworthy. Zcash is one of the original privacy blockchains, started by Zooko Wilcox - of Zooko's triangle fame. It features excellent cryptography, updated frequently but has typiclly been seen as slower, clunkier and offering less privacy than competitors like Monero.
Grin is another popular privacy coin noteable for introducing mimblewimle, which we'll discuss later. It is not widely used, and has properties that some users are uncomfortable with. There are few developers, and it has a small anonymity set, making it not so popular.
layer 2 privacy and anonymity solutions
There are a lot of layer 2 solutions that claim to give users exceptional privacy or anonymity. These claims are often based on the use of modern technology like zero-knowledge proofs. They usually suffer from weak anonymity due to being used by a very small number of users; i.e. the anonymity set is small.
These layer 2 solutions often sit on top of transparent blockchains, which means users can be known and tracked up to the point of transferring to the layer 2, and often, again when coming back. This renders the relatively better anonymity of the layer 2 useless. It's not just the userbase that's small, the dev team is often in over their heads, and introduce exploitble bugs.
mimblewimble
Mimblewimble is named after a vanishing spell in Harry Potter; it's goal is to provide increased privacy and reduced traceability of on-chain activity by the following techniques.
Note that mimblewimble does not prevent timing attacks, or vonvel users entering and exiting the privacy blockchain. In general, blockchains with fewer users can expect lesser privacy.
Confidential Transactions hide the transaction amounts. Users can still verify that inputs equal outputs, meaning that no new coins were created.
Stealth adresses hide the actual addresses. The original mimblewimble used no addresses at all, but is less convenient, as both aprties need to come online to partcipate in creting the transaction.
Transaction aggregation is simply combining multiple transactions into one larger one. If address A pays B, address C pays D, and E pays F, they can be replaced by A, C, E pays to B, D, and F. This is similar to coinjoin.
Cut-through is the idea that if A sends to B and B sends to C, and the amounts are the same, then it can all be replaced by A sends to C.
Compacted transaction history is about only the outputs and a cryptogaphic proof being stored instead of all the transaction details.