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I came across a blog post where it mentions that the taproot update is promised to speed up BTC transactions, lower their fees, etc. but does this mean that literally, anyone sending or receiving BTC will benefit from it? will it require special software to operate?

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Bitcoin transactions require a certain size and with taproot and tapscript we can decrease that size.

This means that effectively we will be able to store more transactions in one block allowing overall a slightly higher throughput of bitcoin transactions in the network.

So even if you continue to use legacy transaction formats you might still benefit from the fact that the blockchain might be less congested as it can fulfill a higher demand with the same space.

Of course if you want to use it you will need a wallet / software that supports the new format but as it seems it will be merged to bitcoin so modern wallets should be compatible and also implement it.

The only direct benefit that you get from switching to taproot is that your tx will be smaller in size allowing you to either save on fees or if you want to pay the same fees allow you to have a higher feerate. Though miners are not forced to mine transactions with highest fee rates first they are certainly economically incentivized to do so. Thus besides doing something good for the network your tx might also be confirmed faster.

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In addition to what Rene wrote, the adoption of Taproot will provide many bitcoin user's with a higher degree of privacy.

The structure of a bitcoin transaction can contain clues about the nature of that transaction. By using certain heuristics, anyone watching the blockchain record can group together certain transactions and addresses, to attempt to identify users/wallets, and track the flow of funds through the network.

The adoption of taproot will allow some types of more complicated transactions to not leave such an obvious footprint on the chain. Instead, these transactions will just look like much more basic transactions, which don't leave as many clues behind. This is of benefit to the users who are creating those transactions, as it will now be less clear what the nature of their transactions are, in the view of third-party blockchain-spies.

Initially, pay-to-taproot outputs will be somewhat unique and obvious on the network, but as time passes and adoption increases, we might expect to see a larger 'anonymity set**' form for users of taproot.

This blog post seems to be a good in-depth discussion of the privacy implications of taproot: https://braiins.com/blog/explain-like-im-not-a-developer-taproot-privacy

** you can think of an anonymity set like a measure of plausible deniability. If the anonymity set of your UTXO is 1, then that means there is no denying it is yours. If the transaction graph history can at best narrow down the ownership of an output to 100 different people, then your anonymity set would be 100 (ie, higher plausible deniability), etc

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