Preamble / Motivation:
Motivated by discussions on various threads, I started looking more thoroughly into L1 blockchain privacy - covering what is available in terms of academic research, implementation in various altcoins and upsides & drawbacks of different methods.

This thread is dedicated for sharing ideas and research, as well as discussing and educating, about privacy solutions that could be implemented in Bitcoin in the future. Hopefully, it could even become the starting ground for development of concrete BIPs.
What I am specifically looking for in existing implementations is that they do have to work with UTXO-based cryptocurrency, they do need to work with PoW, they do need to work without a centralized, trusted setup ceremony and generally have to work on Bitcoin.

This is not an altcoin discussion; its sole goal is trying to find one or more L1 privacy solution candidates for Bitcoin.

As I'm still learning a lot on this subject, I appreciate suggestions for changes and additions to whatever I write next..
I will also add more sections / lists in place of reserved posts over time.

The set of lists and the lists themselves are by no means definitive or authoritative; merely a starting point, and will be maintained. Yes, I even leave question marks wherever I'm sure more information has to be added since I'm not educated enough on these topics. We're all going to learn something together here...

Selected privacy-focused altcoin projects, techniques employed and limitations:

• Monero
  
  • Ring signatures: obfuscate UTXOs
    
  • Ring confidential transactions: hide amounts (range proof)
    
  • Bulletproofs: much more efficient NIZK range proofs
    
  • Stealth addresses: sender generates unlinkable one-time address from given public key
    
  • Drawbacks: larger transaction size, ... ?
• Zcash
  
  • Zerocoin: basically in-protocol mixing for existing coin e.g. Bitcoin, precursor of Zerocash
    
  • Zerocash: successor of Zerocoin: smaller, faster verifiable transactions, variable amounts, spendable directly to receiver
    
  • Drawbacks: centralized 'key creation ceremony' required, larger transaction size, ... ?
    
• Grin
  
  • MimbleWimble: complete new protocol for confidential transactions and smaller transactions
    
  • Drawbacks: ... ?

Layer 1 privacy concepts that could / do work in Bitcoin:

• CoinJoin (Greg Maxwell): combine transactions to hide who pays whom - usable today
  
• CoinSwap (Greg Maxwell): swap coins with someone else to get new transaction history - usable today
  
• Confidential Transactions (Greg Maxwell): hide transaction value - sidechain / softfork needed
  
• MimbleWimble: complete new protocol for confidential transactions and smaller transactions - big fork needed (? To-do: look into how it was done on LTC)