user51641: So the idea is you would have coins and non-coins. A coin is something you could be in possession of but can only prove it by signing messages. If you wanted to transfer it to somebody you would send it to a non-coin's public address and it would become the coin instead. I think this would give a new level of anonymity, so if you don't want people to know you have a thousand coins, they wont. But to prove you do signing each message will have to be shortened by using a program, and then the same program (even the wallet) could be used to verify multiple messages at the same time when sent in a list.

user5757: This is not really different than what we have: you can identify a "coin" as a keypair corresponding to an address with a balance, and a "non-coin" as any other keypair.  I think what you are proposing would correspond to removing the "amount" from all transactions, so that every transaction has value 1, and forbidding address reuse (rather than just discouraging it).  Then every address / keypair has balance either 1 (a "coin") or 0 (a "non-coin").
It would improve anonymity slightly; but people can achieve much the same benefit today by just choosing not to reuse addresses.  And if they don't want to make it obvious that they have a large balance in one address, they are free to split it up, or ask people to pay them across several transactions to several addresses.
Requiring every transaction to transact 1 coin could become awkward - we've seen that cryptocurrency values can fluctuate widely.  The value of 1 coin could become inconveniently small, so huge numbers of transactions would be needed to transact any significant value, causing problems with blockchain space.  (Think of the Weimar Republic photos of people using a wheelbarrow full of cash to buy a loaf of bread.)  Or, the value could become inconveniently large, so that most people could not afford to own 1 coin.  Then you need off-chain solutions for people to own fractional shares of a single coin - this adds a lot of complexity and risk.

51641: <p>So the idea is you would have coins and non-coins. A coin is something you could be in possession of but can only prove it by signing messages. If you wanted to transfer it to somebody you would send it to a non-coin's public address and it would become the coin instead. I think this would give a new level of anonymity, so if you don't want people to know you have a thousand coins, they wont. But to prove you do signing each message will have to be shortened by using a program, and then the same program (even the wallet) could be used to verify multiple messages at the same time when sent in a list.</p>
 5757: <p>This is not really different than what we have: you can identify a "coin" as a keypair corresponding to an address with a balance, and a "non-coin" as any other keypair.  I think what you are proposing would correspond to removing the "amount" from all transactions, so that every transaction has value 1, and forbidding address reuse (rather than just discouraging it).  Then every address / keypair has balance either 1 (a "coin") or 0 (a "non-coin").</p>

<p>It would improve anonymity slightly; but people can achieve much the same benefit today by just choosing not to reuse addresses.  And if they don't want to make it obvious that they have a large balance in one address, they are free to split it up, or ask people to pay them across several transactions to several addresses.</p>

<p>Requiring every transaction to transact 1 coin could become awkward - we've seen that cryptocurrency values can fluctuate widely.  The value of 1 coin could become inconveniently small, so huge numbers of transactions would be needed to transact any significant value, causing problems with blockchain space.  (Think of the Weimar Republic photos of people using a wheelbarrow full of cash to buy a loaf of bread.)  Or, the value could become inconveniently large, so that most people could not afford to own 1 coin.  Then you need off-chain solutions for people to own fractional shares of a single coin - this adds a lot of complexity and risk.</p>
