Oddbean

Ecash seems like a single anonymity set because you can freely transfer in and out of mints using Lightning. i.e make a deposit to one mint, then transfer to one or more other mints. If sats can seamlessly and privately flow throughout all mints then it appears to me that they share the larger anonymity set. Unless I’m missing something, it seems receiving ecash would be the same as receiving monero.

Tokens are unique to each mint. Every time you leave a mint over lightning you reveal amount + destination to the original mint (a potential point of de-anonymization/reduced anonymity). You're also narrowing down your anon set the larger value of tokens you hold (ecash tokens have "buckets" of 1,2,4,8,16, 32...etc, increasingly fewer denominations exist the larger the bucket)

I read somewhere that you can just give the ecash token to a second mint and they can fetch the amount from the first mint. In this way you could move funds between mints, and even spread funds around, without revealing your identity or amount held.

Not sure how you could do that without revealing amounts to the 2nd mint because they'll know the amount they receive in lightning from the 1st mint (and know it's from the 1st mint since they're redeeming it's token), and the 1st mint will know the amount they're sending to the 2nd mint even if they're not colluding. And it still wouldn't solve the reduced anon set from "larger bucket" ecash holders unless you spread funds around like you said or never send/receive larger payments.Still better anonymity and privacy than Bitcoin, but coming back to my original point...ecash doesn't necessarily have a larger group to hide in just because it is ecash. I was kind of surprised the other day to find out that mints can tie IP addresses to specific tokens (maybe that should've been obvious), so I like what Mutiny is doing with Harbor running everything behind Tor

Yes, the second mint would know how much they’re receiving but not how much you have in total. The first mint would know how much they’re sending but wouldn’t know who’s sending it. Sounds like tor is crucial for this to stay private and also important to transact in relatively small amounts. I thought this was helpful: https://docs.cashu.space/faq