As u know, each time u make a payment Satoshi's client generates a new address to send change to. He (or someone else) also advised to create a new address each time someone needs to receive a payment (for anonymity reason). Entropy of an address is 160 bits (due to RIPEMD-160 "compression").
Applying Birthday Paradox we get that when 2^80 addresses are created we will, likely, get a collision. This is not critical, coz "older" address will be empty, probably. But this can be used in black PR against Bitcoin. An adversary (who is generating addresses non-stop) will be able to show 2
different public keys with the
same address. Media will be happy to publish articles with "Bitcoin completely broken" title...
I understand that the eventual collision of two keys will be blown way out of proportion and used as an attack by the media and conflicting interests. However what can we do? The current advice to not reuse keys is very sound and the benefits outweigh the risk by far.
What could a solution be? So that the media never gets this opportunity... CFB, if the key space is now 2^161 how much does this offset the probabilities in the birthday paradox? What keyspace would make any collision unlikely given every human producing a trillion addresses every nano second for thousands of years? 2^1000000?
As I see your claim, that a collision is going happen sooner than the conventional thought allows, the solution would be to make the key space so much larger that any collision is unlikely forever.
