Quote from: raid_n on January 30, 2014, 03:46:35 PM

Quote from: mgburks77 on January 30, 2014, 03:21:21 PM

These collisions are unavoidable due to the nature of multiple access electronic networks?

No, those collisions are unavoidable because of the way you generate your private/public key.
There is no authority issuing you address 1,2,3,....n with the corresponding key. You yourself ( well more likely your software although you could run the algorithm on paper or in your head) are creating the pairings.
Now the address space to choose from is very large, in fact you could give each atom on this planet its own address if you wanted and still have more than enough left [edit] While the private key is 2^256 bit which would fit the approximate 2^166 bits needed to address each atom the corresponding public address derived ( 2^160) does not quite cover it [/edit]

So simply choosing a random number for generating this will be sufficient. This way there does not need to be any authority that creates them and hence knows the private key.

On the other hand if everyone comes and chooses a number between 1 and say 1 million then you are reducing your previous large address space to that of effectively 1 million
In a sense this also happens if your (pseudo) random number generator becomes predictable. Say you use the current time as an input to generate a random number.
If i know the day you created that random number and the algorithm were to only rely on the current time and nothing else to generate random numbers I can try through the very limited time-space of that day to try and figure out what "random number" you used.

In fact I believe the NSA compromised a standard method on random number generation so that it would produce predictable results and allow them to take advantage of that

[edit]

here is the description of how the address is derived: https://en.bitcoin.it/wiki/Technical_background_of_version_1_Bitcoin_addresses
The RIPEMD-160 hashing step reduces the possible address space to 2^160 bits
[/edit]

Thank you!