--no. You are missing the point. The collisions were not the problem, they were the symptom of the problem. The problem was, generating too few keys.
Yes, I agree. However, if one only has access to the public keys (and not the PRNG used to generate the primes), the collisions are the best way of cracking the cryptosystem.
This means the KGB (or whoever planted that bogus not-very-random generator in NETSCAPE or whatever) can break your RSA "secrets" easily by searching a small space, whose definition is known to them. Way smaller than they were supposed to need to search.
Indeed. Although I strongly believe that the poor PRNG is the result of human incompetence (remember RANDU?), rather than a deliberate effort. http://en.wikipedia.org/wiki/RANDU
Unfortunately for the KGB, the world pop of 10^10 would mean to avoid birthdays they would need to make the space be 10^20, which would be too large for them to crack.
Exactly, 2^90 possibilities is far beyond the processing power of any organisation. My e-mail was based on the assumption that true random information is expensive or difficult to obtain, as it cannot be produced by software. Sincerely, Adam P. Goucher