I'm working on the blinding portion of some RSA code. Some implementations I've looked at don't verify that the random number used for blinding is relative prime to N as described on the Wikipedia page for blinding:
RSA blinding involves computing the blinding operation E(x) = (xr)e mod N, where r is a random integer between 1 and N and relatively prime to N (i.e. gcd(r, N) = 1)
I assume this is because finding the blinding factor is expensive (is GDC the fastest/only way?). That being said, how much of a security risk does the random number used for blinding not being relatively prime to N pose?