In one of my assignments, I had the following question (Please read on. Not a homework assignment :) ):
X.509 (1998 version) lists properties that RSA keys must satisfy to be secure. One such requirement is that the public exponent $e > \log_2(n)$ where n is the modulus. Consider the following justifications for this:
- We require $e > \log_2(n)$ in order to prevent an attack to disclose the plaintext by taking the eth root modulus n.
- We require $e > \log_2(n)$ in order to prevent an attack to disclose the plaintext by taking the eth integer root.
Which of these two is the correct justification of the above requirement? For the incorrect justification, explain why is it incorrect.
My question here is: Where is the X.509 certificate listed mentioning the above requirement? I tried googling a lot but could not find any such requirement listed in any online available material unfortunately. Also, if any such requirement does exist, what is the justification for the same?