0
$\begingroup$

In the ElGamal cipher, the key generation algorithm needs to randomly sample a generator g and test whether g is a safe generator or not each time. I wonder whether we can use a fixed safe generator for all users, which may reduce the time of key generation. Will this be safe?

$\endgroup$

1 Answer 1

2
$\begingroup$

The generator $g$ is always assumed to be public and does not need to be generated as part of the KeyGen. Specifically, the whole Diffie-Hellman group description (which includes $g$) can fixed. For example, see https://en.wikipedia.org/wiki/ElGamal_encryption#Key_generation

$\endgroup$
3
  • 1
    $\begingroup$ What's more, in elliptic-curve ElGamal, the base-point is almost always fixed. $\endgroup$
    – DannyNiu
    Nov 18 at 12:11
  • $\begingroup$ Thanks so much! $\endgroup$
    – Saint Gold
    Nov 18 at 14:18
  • $\begingroup$ I think I understand now ... The reason that ElGamal is described in a random generator way is to prove its security under a weaker assumption (HDH). For a fixed generator, we need a stronger assumption ... $\endgroup$
    – Saint Gold
    Nov 18 at 15:47

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Not the answer you're looking for? Browse other questions tagged or ask your own question.