ElGamal Encryption

From: Johanna Bernstein (johanna.bernstein_nospam_at_yahoo.com)
Date: 07/19/05 

Date: Tue, 19 Jul 2005 02:11:35 +0200

Hi,

as far as I know, for the ElGamal-Encryption of a message m \in Z_q a
generator g of the cyclic group Z_q is choosen, where q is a large
prime. Now one calculates her secret key a \in {0,...p-2} and calculates
the public key as: y=g^a mod q.
An encryption of m looks then like: C=(g^r, y^r*m), where r \in Z_q.

I want now to know, whether it is ok to change the ElGamal-scheme a bit:
Let p be a prime, so that q divides p-1. Now g is *not* a generator of
Z_q, rather an element of order q from Z_p. Is it still possible to
encrypt/decrypt with ElGamal? If not in general, then maybe is there a
special case, when it is possible?

Thanks in advance,
Johanna

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