As the Internet becomes omnipresent, people nowa-days depend heavily on the on-line services for their shopping and banking transactions. However, users register for on-line services may not like their activities being logged and analyzed by the service providers. Anonymity Is essential In the protection of users' privacy, especially now when the Internet Is a treacherous place full of embezzlers trying to collect Information of others. In 2001, Rivest et al. Introduced and formalized the ring signature In which the verifier Is convinced that the message must be signed by one of the ring members but Is unable to determine which one. Ring signature Is very useful for proving membership anonymously. With a ring signature scheme, a paid customer can prove his membership by Involving other legitimate users' Identity without help from the manager. In this paper, we propose a ring signature scheme based on the El Gamal digital signature scheme that Is provably secure against adaptively chosen ciphertext attack.