In this paper we formalize the notion of a ring signature, which makes it possible to specify a set of possible signers without revealing which member actually produced the signature. Unlike group signatures, ring signatures have no group managers, no setup procedures, no revocation procedures, and no coordination: any user can choose any set of possible signers that includes himself, and sign any message by using his secret key and the others ’ public keys, without getting their approval or assistance. Ring signatures provide an elegant way to leak authoritative secrets in an anonymous way, to sign casual email in a way which can only be verified by its intended recipient, and to solve other problems in multiparty computations. The main contribution of this paper is a new construction of such signatures which is unconditionally signer-ambiguous, provably secure in the random oracle model, and exceptionally efficient: adding each ring member increases the cost of signing or verifying by a single modular multiplication and a single symmetric encryption.

We propose a signature system that will be very useful for controlled environments, like corporate networks, where regulation of signatures generated using the certified public/private key pairs is essential. We then demonstrate the usefulness of the system by extending it to realise a proxy signature system with revocable delegation.

Introduction Over the years, with varying degrees of success, inventors have repeatedly tried to adapt the latest technology to the cause of improved voting. For example, on June 1, 1869 Thomas A. Edison received U.S. Patent 90,646 for an \Electric Vote-Recorder" intended for use in Congress. It was never adopted because it was allegedly \too fast" for the members of Congress. Yet it is clear that we have not reached perfection in voting technology, as evidenced by Florida's \buttery ballots" and \dimpled chads." Stimulated by Florida's election problems, the California Institute of Technology and MIT have begun a joint study of voting technologies [5], with the dual objectives of analyzing technologies currently in use and suggesting improvements. This study, funded by the Carnegie Foundation, complements the Carter/Ford commision [6], which is focusing on political rather than technological issues. Electronic voting will be studied. Among people considering electronic voting sy