Shared generation of authenticators and signatures

Often it is desired that the power to sign or authenticate messages is shared. This paper presents methods to collectively generate RSA signatures, provably secure authenticators and unconditionally secure authenticators. In the new schemes, l individuals are given shares such that k ≤ l are needed to generate a signature (authenticator) but less than k can not. When the k people have finished signing (authenticating), nobody can perform an impersonation or substitution attack. These schemes are called threshold signature (authentication) schemes. Clearly these schemes are better than each of the k individuals sending a separate authenticator for each message or if each of the k individuals each send their share to a “trusted” person who will sign for them.In all of the schemes we assume that the shareholders (senders) and receiver have secure workstations but the network and servers are not necessarily secure.