The new signature scheme presented by the authors in (9) is the first signature scheme based on the discrete logarithm problem that gives message recovery. The purpose of this paper is to show that the message recovery feature is inddependent of the choice of the signature equation and that all ElGamal type schemes have variants giving message recovery and achieve five new signature schemes giving message recovery. These schemes have different properties as to implementation and security. It turns out that the scheme proposed in (9) is the only inversionless scheme whereas the message recovery variant of the DSA requires computing of inverses in both generation and verification of signatures. In (9) two applications of message recovery were proposed. In the present paper it is shown how to combine ElGamal encryption and the message recovery scheme of (9) and how to securely integrate the DSA into Diffie-hellman key exchange.
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