Efficient Designated Verifier Signature Schemes

This paper proposes a designated verifier signature based on the Schnorr signature scheme. One of the advantages of the new scheme compared with the one proposed by Jakobsson, Sako and Impagliazzo is that not only the designated verifier (Bob) cannot convince a third party (Cindy) that a signature is originated by a given signer (Alice), but also nobody else other than Bob can even check the validity or invalidity of such a signature without the intervention of Bob. Other advantages of our scheme are the low computational cost and the small size of the resulting signature. Generating a signature requires only 1 modular exponentiation, while the verification needs 2 modular exponentiations.