Proxy signatures, which was proposed by Mambo, Usuda, and Okamoto in 1996, allow a designated person to sign on behalf of an original signer. In this paper, we present a new concept of proxy signature scheme, which can diminish the computational cost and the amount of the memory. This concept is suitable for the application of smart cards, whose processors and memories are rather limited even now. Furthermore, we propose two concrete schemes which are based on the Nyberg-Ruppel shceme and on the RSA scheme, respectively. We also consider the rigorous security of our proposed schemes by using the reduction among functions.
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