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Proxy signatures allow a signer to delegate signing ability to a proxy signer. Many schemes have been proposed for proxy signatures under typical security requirements. The authors propose a proxy signature model with extended security requirements. Based on Shamir's online/offline signature scheme, a proxy signature scheme is proposed for the model. In addition to the typical requirements, the proposed scheme satisfies other very important security requirements. It is shown that the scheme can provide signature indistinguishability, restrict the proxy signing power, provide signature unlinkability, resolve internal disputes, and is more efficient.