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Because the mobile agent can provide the essential properties of personalization, automation, intelligence, etc., it plays an increasingly important role in electronic business applications. As far as mobile agent security is concerned, we develop a proxy signature scheme for protecting mobile agents against malicious agent hosts. The proposed proxy signature scheme can protect users' private keys stored in smart cards, and provide the fairness of contracts signed by agents. In addition, we also design a proxy authenticated encryption scheme so that the signature of the contracts will satisfy users' constraints, and the non-repudiation of servers can be achieved. On the other hand, as far as agent host security is concerned, we apply the idea of proxy signature to construct an authentication scheme for protecting agent hosts. This scheme is to achieve the requirements of authentication and authorization. Hence, we affirm that the proposed security schemes are suitable for practical electronic business applications in mobile-agent-based network environments.