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To the best of our knowledge, all most previously proposed schemes based on smart cards which have the tamper resistance assumption for the smart card. However, many researches have shown that the secrets stored in a smart card can be breaches by analyzing the leaked information or monitoring the power consumption. This article will propose a new mutual authentication scheme based on nonce and smart cards. In the proposed scheme, the assumption of tamper resistance for smart cards is not essential. The computation cost, security, and efficiency of the proposed method are well suitable for the practical applications environment.