The telecare medicine information system enables or supports health-care delivery services. In order to safeguard patients' privacy, such as telephone number, medical record number, health information, etc., a secure authentication scheme will thus be in demand. Recently, Wu et al. proposed a smart card based password authentication scheme for the telecare medicine information system. Later, He et al. pointed out that Wu et al.'s scheme could not resist impersonation attacks and insider attacks, and then presented a new scheme. In this paper, we show that both of them fail to achieve two-factor authentication as smart card based password authentication schemes should achieve. We also propose an improved authentication scheme for the telecare medicine information system, and demonstrate that the improved one satisfies the security requirements of two-factor authentication and is also efficient.
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