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SummaryWith the fast development of the Internet and the telecommunication technologies, internet users are carrying out various electronic transactions over internet by means of the authentication protocols. To ensure efficient and robust online transaction, security of authentication protocol turns out to be a great concern nowadays. As a result, smartcard‐based password authentication and session key agreement scheme receives significant attention in recent years. In the literature, various authentication schemes have been proposed by the cryptographic research community. Recently, Li et al. analyze some security weaknesses of the authentication scheme of Chen et al. and propose an enhancement based on the discrete logarithm problem and computational Diffie–Hellman problem. This paper further cryptanalyzes the scheme of Li et al. and identifies various security loopholes and then constructs a modified authentication scheme as a remedy. The security and efficiency evaluations demonstrate that our scheme has more security features and low computation costs than the related schemes. Copyright © 2014 John Wiley & Sons, Ltd.