Fast remote user authentication scheme with smart card based on quadratic residue

There are many kinds of online services in our daily life, such as e-mail and messenger. When we link to a remote host, we are required to login first, supplying a username and the corresponding password, and then obtain the resources or have services. Most commonly, we might use a smart card to assistant us to login a remote site. In 1981, Lamport proposed a remote authentication scheme for communication through insecure channels. Lu and Cao further proposed an efficient scheme based on quadratic residue in 2005. In the Lu-Cao scheme, it is unnecessary for the server to store the verification table. However, some obvious drawbacks are that users cannot freely choose their own passwords and their scheme is inefficient due to complex computations. In this paper, we proposed an improvement of the Lu-Cao scheme to make it more efficient and secure.