Hash chains are used extensively in various cryptography applications such as one-time passwords, server-supported signatures and micropayments. In this paper, we present a method, called infinite length hash chains to improve the flexibility of this chaining idea by using public-key techniques. One of its distinguishing features is that communication and computation overhead of restarting of the system is avoided For the owner of the chain it is possible to go in either way in the chain at any time without any restriction in the chain length, but others see no difference as the functionality it provides with respect to traditional hash chains. On the other hand the drawback here is the increased computation cost due to public-key operations. Part of our work would be considered as one additional step after traditional one-time passwords in the natural progression from fixed password schemes to challenge-response identification protocols.