In the year (1879–1884), George Cantor coined few problems and consequences in the field of set theory. One of them was the Cantor ternary set as a classical example of fractals. In this paper, 5-adic Cantor one-fifth set as an example of fractal string have been introduced. Moreover, the applications of 5-adic Cantor one-fifth set in string theory have also been studied.

Chaotic cryptosystems are using for securing text data and images over the network. In 1998, M S Baptista suggested a chaotic cryptosystem based on partitioning the visiting interval of chaotic orbits of the logistic map, which attracted much attention. In 2002, K W Wong presented a prompt chaotic cryptosystem based onthe dynamic lookup table using a logistic maptoimprove the security in Baptista type cryptosystem. In 2004, Alvarezet al. [1] found that Wong’s cryptosystem [15] is not resistant tochosen-plaintext and known-plaintext attacks. To improve the security of the dynamic lookup table, weintroduce an alternate dynamic lookup table that will be more secure in context to the existing system.