In this paper, a class of topologically conjugated maps of tent map is established, and the sampling rule is proved to generate the independently and uniformly distributed key streams. One example is given to show that the established chaotic system does not converge into zero in each parameter due to its nonlinear characteristic. Another example with different initial values and lengths of sequence is illustrated, in which the chaotic key stream generated by the proposed theorem is independently and uniformly distributed chaotic system and can successfully satisfy the randomness requirements in Federal Information Processing Standard 140-2(FIPS PUB 140-2) and National Institute of Standards and Technology Special Publication 800-22 (NIST SP800-22) test. The result in this paper can provide the theoretical foundation and more selections of systems to generate independently and uniformly distributed chaotic key stream.