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Most of the web applications require security which in turn requires random numbers. Pseudo-random numbers are required with good statistical properties and efficiency. Use of chaotic map to dynamically perturb another chaotic map that generates the random bit output is introduced in this work. Perturbance is introduced to improvise the chaotic behaviour of a base map and increase the periodicity. PRNG with this architecture is devised to generate random bit sequence from initial keyspace. The statistical properties of newly constructed PRNG are tested with NIST SP 800-22 statistical test suite and were shown to have good randomness. To ensure its usability in cryptographic applications, it has been analyzed for the size of its keyspace, key sensitivity and performance speed. The test results provide evidence that newly designed PRNG has a 3.6% increase in keyspace and a 5% increase in its performance speed compared to existing chaotic PRNGs. The novel PRNG can be used for cryptographic applications with a faster generation of keys and increased security.