A transcendental number has the nice property of being random with its digit expansion, but its potential for cryptography and security protocol applications has not been fully explored to date. In this paper, we bring out a random insertion method using the transcendental numbers that can be applied toward new challenges in security and privacy fields like defending machine learning based privacy attacks. To make the random insertion method applicable toward continuous back-and-forth communications, we propose to explore the nice properties of a transcendental number generator that allows low cost for frequent key distributions. We further analyze the security of the encryption method, identify the limits, and bring out a security protocol to overcome the limits.