Abstract One-dimensional (1D) chaotic maps play a pivotal role in diverse fields, including control systems, secure communication, and modeling complex systems, enabling to capture and analyze the intricate behaviors of dynamical processes. However, their limited control parameter ranges constrain their effectiveness in security applications such as cryptography and pseudo-random number generation. Addressing these concerns, the paper proposes a universal $$e$$ e -CM chaotification model, based on Euler’s number, to enhance the chaotic control parameter range of one-dimensional maps to infinity. The efficacy of the $$e$$ e -CM model has been assessed for thirteen 1D chaotic maps including, Chebyshev, Logistic, Sine, Cubic, Coupled Sine, Cubic Logistic, Quadratic, Renyi, Simple Quadratic, Sine-Sinh-Sine, Singer, Squared Sine Logistic, and Tent maps. Various tests have been conducted to evaluate the enhanced $$e$$
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