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Insecure communication in digital image security and image storing are considered as important challenges. Moreover, the existing approaches face problems related to improper security at the time of image encryption and decryption. In this research work, a wavelet environment is obtained by transforming the cover image utilizing integer wavelet transform (IWT) and hybrid discrete cosine transform (DCT) to completely prevent false errors. Then the proposed hybrid chaotic map with L-shaped fractal Tromino offers better security to maintain image secrecy by means of encryption and decryption. The proposed work uses fractal encryption with the combination of L-shaped Tromino theorem for enhancement of information hiding. The regions of L-shaped fractal Tromino are sensitive to variations, thus are embedded in the watermark based on a visual watermarking technique known as reversible watermarking. The experimental results showed that the proposed method obtained peak signal-to-noise ratio (PSNR) value of 56.82dB which is comparatively higher than the existing methods that are, Beddington, Free, and Lawton (BFL) map with PSNR value of 8.10 dB, permutation substitution, and Boolean operation with PSNR value of 21.19 dB and deoxyribonucleic acid (DNA) level permutation-based logistic map with PSNR value of 21.27 dB. [ABSTRACT FROM AUTHOR]