Human biometric images are utilized for cell phone authentication, airport security, and biometric passports. To improve the biometric identification process, this should be protected from cyber attackers because it is sensitive to any minor changes. Thus, security is a major concern in biometric images. Traditional encryption and compression methods are ineffective for encrypting biometric images due to their high execution time and algorithm complexity. In this paper, a novel 2D chaotic sine map is proposed for generating encryption keys and improving security for biometric identification systems. The proposed scheme uses the 2D chaotic map to generate the private key and diffusion process. Here, the Hénon-Sine Map (HSM-512), Secure Hash Algorithm (SHA-256), and DNA computing are also used in the key generation process. The pixel values of the original images in the proposed schemes are shuffled using Mersenne Twister (MT) to improve the security of biometric images. Moreover, the Differential Huffman Compression (DHC) method is used for lossless compression while performing the XOR-based encryption process. The proposed model has been tested on different RGB biometric images, namely the SOCOFing dataset and the COVID-19 chest X-ray dataset. The experiment results have been evaluated using many performance metrics, such as entropy, key space, histogram analysis, key sensitivity, robustness analysis, correlation, and similarity analysis. The outcomes demonstrate that the proposed scheme is more effective than the state-of-the-art schemes.