Biometric authentication in high-security environments such as customs and defense facilities requires strong protection of raw and intermediate data, especially when incomplete fingerprints are involved. Conventional encryption schemes, designed for intact images, often fail to adapt to such degraded samples. To address this issue, we propose an image encryption framework based on the two-dimensional Exponential-Logistic-Sine Chaotic Map (2D-ELSCM). The framework integrates a logarithmic fractional digit-driven scrambling strategy and a bidirectional ciphertext feedback diffusion mechanism, achieving global decorrelation, enhanced avalanche effects, and strict reversibility. Experimental results confirm its strong security, adaptability, and feasibility for protecting biometric privacy.