Approximating Step and Sigmoid Functions for Homomorphic Biometric Decision Gates

Core engineering and protocols for Encrypted Threshold Comparison.

The Challenge of Non-Linearity in Homomorphic Encryption

Homomorphic cryptosystems natively support only addition and multiplication. Evaluating whether a match score s exceeds an authentication threshold T requires a step function, which is non-linear and non-polynomial. FHEID utilizes high-degree Chebyshev polynomial approximations to compute continuous step approximations homomorphically.

Client-Side Zero-Knowledge Verification

The output of the homomorphic comparison is an encrypted single bit representing success or failure. The verifying terminal decrypts this single bit using its private key: if 1, access is granted; if 0, access is denied. Neither the cloud server nor potential eavesdroppers learn the actual biometric match score, preventing biometric hill-climbing attacks.