Packed Homomorphic Encryption Based on Ideal Lattices and Its Application to Biometrics

Abstract

Among many approaches for privacy-preserving biometric authentication, we focus on the approach with homomorphic encryption, which is public key encryption supporting some operations on encrypted data. In biometric authentication, the Hamming distance is often used as a metric to compare two biometric feature vectors. In this paper, we propose an efficient method to compute the Hamming distance on encrypted data using the homomorphic encryption based on ideal lattices. In our implementation of secure Hamming distance of 2048-bit binary vectors with a lattice of 4096 dimension, encryption of a vector, secure Hamming distance, and decryption respectively take about 19.89, 18.10, and 9.08 milliseconds (ms) on an Intel Xeon X3480 at 3.07 GHz. We also propose a privacy-preserving biometric authentication protocol using our method, and compare it with related protocols. Our protocol has faster performance and shorter ciphertext size than the state-of-the-art prior work using homomorphic encryption.

Privacy-Preserving Biometric Authentication: Challenges and Directions

“…A common practice is to preserve the user's privacy by encrypting the sensitive data. For example, Yasuda et al 's privacy-preserving biometric authentication scheme works as follows [14]. The sensor S encrypts the provided fresh biometric template obtaining̃= Enc( ) (here the encryption scheme is based on a packing method for polynomials).…”

“…In fact, cryptography tends to amplify small differences and it is not errortolerant (e.g., hashing, AES, and RSA). The main cryptographic tools used to combat the leakage of private information during biometric authentication are secure multiparty computation (SMPC) [14], verifiable computation (VC), and bloom filters (see Box 2).…”

Efficient Verifiable Computation of XOR for Biometric Authentication

“…By mounting a variant of the hill climbing attack [5], performing multiple repeated attempts, each time carefully choosing v, the stored template b i can be retrieved. Such attacks against several protocols proposed in [6][7][8] are presented in [9][10][11]. Therefore, in similar applications it is important to verify the correctness of the outsourced computation, namely, the computation of XORing encrypted bitstrings.…”

“…There are also other protocols for privacy-preserving biometric authentication that are based on additive HE [14,20] such as [21] for face recognition and its subsequent improvement in [22], as well as the protocol in [23]. Yasuda et al proposed two biometric authentication protocols using somewhat HEs based on ideal lattices [6] and ring learning with errors [7], and the security of these protocols is scrutinised in [9,10]. In most of these schemes, biometric templates are extracted as bitstrings and the similarity of two biometric templates is measured by computing the Hamming distance between them.…”

Efficient homomorphic encryption on integer vectors and its applications

“…In [16], Smart and Vercauteren develop a technique to pack ciphertexts based on polynomial-CRT. In [17], Yasuda, et al, develop a technique to pack ciphertexts based on ideal lattices and apply it to biometrics. In [18], Cheon, et al, extend the scheme of van Dijk, et al, [12] to support encrypting and processing a binary vector.…”