Secure Relative Detection in (Forensic) Database with Homomorphic Encryption

Although relative (kinship) detection has important applications in biological research, forensic identification, and many other fields, the privacy of genotype data used in the process is often overlooked. Homomorphic encryption allows for computing on encrypted genotype data directly without decryption, making it particularly suitable for privacy-preserving relative detection. Therefore, it became the competition topic for iDASH-2023 Track 1. However, combining existing kinship estimation with homomorphic encryption has two challenges: the high-dimensional matrix multiplication over encrypted data and the more time-consuming comparison over encrypted data. In this paper, we propose a secure relative detection protocol that uses homomorphic encryption to estimate the kinship between samples from two parties while protecting data privacy. We devise two new kinship estimation methods avoiding ciphertext comparisons while reducing matrix multiplication to matrix-vector multiplication. Additionally, we convert high-dimensional matrix-vector multiplication to multiple small-dimensional matrix-vector multiplications using binary dividing, which can then be processed with Halevi and Shoup's algorithm. We test the accuracy and efficiency of the protocol on the iDASH-2023 dataset. Experimental results indicate that the presented protocol outperforms existing methods with similar setups.