A method includes encrypting a first plaintext vector using a relational linearity encryption scheme to generate a first linearity ciphertext and using a relational proximity encryption scheme to generate a first proximity ciphertext. The method includes communicating the first linearity and the first proximity ciphertexts to a server. The method includes encrypting a second plaintext vector using the relational linearity encryption scheme to generate a second linearity ciphertext and using the relational proximity encryption scheme to generate a second proximity ciphertext. The method includes communicating the second linearity and second proximity ciphertexts, a relational linearity key, and a relational proximity key to the server. The method includes receiving an authentication signal indicative of a linearity relationship between the first and the second linearity ciphertexts discovered using the relational linearity key and of a proximity between the first and the second proximity ciphertexts detected using the relational proximity key.