Relational Encryption For Password Verification

A method of equality verification using relational encryption including receiving a relational key that includes a first relational key component and a registration ciphertext that includes an encryption of a first plaintext data set. The method includes storing the registration ciphertext without decrypting the registration ciphertext. After the storing of the registration ciphertext, the method includes receiving an authentication request and communicating a safeguard data set that includes a random challenge in response to the authentication request. The method includes receiving an encrypted response that is generated based on the safeguard data set and a second plaintext data set. The method includes verifying a relationship between the encrypted response and the registration ciphertext using the relational key without decrypting the encrypted response and without decrypting the registration ciphertext. The relationship indicates that equality exists between the first and the second plaintext data sets.