Oblivious Polynomial Evaluation from Elliptic Code-based Symmetric Homomorphic Encryption

Oblivious Polynomial Evaluation (OPE) is an essential component of various two-party computation protocols, such as private set intersection, data mining, and oblivious keyword search. Therefore, constructing an OPE protocol that can be efficiently implemented is of utmost importance. Leveraging the homomorphic properties of encryption algorithms is an effective approach to constructing an OPE protocol. In this paper, we propose an elliptic code-based symmetric homomorphic encryption scheme utilizing the ideas of Armknecht et al., and provide parameter selections for different security levels. The encryption scheme allows for arbitrary additions and a finite number of multiplications. Building upon our encryption scheme, we further introduce two simple and practical OPE protocols, which are consistent with our encryption scheme. Our protocols achieve a high level of security and can be executed efficiently, requiring only two message transmissions for the entire OPE process. Importantly, our protocols have the capability to simultaneously compute multiple function values with minor modifications.