Elliptic code-based oblivious polynomial evaluation

Oblivious polynomial evaluation (OPE) constitutes a crucial element in various two-party computation protocols, including private set intersection, data mining, and oblivious keyword search. Consequently, the development of an efficient OPE protocol is of paramount significance. Leveraging the homomorphic properties of encryption algorithms offers an effective avenue for constructing such a protocol. In this paper, we propose an elliptic code-based symmetric homomorphic encryption scheme that incorporates concepts introduced by Armknecht et al. We also provide parameter selection tailored to various security levels. This encryption scheme accommodates arbitrary additions and a finite number of multiplication operations. Expanding on our encryption scheme, we introduce three practical and straightforward OPE protocols that are fully compatible with our encryption framework. We complement these protocols with a comprehensive security analysis. Our protocols not only achieve a high level of security but also exhibit efficiency, requiring only two message transmissions for the entire OPE process. Furthermore, our protocols can concurrently compute function values at multiple evaluation points, whether for distinct functions or the same function.