Efficient Decryption Algorithms for Extension Field Cancellation Type Encryption Schemes

Abstract

Extension Field Cancellation (EFC) was proposed by Alan et al. at PQCrypto 2016 as a new trapdoor for constructing secure multivariate encryption cryptographic schemes. Along with this trapdoor, two schemes $\text {EFC}_p^{-}$ and $\text {EFC}_{pt^2}^{-}$ that apply this trapdoor and some modifiers were proposed. Though their security seems to be high enough, their decryption efficiency has room for improvement. In this paper, we introduce a new and more efficient decryption approach for $\text {EFC}_p^{-}$ and $\text {EFC}_{pt^2}^{-}$, which manages to avoid all redundant computation involved in the original decryption algorithms, and theoretically speed up the decryption process of $\text {EFC}_p^{-}$ and $\text {EFC}_{pt^2}^{-}$ by around 3.4 and 8.5 times, respectively, under 128-bit security parameters with our new designed private keys for them. Meanwhile, our approach does not interfere with the public key, so the security remains the same. The implementation results of both decryption algorithms for $\text {EFC}_p^{-}$ and $\text {EFC}_{pt^2}^{-}$ are also provided.