New Proof for BKP IBE Scheme and Improvement in the MIMC Setting

Abstract

In CRYPTO 2014, Blazy et al. [2] proposed a new and efficient identity-based encryption scheme (denoted by BKP) with almost tight security in the prime order setting. However, their scheme is transformed from affine message authentication code and cannot give a standard proof in the IBE setting. Furthermore, it is not proven secure in the multi-instance, multi-ciphertext (MIMC, or multi-challenge) setting. Based on Blazy et al.’s work, we propose a generalized almost tightly secure IBE scheme from BKP IBE scheme and give a new proof in the standard security model under the Matrix Diffie-Hellman (MDDH) assumption. Based on the generalized IBE scheme, we propose a new almost tightly secure IBE scheme in the MIMC setting. Compared with a recent IBE scheme proposed by Gong et al. in the MIMC setting, our scheme is more efficient under the decisional linear (DLIN, or 2-LIN) assumption in the symmetric bilinear groups.