## Cryptology ePrint Archive: Report 2017/004

A New Approach for Practical Function-Private Inner Product Encryption

Sungwook Kim and Jinsu Kim and Jae Hong Seo

Abstract: Functional Encryption (FE) is a new paradigm supporting restricted decryption keys of function $f$ that allows one to learn $f(x_j)$ from encryptions of messages $x_j$. A natural and practical security requirements for FE is to keep not only messages $x_1,\ldots,x_q$ but also functions $f_1,\ldots f_q$ confidential from encryptions and decryptions keys, except inevitable information $\{f_i(x_j)\}_{i,j\in[q]}$, for any polynomial a-priori unknown number $q$, where $f_i$'s and $x_j$'s are adaptively chosen by adversaries. Such the security requirement is called {\em full function privacy}. In this paper, we particularly focus on function-private FE for inner product functionality in the {\em private key setting} (simply called Inner Product Encryption (IPE)). To the best of our knowledge, there are two approaches for fully function-private IPE schemes in the private key setting. One of which is to employ a general transformation from (non-function-private) FE for general circuits (Brakerski and Segev, TCC 2015). This approach requires heavy crypto tools such as indistinguishability obfuscation (for non-function-private FE for general circuits) and therefore inefficient. The other approach is relatively practical; it directly constructs IPE scheme by using {\em dual pairing vector spaces (DPVS)} (Bishop et al. ASIACRYPT 2015, Datta et al. PKC 2016, and Tomida et al. ISC 2016).

\quad We present a new approach for practical function-private IPE schemes that does not employ DPVS but generalizations of Brakerski-Segev transformation. Our generalizations of Brakerski-Segev transformation are easily combinable with existing (non-function-private) IPE schemes as well as (non-function-private) FE schemes for general circuits in several levels of security. Our resulting IPE schemes achieve better performance in comparison with Bishop et al. IPE scheme as well as Datta et al. IPE scheme while preserving the same security notion under the same complexity assumption. In comparison with Tomida et al. IPE scheme, ours have comparable performance in the size of both ciphertext and decryption key, but better performance in the size of master key.

Category / Keywords: public-key cryptography / Functional encryption, inner product encryption, function privacy