Cryptology ePrint Archive: Report 2020/1154
Functional Encryption for Set Intersection in the Multi-Client Setting
Kwangsu Lee and Minhye Seo
Abstract: Functional encryption for set intersection (FE-SI) in the multi-client environment is that each client $i$ encrypts a set $X_i$ associated with time $T$ by using its own encryption key and uploads it to a cloud server, and then the cloud server which receives a function key of the client indexes $i, j$ from a trusted center can compute the intersection $X_i \cap X_j$ of the two client ciphertexts. In this paper, we first newly define the concept of FE-SI suitable for the multi-client setting. Then, we propose an efficient FE-SI scheme in asymmetric bilinear groups and prove the static security of our scheme under newly introduced assumptions. In our FE-SI scheme, a ciphertext consists of $O(\ell)$ group elements, a function key consists of a single group element, and the decryption algorithm has $O(\ell^2)$ complexity where $\ell$ is the size of a set in the ciphertext. Next, we propose another FE-SI scheme with time-constrained keys that limits the ability of function keys to be valid only for a specified time period $T$, and proves the static security of our scheme. Finally, we prove that the two assumptions hold in the general group model to provide confidence in the two newly introduced assumptions.
Category / Keywords: public-key cryptography / Functional encryption, Private set intersection, Multi-client setting, Bilinear maps
Date: received 21 Sep 2020
Contact author: kwangsu at sejong ac kr
Available format(s): PDF | BibTeX Citation
Version: 20200925:183806 (All versions of this report)
Short URL: ia.cr/2020/1154
[ Cryptology ePrint archive ]