Functional encryption for set intersection in the multi-client setting

• Published in: Designs, codes, and cryptography Vol. 90; no. 1; pp. 17 - 47
• Main Authors: Lee, Kwangsu, Seo, Minhye
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.01.2022; Springer Nature B.V
• Subjects: Algorithms; Cloud computing; Coding and Information Theory; Computer Science; Cryptology; Cybersecurity; Discrete Mathematics in Computer Science; Encryption; Intersections; Servers; Private set intersection; Contact tracing; Multi-client setting; Bilinear maps; Functional encryption; 94A60
• ISSN: 0925-1022; 1573-7586; 1573-7586
• DOI: 10.1007/s10623-021-00961-w

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 ∩ 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 ( ℓ ) group elements, a function key consists of a single group element, and the decryption algorithm has O ( ℓ 2 ) complexity where ℓ 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.