Paper 2025/1167 Original: eprint.iacr.org/2025/1167 ↗

Security Analysis on a Public-Key Inverted-Index Keyword Search Scheme with Designated Tester

Abstract

Gao et al. (IEEE Internet of Things Journal 2024) proposed public-key inverted-index keyword search with designated tester as an extension of public key encryption with keyword search (PEKS). In their scheme, a server (a tester) has a secret key and uses the key for running the search algorithm due to the designated tester setting. They proved that no information of keyword is revealed from trapdoors under the decisional Diffie-Hellman (DDH) assumption. However, they also employed a symmetric pairing which can be seen as a DDH-solver. Thus, it is expected that information of keyword is revealed from trapdoors since the underlying complexity assumption does not hold. In this paper, we demonstrate two attacks against the Gao et al.'s scheme where information of keyword is revealed from a trapdoor. The first attack completes by using only the server's secret key in addition to the challenge trapdoor, without any additional encryption/trapdoor queries. We remark that an adversary is not allowed to obtain the server's secret key in their security model, and our attack is outside of their security model. Thus, we discuss the roles of the server, and stress that our attack scenario is reasonable. The second attack does not employ the server's secret key and utilizes linkability of two trapdoors. In both attacks, the attack complexity is just two pairing computations and is feasible in terms of the computational cost.