International Association
for Cryptologic Research

As a generalization of public key encryption with keyword search, public key encryption with equality test was proposed, and identity-based encryption with equality test (IBEET) is its identity-based variant. In IBEET, anyone can check whether two ciphertexts of distinct identities are encryptions of the same plaintext or not using trapdoors. Due to its functionality, IBEET cannot provide any indistinguishability-based security for trapdoor holders. As a variant of IBEET, IBEET against insider attacks (IBEETIA) was proposed, where a token is defined for each identity and is used for encryption, and anyone can check whether two ciphertexts of distinct identities are encryptions of the same plaintext or not without using trapdoors, and an indistinguishability security of IBEETIA was defined. Lee et al. (ACISP 2018) and Duong et al. (ProvSec 2019) proposed a paring-based and a lattice-based constructions, respectively. That is, current concrete IBEETIA schemes are constructed by identity-based encryption (IBE) related complexity assumptions. According to the implication result shown by Boneh et al. (FOCS 2008), IBE is recognized as a strong cryptographic primitive because no black-box construction of IBE from trapdoor permutations exist. However, Emura and Takayasu (IEICE Transactions 2023) demonstrated that symmetric key encryption and pseudo-random permutations are sufficient to construct IBEETIA which is secure in the previous security definition. These results suggest us to explore a condition of IBEETIA that requires to employ IBE-related complexity assumptions. In this paper, we demonstrate a sufficient condition that IBEETIA implies IBE. We define one-wayness against chosen-plaintext/ciphertext attacks for the token generator (OW-TG-CPA/CCA) and for token holders (OW-TH-CPA/CCA), which were not considered in the previous security definition. We show that OW-TG-CPA secure IBEETIA with additional conditions implies OW-CPA secure IBE, and show that Lee et al. and Duong et al. schemes provide the OW-TG-CPA security. On the other hand, we propose a generic construction of OW-TH-CCA secure IBEETIA from public key encryption. Our results suggest a design principle to efficiently construct IBEETIA without employing IBE-related complexity assumptions.