SM9 Identity-Based Encryption with Designated-Position Fuzzy Equality Test

Public key encryption with equality test (PKEET) is a cryptographic primitive that enables a tester to determine whether two ciphertexts encrypted with same or different public keys have been generated from the same message without decryption. Previous studies extended PKEET to public key encryption with designated-position fuzzy equality test (PKE-DFET), enabling testers to verify whether plaintexts corresponding to two ciphertexts are equal while ignoring specific bits at designated positions. In this work, we have filled the research gap in the identity-based encryption (IBE) cryptosystems for this primitive. Furthermore, although our authorization method is the all-or-nothing (AoN) type, it overcomes the shortcomings present in the majority of AoN-type authorization schemes. In our scheme, equality tests can only be performed between a ciphertext and a given plaintext. Specifically, even if a tester acquires multiple AoN-type authorizations, it cannot conduct unpermitted equality tests between users. This significantly reduces the risk of user privacy leaks when handling sensitive information in certain scenarios, while still retaining the flexible and simple characteristics of AoN-type authorizations. We use the Chinese national cryptography standard SM9-IBE algorithm to provide the concrete construction of our scheme, enhancing the usability and security of our scheme, while making deployment more convenient. Finally, we prove that our scheme achieves F-OW-ID-CCA security when the adversary has the trapdoor of the challenge ciphertext, and achieves IND-ID-CCA security when the adversary does not have the trapdoor of the challenge ciphertext.