FFEC: Fast and forward-secure equivalence-based ciphertext comparability for multiple users in cloud environment

With the expansion of cloud computing, an increasing amount of sensitive data is being encrypted and stored in public clouds to alleviate storage and management burdens. Secure equivalence-based retrieval of ciphertexts for multiple users is crucial in a cloud environment where diverse user data resides for processing purposes. Public key encryption with equality test (PKEET) has been introduced as a cryptographic tool to verify if two ciphertexts under different public keys contain the same message. However, existing PKEET schemes often face misuse of trapdoors due to their unlimited lifespan, potentially leading to unauthorized disclosure of user privacy. In this paper, we propose a novel approach called fast and forward-secure equivalence-based comparability (FFEC) for multiple users by employing a forward-secure PKEET (FS-PKEET). This restricts the retrieval process only to ciphertexts generated prior to the most recent trapdoor update. We present a concrete FS-PKEET scheme based on bilinear pairing and demonstrate its security using Bilinear Diffie–Hellman (BDH) assumption in the random oracle model. Comprehensive performance evaluation shows that our work has much efficiency of decryption, trapdoor generation and test execution thanks to greatly reducing the cost of trapdoor generation and thus is practical for the application of secure ciphertext information retrieval in cloud environment.