Public Key Encryption With Equality Test Research Articles

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.

Cryptanalysis and improvement of “group public key encryption scheme supporting equality test without bilinear pairings”

Public key encryption with equality test (PKEET) is a novel primitive which supports equality comparisons on two encrypted messages. Currently, most of the existing PKEET schemes are based on bilinear pairing and require heavy computational overheads. To address this issue, Shen et al. recently proposed an efficient group public key encryption supporting equality test without bilinear pairings scheme. Compared with other schemes, their scheme reduces the usage of expensive bilinear pairing operations and enjoys higher computation efficiency. They claimed that their scheme achieved one-wayness security in the random oracle model and resisted offline message recovery attack. In this letter, we analyze Shen et al.'s scheme through two concrete attacks and demonstrate that their scheme can not support the above two security requirements. An improved scheme is provided to overcome the security vulnerabilities in their scheme. Performance analysis shows that our improved scheme has certain advantages in both computation overhead and storage overhead.

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.

Certificateless Encryption Supporting Multi-Ciphertext Equality Test with Proxy-Assisted Authorization

Public key encryption with equality test (PKEET) is a cryptographic primitive that enables a tester to determine, without decryption, whether two ciphertexts encrypted with different public keys generate from the same message. In previous research, public key encryption with equality test (PKEET) was extended to include identity-based encryption with equality test (IBEET), thereby broadening the application of PKEET. Subsequently, certificateless encryption with equality test (CLEET) was introduced to address the key escrow problem in IBEET. However, existing CLEET schemes suffer from inefficiency and potential information leakage when dealing with multiple ciphertexts due to the need for pairwise equality tests. To address this issue, we propose a concept of certificateless encryption supporting multi-ciphertext equality test with proxy-assisted authorization (CLE-MET-PA). CLE-MET-PA incorporates the functionality of the multi-ciphertext equality test into CLEET, enabling a tester to perform a single equality test on multiple ciphertexts to determine whether the underlying plaintexts are equal, without revealing any additional information. This enhances the security of our scheme while significantly reducing the computational overhead compared to multiple pairwise equality tests, making our scheme more efficient. Additionally, our approach integrates proxy-assisted authorization, allowing users to delegate a proxy to grant authorizations for equality tests on their behalf when offline. Importantly, the proxy token used in our scheme does not include any portion of the user’s private key, providing enhanced protection compared to traditional PKEET schemes in which the user token is often part of the user’s private key. We construct a concrete CLE-MET-PA scheme and prove that it achieves CPA security and attains CCA security through an FO transformation.

Public-Key Encryption With Tester Verifiable Equality Test for Cloud Computing

Public-key encryption with equality test (PKEET) provides cloud servers with an effective way to check the equality of outsourced encrypted data without decryption. This enables PKEET to attract much attention and be widely researched in cloud computing. However, we claim that the existing PKEET schemes suffer from an inherited problem, called message-consistency unverifiability of testers (MCUT). Applying the MCUT problem, outsourcers can fool cloud servers into outputting incorrect testing results of encrypted data, which negates the practicability of PKEET in cloud computing. We investigate the PKEET literature and find the main reason for the MCUT problem is the independence between the messages inserted in the decryption and testing modules in their ciphertexts. To bridge the technical gap between PKEET and its practical applications, we present a new notion, called PKE with tester verifiable equality test (PKE-TVET), which solves the MCUT problem by allowing testers to verify the message consistency in two modules. We then instantiate the PKE-TVET and give a specific construction in the standard model. In our PKE-TVET scheme, the testing module is integrated into the decryption module so that there is only one message inserted in the ciphertext for both decryption and testing. This special setting lets our scheme directly get rid of the MCUT problem. For better applications in actual scenarios, we further extend the scheme to support authorization and tester designation. Finally, we analyze the tradeoff of parameter sizes and computation costs for the security against MCUT attacks in our PKE-TVET scheme.

Secure Replication-Based Outsourced Computation Using Smart Contracts

The replication-Based Outsourced Computation (RBOC) mechanism allows a client to outsource the same computing job to multiple contractors and the honest contractors will get paid in the incentivized system based on the fact that a majority of contractors will honestly perform the computation. As self-executing contracts, smart contracts are utilized in the decentralized blockchain networks to execute coded programs automatically transparently, and publicly. It is natural to apply smart contracts to RBOC to improve performance by setting smart contracts as the converter between the client and contractors to reduce the load on the client. However, it is infeasible to directly combine these two blocks together because the data including returned computing results from contractors in the decentralized blockchain are in the form of plaintexts such that some lazy contractors could copy others' results as their own and still get paid, which will compromise the security of RBOC. The existing public-key encryption with equality test (PKEET) is a promising candidate solution to stop the above lazy contractors, where the results are encrypted by PKEET and then transferred without hindering smart contracts to compare the equality of underlying results. Unfortunately, we found that the advanced lazy contractors can still compromise security by forging ciphertexts to pass the equality test only with the encrypted results of other contractors. In this paper, to achieve security against lazy contractors, we introduce the notion of PKEET against lazy encryptors (PKEET-LE). Besides the fundamental property of PKEET that performs equality test on ciphertexts without decryption, PKEET-LE additionally realizes the security against the lazy encryptors who aim to forge a ciphertext for a given one to pass the equality test between them without the knowledge of the underlying plaintext. We further propose a concrete and practical PKEET-LE construction along with formal security proof. Finally, we conduct a performance evaluation to demonstrate that our PKEET-LE scheme is efficient and practical in the RBOC system using smart contracts.

An Identity-Based Encryption with Equality Test scheme for healthcare social apps

It is tricky to determine whether two ciphertexts contain the same message when the messages are encrypted with different public keys. public key encryption with equality test (PKEET) addresses this problem without decryption. By integrating PKEET with identity-based encryption, identity-based encryption with equality test (IBEET) simplifies the certificate management in PKEET. In this paper, we first propose an IBEET scheme that can resist offline message recovery attacks (OMRA) and requires neither the dual-tester setting nor the group mechanism. With the help of some mathematical assumptions, we demonstrate the security of our scheme. Experiment results reveal that our scheme is efficient. From the perspective of usability, we explain why our scheme is more appropriate to be applied in healthcare social Apps than other OMRA-resistant schemes.

More efficient tightly-secure lattice-based IBE with equality test

Identity-based encryption with equality test (IBEET) combines public key encryption with equality test (PKEET) and identity-based encryption (IBE). In an IBEET scheme, a user with trapdoors is allowed to verify whether different ciphertexts encrypted under different identities correspond to equal plaintexts through the equality test algorithm. Recently, several IBEET schemes were constructed over lattices to resist the potential quantum threats, perhaps since the latticed-based candidates are the most favored ones in the current NIST PQC standardization. However, almost all of the schemes are developed from Lee et al.’s generic construction and hence double both public parameters and ciphertext sizes. In this paper, we propose a more efficient and tightly-secure IBEET scheme which not only achieves a tight reduction with the semi-adaptive security, but also reduces both public parameters and ciphertext sizes.

Lattice-based public-key encryption with equality test supporting flexible authorization in standard model

As cloud computing has developed rapidly, outsourcing data to cloud servers for remote storage has become an attractive trend. However, when cloud clients store their data in the cloud, the security and privacy of cloud data would be threatened due to accidental corruptions or purposive attacks caused by a semi-trusted cloud server. The widely used method of addressing the security and privacy of cloud data is to store encrypted data instead of plain data. As the resulting system is unusable, since the cloud can no longer search throughout the data, new cryptographic primitive such as public-key encryption with equality test (PKEET) has been introduced. PKEET has many interesting applications such as keyword search on encrypted data, encrypted data partitioning for efficient encrypted data management, personal health record systems, spam filtering in encrypted email systems and so forth. PKEET allows checking whether two ciphertexts encrypted under different public keys contain the same message or not. However, unrestricted access to equality tests can reveal information about the underlying data. This is not acceptable in respect of users' privacy. In 2015, Ma et al. introduce the notion of PKEET with flexible authorization (PKEET-FA) which strengthens privacy protection. Since 2015, there are several follow-up works on PKEET-FA. However, all are secure in the random oracle model and vulnerable to quantum attacks. In this paper, we provide two constructions of quantum-safe PKEET-FA secure in the standard model based on the hardness assumptions of integer lattices and ideal lattices. Finally, we implement the PKEET-FA scheme over ideal lattices.

Group public key encryption supporting equality test without bilinear pairings

In cloud computing scenarios, it is a common approach to encrypt the data before uploading in order to maintain the privacy. Public key encryption with equality test (PKEET) provides a generic solution to equality comparisons on encrypted data. Considering the practical requirements of PKEET in group user scenarios, Ling et al. presented a group public key encryption scheme with equality test (G-PKEET) by utilizing the computationally expensive bilinear pairing operations. In this paper, we propose an efficient and verifiable group public key encryption with equality test construction without bilinear pairings (GPKEET/BP). Our proposal is developed from a basic observation that two points determine a straight line, and is proven to be indistinguishable against the chosen-ciphertext attacks (IND-CCA) in the random oracle model under the computational Diffie-Hellman (CDH) assumption. Theoretical analysis shows that our construction only involves several modular exponentiations in the encryption, decryption and test algorithms. The theoretical results are well supported by experimental simulations, which show that the test algorithm of GPKEET/BP performs about 92% faster than that of Ling et al.’s scheme. So our GPKEET/BP scheme turns out to be better suited for group ciphertext equality test situations.

Efficient Public Key Encryption With Outsourced Equality Test for Cloud-Based IoT Environments

Cloud-based Internet of Things (IoT) system is becoming a promising architecture in our modern society. However, cloud-based IoT system brings a number of challenges in the security aspect while improving the efficiency of data analytics. Especially, searching on encrypted data is challenging given today’s technology. Thus searchable encryption has emerged as one of the important research fields. Public key encryption with equality test (PKEET) provides a simple but useful mechanism to cryptographically protect data while keeping it available for equality test on ciphertexts. However, PKEET schemes in the literature are not suitable for cloud-based IoT system with privacy protection enhancement since the untrustworthy cloud server may be interested in query results by itself and hence reveal the private information of data owner out of the expectation of data user. Even worse, it could launch offline message recovery attack (OMRA) based on the returned query results. In this paper, we introduce a new notion of public key encryption with outsourced equality test (PKE-OET) for adapting to cloud-based IoT environments as well as providing a flexible solution to resist against OMRA without taking any information about entrusted parties as input in encryption. We formally define the security model of PKE-OET against three types of adversary including IND-CCA-I, IND-CCA-II and IND-CCA-III. We present a generic PKE-OET construction using a new variant of smooth projective hash function (SPHF) with a novel Lin-Hom property, which is of independent interest. Then we provide an efficient PKE-OET instantiation from Symmetric eXternal Diffie-Helllman (SXDH) assumption and show its practicality for cloud-based IoT environments through a series of experiments on Cloud Server and Raspberry Pi.

A Survey of Public-Key Encryption With Search Functionality for Cloud-Assisted IoT

Nowadays, Internet of Things (IoT) is an attractive system to provide broad connectivity of a wide range of applications, and clouds are natural promoters. Cloud-assisted IoT combines the advantages of cloud computing and IoT, which is able to collect data from the real world and maximizes the value of the collected data by the means of data sharing and data analysis. Meanwhile, secure and convenient data retrieval in cloud servers becomes an important requirement for both enterprises and individual users. Public-key encryption with search functionality (shorten as PKE-SF) is a widely used cryptographic technique that allows users to retrieve encrypted data without decryption. PKE-SF mainly contains the primitives of public-key encryption with keyword search (PKE-KS), public-key encryption with equality test (PKE-ET), and plaintext-checkable encryption (PCE). In light of the overwhelming variety and multitude of PKE-SF schemes, this survey presents these schemes from different perspectives to provide better comprehension for beginners and advanced researchers. More concretely, this survey concentrates on the state of the art of PKE-SF by analyzing the design rationale, examining the framework and security model, and assessing the existing schemes in accordance with theoretic efficiency, security properties, and experimental performance. Furthermore, we discuss the extensions of traditional PKE-SF schemes which feature with the access control delegation, conjunctive keyword search, certificate-free, and offline keyword guessing attack resilience. Finally, we point out some promising directions for readers.

Chosen-ciphertext lattice-based public key encryption with equality test in standard model

With the rapid growth of cloud storage and cloud computing services, many organizations and users choose to store the data on a cloud server for saving costs. However, due to security concerns, data of users would be encrypted before sending to the cloud. However, this hinders a problem of computation on encrypted data in the cloud, especially in the case of performing data matching in various medical scenarios. Public key encryption with equality test (PKEET) is a powerful tool that allows the authorized cloud server to check whether two ciphertexts are generated by the same message. PKEET has then become a promising candidate for many practical applications like efficient data management on encrypted databases. Lee et al. (Information Sciences 2020) proposed a generic construction of PKEET schemes in the standard model and hence it is possible to yield the first instantiation of post-quantum PKEET schemes based on lattices. At ACISP 2019, Duong et al. proposed a direct construction of PKEET over integer lattices in the standard model. However, their scheme does not reach the CCA2-security. In this paper, we propose an efficient CCA2-secure PKEET scheme based on ideal lattices. In addition, we present a modification of the scheme by Duong et al. over integer lattices to attain the CCA2-security. Both schemes are proven secure in the standard model, and they enjoy the security in the upcoming quantum computer era.

Public key encryption supporting equality test and flexible authorization without bilinear pairings

Public key encryption with equality test (PKEET) is an important cryptographic primitive for protecting users’ outsourced data in the cloud-based email systems. Due to the fact that it is required to deploy different authorization policies for the demand of dynamic privacy protection in the cloud-based email systems, Ma et al. recently presented a new related primitive, called public key encryption with equality test supporting flexible authorization (PKEET-FA). In their proposal, four types of authorization were considered to support different authorization policies. Their proposal is based on the bilinear pairings. However, as the basic operation of equality test, bilinear pairings are expensive operations compared with modular multiplications and modular inverses. Hence, it is desired to propose a new method for constructing efficient equality test with modular multiplications and modular inverses. In this paper, we present such a PKEET-FA scheme. Compared with Ma et al.’s, our proposal is (surprisingly) more efficient, especially in terms of equality test. Moreover, our proposal supports an additional type of authorization, called user-specific ciphertext-to-user (or user-specific user-to-ciphertext) level authorization. Hence, ours is more flexible than Ma et al.’s.

Proxy re‐encryption with equality test for secure data sharing in Internet of Things‐based healthcare systems

AbstractThe integration of the Internet of Things (IoT) and cloud computing brings tremendous convenience and efficiency to process and store growing sensor data in healthcare systems. For the security of sensor data collected by healthcare systems, encrypting data before uploading is necessary. Nevertheless, these encrypted form sensor data make it a research challenge to achieve efficient data search and data sharing on the cloud‐assisted IoT simultaneously. Encrypting data by public key encryption with equality test (PKE‐ET) scheme, identified as a viable solution, is capable to search data encrypted with different keys efficiently. However, how to efficiently share searched healthcare record on the cloud server is still an unsettled problem. To address this problem, we combine the concepts of proxy re‐encryption (PRE) and PKE‐ET to obtain proxy re‐encryption with equality test (PRE‐ET). Inheriting the advantages of PKE‐ET and PRE, the user can search the required healthcare record data from data encrypted under different public keys. Meanwhile, the searched healthcare record can be shared securely and flexibly without disclosing the secret key and plaintext. We prove the security of our PRE‐ET construction based on divisible computation Diffie‐Hellman assumption in the random oracle model. Eventually, the proposed scheme is proven useful according to extensive efficiency analysis and comparison.

PKE-MET: Public-Key Encryption With Multi-Ciphertext Equality Test in Cloud Computing

Cloud computing enables users to remove the necessity of the need of local hardware architecture, which removes the burden of the users from high computation costs. Therefore, it has attracted much attention and research has been conducted heavily on it. To protect users’ privacy, data is usually encrypted prior to being sent to the cloud server. As the resulting system is unusable, since the cloud can no longer search throughout the data, new cryptographic primitive such as public-key encryption with equality test (PKEET) has been introduced. In PKEET, users can test whether the underlying messages of two ciphertexts encrypted under different public keys are equal or not without the need to decrypt those ciphertexts. This is a very useful tool, especially for the cloud database, since PKEET mainly focuses on the equality test between two ciphertexts. However, in practice, the cloud server may need to verify the equivalence among more than two ciphertexts. This leads to disclosing unnecessary information of users and redundant computation cost will also occur when using traditional PKEET schemes. How to make this more efficient and practical remains an interesting research problem. In this article, to solve the aforementioned problems by providing a novel concept of public-key encryption with multi-ciphertext equality test (PKE-MET). In PKE-MET, each ciphertext can designate a number <inline-formula><tex-math notation="LaTeX">$s$</tex-math></inline-formula> such that the cloud server can only perform equality test on this ciphertext with other <inline-formula><tex-math notation="LaTeX">$s-1$</tex-math></inline-formula> ciphertexts, where all their designated numbers are <inline-formula><tex-math notation="LaTeX">$s$</tex-math></inline-formula> . For PKE-MET, besides traditional OW-CPA and IND-CPA security, we specially define Number security. We instantiate PKE-MET to a concrete scheme and give its security proof. Furthermore, to enable the primitive to be more practical in applications, we extend it to the concept of PKE with flexible MET (PKE-FMET). In PKE-FMET, the cloud server can perform equality test on any number of ciphertexts as long as the maximum number of their designated numbers is less than or equal to the number of ciphertexts. We construct a PKE-FMET scheme based on our PKE-MET construction and prove its security under the defined security models. Besides, the performance analysis mainly of efficiency and security between our constructions and existing equality test schemes in cloud computing show that our proposed schemes are more efficient and secure in the multi-ciphertext scenario.

Constructing secure‐channel free identity‐based encryption with equality test for vehicle‐data sharing in cloud computing

AbstractWith the rapid rise of connected vehicles on the road, there is an exponential growth in vehicle‐related data (vehicle‐data) generated and accumulated by connected vehicles. Taking advantage of cloud computing, enabling a vehicle‐data sharing system can make various services based on vehicle‐data available. However, the untrusted nature of the cloud server raises a challenge on how to balance privacy and functionality over the vehicle‐data outsourced to the vehicle‐data sharing system. Identity‐based encryption with equality test (IBEET) is a viable solution to this challenge as it not only ensures data privacy but also enables searchable functionality over the encrypted data while dealing with the certificate management issue that exists in public key encryption with equality test (PKEET). However, the existing IBEET schemes are unable to be applicable into the vehicle‐data sharing in cloud computing due to the fact that they did not consider the consequences of unexpected exposure of trapdoors given to cloud server and different levels of computing capabilities of the system entities. Therefore, this article introduces the notion of secure‐channel‐free IBEET (SCF‐IBEET) scheme and presents a generic construction of the SCF‐IBEET scheme by addressing the above‐mentioned issues simultaneously. The proposed SCF‐IBEET construction achieves one‐wayness under chosen‐identity and chosen‐ciphertext attacks, indistinguishability under chosen‐identity and chosen‐ciphertext attacks, and trapdoor anonymity securities with respect to five different types of adversaries. Furthermore, the security comparison and efficiency analysis indicate that the proposed construction is reasonable with regard to security and viable in terms of efficiency to be applied to practical scenarios as vehicle‐data sharing in cloud computing.

A Multivariate Public Key Encryption Scheme With Equality Test

The public key encryption with equality test (PKEET) allows the cloud server to judge whether two different ciphertexts are generated by the same message without decryption. Through this technique, PKEET provides an effective solution for building secure outsourced databases, and has made some rich achievements. This paper combines multivariate public key encryption and equality test, and proposes the first multivariate public key encryption scheme with equality test (MPKEET), which inherits the advantages of both primitives. Moreover, the equality test algorithm proposed in this paper is based on a straight line. Compared with the schemes based on bilinear pairing, it is simpler and easier to implement. And our MPKEET scheme achieves desirable security, which can resist linearization equation attacks, differential attacks, XL attacks, Grobner basis attacks and the attack of quantum computer, when appropriate parameters are selected.

Attribute-Based Equality Test Over Encrypted Data Without Random Oracles

Sensitive data would be encrypted before uploading to the cloud due to the privacy issue. However, how to compare the encrypted data efficiently becomes a problem. Public Key Encryption with Equality Test (PKEET) provides an efficient way to check whether two ciphertexts (of possibly different users) contain the same message without decryption. As an enhanced variant, Attribute-based Encryption with Equality Test (ABEET) provides a flexible mechanism of authorization on the equality test. Most of the existing ABEET schemes are only proved to be secure in the random oracle model. Their security, however, would not be guaranteed if random oracles are replaced with real-life hash functions. In this work, we propose a construction of CP-ABEET scheme and prove its security based on some reasonable assumptions in the standard model. We then show how to modify the scheme to outsource complex computations in decryption and equality test to a third-party server in order to support thin clients.

Public key encryption with equality test in the standard model

Public key encryption with equality test (PKEET) is a cryptosystem that allows a tester who has trapdoors issued by one or more users Ui to perform equality tests on ciphertexts encrypted using public key(s) of Ui. Since this feature has a lot of practical applications including search on encrypted data, several PKEET schemes have been proposed so far. However, to the best of our knowledge, all the existing proposals are proven secure only under the hardness of number-theoretic problems and/or the random oracle heuristics.In this paper, we show that this primitive can be achieved not only generically from well-established other primitives but also even without relying on the random oracle heuristics. More precisely, our generic construction for PKEET employs a two-level hierarchical identity-based encryption scheme, which is selectively secure against chosen plaintext attacks, a strongly unforgeable one-time signature scheme and a cryptographic hash function. Our generic approach toward PKEET has several advantages over all the previous works; it directly leads the first standard model construction and also directly implies the first lattice-based construction. Finally, we show how to extend our approach to the identity-based setting.