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arXiv:2005.03178

Lattice-based public key encryption with equality test in standard model, revisited.

Dung Hoang Duong, Partha Sarathi Roy, Willy Susilo, Kazuhide Fukushima, Shinsaku Kiyomoto, Arnaud Sipasseuth

Published May 7, 2020• 0 citations
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Abstract

Public key encryption with equality test (PKEET) allows testing whether two ciphertexts are generated by the same message or not. PKEET is a potential candidate for many practical applications like efficient data management on encrypted databases. Potential applicability of PKEET leads to intensive research from its first instantiation by Yang et al. (CT-RSA 2010). Most of the followup constructions are secure in the random oracle model. Moreover, the security of all the concrete constructions is based on number-theoretic hardness assumptions which are vulnerable in the post-quantum era. Recently, Lee et al. (ePrint 2016) proposed a generic construction of PKEET schemes in the standard model and hence it is possible to yield the first instantiation of PKEET schemes based on lattices. Their method is to use a $2$-level hierarchical identity-based encryption (HIBE) scheme together with a one-time signature scheme. In this paper, we propose, for the first time, a direct construction of a PKEET scheme based on the hardness assumption of lattices in the standard model. More specifically, the security of the proposed scheme is reduces to the hardness of the Learning With Errors problem.

Related papers

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

Dung Hoang Duong, Kazuhide Fukushima, Shinsaku Kiyomoto +3 more

Public key encryption with equality test (PKEET) supports to check whether two ciphertexts encrypted under different public keys contain the same message or not. 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 on. However, the PKEET scheme lacks an authorization mechanism for a user to control the comparison of its ciphertexts with others. 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. But, all are secure in the random-oracle model. Moreover, all are vulnerable to quantum attacks. In this paper, we provide three constructions of quantum-safe PKEET-FA secure in the standard model. Proposed constructions are secure based on the hardness assumptions of integer lattices and ideal lattices. Finally, we implement the PKEET-FA scheme over ideal lattices.

arXiv:2005.05308•May 9, 2020•0 citations

Efficient Post-quantum Identity-based Encryption with Equality Test

Willy Susilo, Dung Hoang Duong, Huy Quoc Le

Public key encryption with equality test (PKEET) enables the testing whether two ciphertexts encrypt the same message. Identity-based encryption with equality test (IBEET) simplify the certificate management of PKEET, which leads to many potential applications such as in smart city applications or Wireless Body Area Networks. Lee et al. (ePrint 2016) proposed a generic construction of IBEET scheme in the standard model utilising a 3-level hierachy IBE together with a one-time signature scheme, which can be instantiated in lattice setting. Duong et al. (ProvSec 2019) proposed the first direct construction of IBEET in standard model from lattices. However, their scheme achieve CPA security only. In this paper, we improve the Duong et al.'s construction by proposing an IBEET in standard model which achieves CCA2 security and with smaller ciphertext and public key size.

IEEE International Conference on Parallel and Distributed Systems (ICPADS)•Dec 1, 2020•17 citations

A compact public key encryption with equality test for lattice in cloud computing

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The rapid proliferation of cloud computing enables users to access computing resources and storage space over the internet, but it also presents challenges in terms of security and privacy. Ensuring the security and availability of data has become a focal point of current research when utilizing cloud computing for resource sharing, data storage, and querying. Public key encryption with equality test (PKEET) can perform an equality test on ciphertexts without decrypting them, even when those ciphertexts are encrypted under different public keys. That offers a practical approach to dividing up or searching for encrypted information directly. In order to deal with the threat raised by the rapid development of quantum computing, researchers have proposed post-quantum cryptography to guarantee the security of cloud services. However, it is challenging to implement these techniques efficiently. In this paper, a compact PKEET scheme is pro-posed. The new scheme does not encrypt the plaintext's hash value immediately but embeds it into the test trapdoor. We also demon-strated that our new construction is one-way secure under the quantum security model. With those efforts, our scheme can withstand the chosen ciphertext attacks as long as the learning with errors (LWE) assumption holds. Furthermore, we evaluated the new scheme's performance and found that it only costs approximately half the storage space compared with previous schemes. There is an almost half reduction in the computing cost throughout the encryption and decryption stages. In a nutshell, the new PKEET scheme is less costly, more compact, and applicable to cloud computing scenarios in a post-quantum environment.

Scientific Reports•Jul 28, 2025•3 citations

Communication-efficient public key encryption with (fine-grained delegated) equality test

Wanqing Wang, Xiangxue Li, Xiaogang Zhou

Abstract With the rise of cloud storage and the looming threat of quantum computing, traditional encryption methods are encountering significant challenges that hinder data manipulation without decryption. To counter quantum attacks while maintaining data manipulation capabilities, new architectures such as quantum-resistant public key encryption with equality test (PKEET) must be developed. Our study presents the initial PKEET that leverages the Learning with Rounding (LWR) problem, which provides security within standard model. We also introduce its variants, public key encryption with delegated equality test (PKE-DET) and PKEET supporting flexible authorization (PKEET-FA). Our proposals could achieve fine-grained delegation at the ciphertext-specified level compared to previous PKE-DET schemes. For example, our PKE-DET supports a delegated tester function while ensuring security against quantum computing threats. Our PKEET-FA could accord users even more controls over what ciphertexts they want to compare. Our schemes’ security is founded on the LWR problem which avoids the need for discrete Gaussian sampling, unlike the Learning with Errors (LWE) problem. This distinction renders our methods both simpler and more efficient compared to those based on LWE. Moreover, our schemes enjoy smaller-sized ciphertexts.

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

Willy Susilo, Fuchun Guo, Zhen Zhao +1 more

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$s$such that the cloud server can only perform equality test on this ciphertext with other$s-1$ciphertexts, where all their designated numbers are$s$. 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.

IEEE Transactions on Cloud Computing•Apr 28, 2020•44 citations

Efficient hierarchical identity based encryption scheme in the standard model over lattices

Fenghe Wang, Chunxiao Wang, Zhenhua Liu

Using lattice basis delegation in a fixed dimension, we propose an efficient lattice-based hierarchical identity based encryption (HIBE) scheme in the standard model whose public key size is only ( dm 2 + mn ) log q bits and whose message-ciphertext expansion factor is only log q , where d is the maximum hierarchical depth and ( n , m , q ) are public parameters. In our construction, a novel public key assignment rule is used to averagely assign one random and public matrix to two identity bits, which implies that d random public matrices are enough to build the proposed HIBE scheme in the standard model, compared with the case in which 2 d such public matrices are needed in the scheme proposed at Crypto 2010 whose public key size is (2 dm 2 + mn + m ) log q . To reduce the message-ciphertext expansion factor of the proposed scheme to log q , the encryption algorithm of this scheme is built based on Gentry’s encryption scheme, by which m 2 bits of plaintext are encrypted into m 2 log q bits of ciphertext by a one time encryption operation. Hence, the presented scheme has some advantages with respect to not only the public key size but also the message-ciphertext expansion factor. Based on the hardness of the learning with errors problem, we demonstrate that the scheme is secure under selective identity and chosen plaintext attacks.

Frontiers of Information Technology & Electronic Engineering•Aug 1, 2016•5 citations
Public key encryption with equality test (PKEET) allows testing whether two ciphertexts are generated by the same message or not. PKEET is a potential candidate for many practical applications like efficient data management on encrypted databases. Potential applicability of PKEET leads to intensive research from its first instantiation by Yang et al. (CT-RSA 2010). Most of the followup constructions are secure in the random oracle model. Moreover, the security of all the concrete constructions is based on number-theoretic hardness assumptions which are vulnerable in the post-quantum era. Recently, Lee et al. (ePrint 2016) proposed a generic construction of PKEET schemes in the standard model and hence it is possible to yield the first instantiation of PKEET schemes based on lattices. Their method is to use a 222-level hierarchical identity-based encryption (HIBE) scheme together with a one-time signature scheme. In this paper, we propose, for the first time, a direct construction of a PKEET scheme based on the hardness assumption of lattices in the standard model. More specifically, the security of the proposed scheme is reduces to the hardness of the Learning With Errors problem.
Public key encryption with equality test (PKEET) supports to check whether two ciphertexts encrypted under different public keys contain the same message or not. 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 on. However, the PKEET scheme lacks an authorization mechanism for a user to control the comparison of its ciphertexts with others. 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. But, all are secure in the random-oracle model. Moreover, all are vulnerable to quantum attacks. In this paper, we provide three constructions of quantum-safe PKEET-FA secure in the standard model. Proposed constructions are secure based on the hardness assumptions of integer lattices and ideal lattices. Finally, we implement the PKEET-FA scheme over ideal lattices.
Public key encryption with equality test (PKEET) enables the testing whether two ciphertexts encrypt the same message. Identity-based encryption with equality test (IBEET) simplify the certificate management of PKEET, which leads to many potential applications such as in smart city applications or Wireless Body Area Networks. Lee et al. (ePrint 2016) proposed a generic construction of IBEET scheme in the standard model utilising a 3-level hierachy IBE together with a one-time signature scheme, which can be instantiated in lattice setting. Duong et al. (ProvSec 2019) proposed the first direct construction of IBEET in standard model from lattices. However, their scheme achieve CPA security only. In this paper, we improve the Duong et al.'s construction by proposing an IBEET in standard model which achieves CCA2 security and with smaller ciphertext and public key size.
The rapid proliferation of cloud computing enables users to access computing resources and storage space over the internet, but it also presents challenges in terms of security and privacy. Ensuring the security and availability of data has become a focal point of current research when utilizing cloud computing for resource sharing, data storage, and querying. Public key encryption with equality test (PKEET) can perform an equality test on ciphertexts without decrypting them, even when those ciphertexts are encrypted under different public keys. That offers a practical approach to dividing up or searching for encrypted information directly. In order to deal with the threat raised by the rapid development of quantum computing, researchers have proposed post-quantum cryptography to guarantee the security of cloud services. However, it is challenging to implement these techniques efficiently. In this paper, a compact PKEET scheme is pro-posed. The new scheme does not encrypt the plaintext's hash value immediately but embeds it into the test trapdoor. We also demon-strated that our new construction is one-way secure under the quantum security model. With those efforts, our scheme can withstand the chosen ciphertext attacks as long as the learning with errors (LWE) assumption holds. Furthermore, we evaluated the new scheme's performance and found that it only costs approximately half the storage space compared with previous schemes. There is an almost half reduction in the computing cost throughout the encryption and decryption stages. In a nutshell, the new PKEET scheme is less costly, more compact, and applicable to cloud computing scenarios in a post-quantum environment.
Abstract With the rise of cloud storage and the looming threat of quantum computing, traditional encryption methods are encountering significant challenges that hinder data manipulation without decryption. To counter quantum attacks while maintaining data manipulation capabilities, new architectures such as quantum-resistant public key encryption with equality test (PKEET) must be developed. Our study presents the initial PKEET that leverages the Learning with Rounding (LWR) problem, which provides security within standard model. We also introduce its variants, public key encryption with delegated equality test (PKE-DET) and PKEET supporting flexible authorization (PKEET-FA). Our proposals could achieve fine-grained delegation at the ciphertext-specified level compared to previous PKE-DET schemes. For example, our PKE-DET supports a delegated tester function while ensuring security against quantum computing threats. Our PKEET-FA could accord users even more controls over what ciphertexts they want to compare. Our schemes’ security is founded on the LWR problem which avoids the need for discrete Gaussian sampling, unlike the Learning with Errors (LWE) problem. This distinction renders our methods both simpler and more efficient compared to those based on LWE. Moreover, our schemes enjoy smaller-sized ciphertexts.
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 numberssssuch that the cloud server can only perform equality test on this ciphertext with others−1s-1s−1ciphertexts, where all their designated numbers aresss. 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.
Using lattice basis delegation in a fixed dimension, we propose an efficient lattice-based hierarchical identity based encryption (HIBE) scheme in the standard model whose public key size is only ( dm 2 + mn ) log q bits and whose message-ciphertext expansion factor is only log q , where d is the maximum hierarchical depth and ( n , m , q ) are public parameters. In our construction, a novel public key assignment rule is used to averagely assign one random and public matrix to two identity bits, which implies that d random public matrices are enough to build the proposed HIBE scheme in the standard model, compared with the case in which 2 d such public matrices are needed in the scheme proposed at Crypto 2010 whose public key size is (2 dm 2 + mn + m ) log q . To reduce the message-ciphertext expansion factor of the proposed scheme to log q , the encryption algorithm of this scheme is built based on Gentry’s encryption scheme, by which m 2 bits of plaintext are encrypted into m 2 log q bits of ciphertext by a one time encryption operation. Hence, the presented scheme has some advantages with respect to not only the public key size but also the message-ciphertext expansion factor. Based on the hardness of the learning with errors problem, we demonstrate that the scheme is secure under selective identity and chosen plaintext attacks.