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Revocable cryptosystems from lattices

Juanyang Zhang

Published Jan 1, 2018• 0 citations
Publisher

Abstract

In the last decade, lattices have become one of the most powerful tools in constructing cryptographic schemes, which enjoy conjectured resistance against quantum computers and strong security guarantees from worst-case to average-case reductions, as well as asymptotic efficiency. For a multi-user cryptosystem, user revocation has been a necessary but challenging problem. However, all known revocable schemes are either based on number-theoretic assumptions or lattice-based but less efficient compared to the art-of-date systems. In this thesis, we focus on investigating user revocation model and the associated lattice-based instantiations. Our constructions have two goals: (i) to improve the existing revocable lattice-based cryptosystems in terms of efficiency and security; (ii) to consider the revocation functionality in new contexts from lattices. For the former, we carefully adapt the very recent revocation model into the lattice setting. The latter can be achieved either by using the existing revocation models (without concrete constructions from lattices) or by proposing new revocation models. We construct a series of cryptosystems supporting efficient revocations as follows. A revocable identity-based encryption (IBE) scheme, which is more efficient than all existing such schemes from lattices. We follow the architecture of the server-aided revocable encryptions, proposed by Qin et al. (ESORICS 2015). This paradigm provides significant efficiency advantages over previous revocation techniques in the setting of IBE. In the server-aided revocation model, most of the workloads on the user side are outsourced to an untrusted server, which can be untrusted since it does not possess any private information. With the help of this server, non-revoked users do not need to update anything when the system revokes other users. We equip Agrawal, Boneh, and Boyen's IBE (EUROCRYPT 2010) with the server-aided revocation method. In the technical view, we observe that a ``double encryption'' mechanism is well-suited in such a server-aided system. We also show that our scheme is provably secure provided with the strong hardness of the Learning With Errors (LWE) problem. A revocation model called server-aided revocable predicate encryption (SR-PE) and an instantiation from lattices. We consider the server-aided revocation mechanism in the predicate encryption (PE) setting and formalize the notion of SR-PE with rigorous definitions and security model. Moreover, we introduce a construction of SR-PE for the scheme introduced by Agrawal, Freeman, and Vaikuntanathan (ASIACRYPT 2011) and prove that our scheme is selectively secure in the standard model. The correctness of our scheme relies on a special property of lattice-based encryption schemes. A lattice-based construction of predicate encryption following the direct revocation mechanism. In such a mechanism, it forces the ciphertexts to carry on the revocation information. Nieto, Manulis, and Sun (ACISP 2012) considered direct revocations in the PE setting and suggested the notion of full-hiding security for revocable PE schemes, which demands that the encrypted data keeps the privacy of not only the plaintext and the associated attribute, but also the revocation information. Following their pairing-based construction, we introduce a corresponding instantiation from lattice assumptions. Regarding efficiency, our lattice-based scheme is somewhat comparable to the construction by Nieto, Manulis, and Sun. Our scheme achieves the full-hiding security thanks to the anonymity of one IBE instance we additionally introduce into the system.

DOI
10.32657/10356/75927

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Abstract. In this paper, we present an identity-based encryption (IBE) scheme from lattices with efficient key revocation. We adopt multiple trapdoors from the Agrawal-Boneh-Boyen and Gentry-Peikerty-Vaikuntanathan lattice IBE schemes to realize key revocation, which in turn, makes use of binary-tree data structure. Using our scheme, key update requires logarithmic complexity in the maximal number of users and linear in the number of revoked users for the relevant key authority. We prove that our scheme is selective secure in the standard model and under the LWE assumption, which is as hard as the worst-case approximating short vectors on arbitrary lattices. Moreover, our key revocation techniques from lattices can be applied to obtain revocable functional encryption schemes in the similar setting.

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In the last decade, lattices have become one of the most powerful tools in constructing cryptographic schemes, which enjoy conjectured resistance against quantum computers and strong security guarantees from worst-case to average-case reductions, as well as asymptotic efficiency. For a multi-user cryptosystem, user revocation has been a necessary but challenging problem. However, all known revocable schemes are either based on number-theoretic assumptions or lattice-based but less efficient compared to the art-of-date systems. In this thesis, we focus on investigating user revocation model and the associated lattice-based instantiations. Our constructions have two goals: (i) to improve the existing revocable lattice-based cryptosystems in terms of efficiency and security; (ii) to consider the revocation functionality in new contexts from lattices. For the former, we carefully adapt the very recent revocation model into the lattice setting. The latter can be achieved either by using the existing revocation models (without concrete constructions from lattices) or by proposing new revocation models. We construct a series of cryptosystems supporting efficient revocations as follows. A revocable identity-based encryption (IBE) scheme, which is more efficient than all existing such schemes from lattices. We follow the architecture of the server-aided revocable encryptions, proposed by Qin et al. (ESORICS 2015). This paradigm provides significant efficiency advantages over previous revocation techniques in the setting of IBE. In the server-aided revocation model, most of the workloads on the user side are outsourced to an untrusted server, which can be untrusted since it does not possess any private information. With the help of this server, non-revoked users do not need to update anything when the system revokes other users. We equip Agrawal, Boneh, and Boyen's IBE (EUROCRYPT 2010) with the server-aided revocation method. In the technical view, we observe that a ``double encryption'' mechanism is well-suited in such a server-aided system. We also show that our scheme is provably secure provided with the strong hardness of the Learning With Errors (LWE) problem. A revocation model called server-aided revocable predicate encryption (SR-PE) and an instantiation from lattices. We consider the server-aided revocation mechanism in the predicate encryption (PE) setting and formalize the notion of SR-PE with rigorous definitions and security model. Moreover, we introduce a construction of SR-PE for the scheme introduced by Agrawal, Freeman, and Vaikuntanathan (ASIACRYPT 2011) and prove that our scheme is selectively secure in the standard model. The correctness of our scheme relies on a special property of lattice-based encryption schemes. A lattice-based construction of predicate encryption following the direct revocation mechanism. In such a mechanism, it forces the ciphertexts to carry on the revocation information. Nieto, Manulis, and Sun (ACISP 2012) considered direct revocations in the PE setting and suggested the notion of full-hiding security for revocable PE schemes, which demands that the encrypted data keeps the privacy of not only the plaintext and the associated attribute, but also the revocation information. Following their pairing-based construction, we introduce a corresponding instantiation from lattice assumptions. Regarding efficiency, our lattice-based scheme is somewhat comparable to the construction by Nieto, Manulis, and Sun. Our scheme achieves the full-hiding security thanks to the anonymity of one IBE instance we additionally introduce into the system.
Abstract. In this paper, we present an identity-based encryption (IBE) scheme from lattices with efficient key revocation. We adopt multiple trapdoors from the Agrawal-Boneh-Boyen and Gentry-Peikerty-Vaikuntanathan lattice IBE schemes to realize key revocation, which in turn, makes use of binary-tree data structure. Using our scheme, key update requires logarithmic complexity in the maximal number of users and linear in the number of revoked users for the relevant key authority. We prove that our scheme is selective secure in the standard model and under the LWE assumption, which is as hard as the worst-case approximating short vectors on arbitrary lattices. Moreover, our key revocation techniques from lattices can be applied to obtain revocable functional encryption schemes in the similar setting.
Abstract Public key encryption scheme with keyword search is a promising technique supporting search on encrypted data without leaking any information about the keyword. In real applications, it’s critical to find an effective revocation method to revoke users in multi-user cryptosystems, when user’s secret keys are exposed. In this paper, we propose the first designated server-aided revocable identity-based encryption scheme with keyword search (dSR-IBKS) from lattice. The dSR-IBKS model requires each user to keep just one private key corresponding with his identity and does not need to communicate with the key generation center or the server during key updating. We have proved that our scheme can achieve chosen keyword indistinguishability in the standard model. In particular, our scheme can designate a unique tester to test and return the search results, therefore no other entity can guess the keyword embedded in the ciphertext by generating search queries and doing the test by itself. We provide a formal security proof of our scheme assuming the hardness of the learning with errors problem on the standard model.
A revocable identity-based encryption (IBE) scheme under learning with error (LWE) assumption from lattice is proposed; compared with the existing IBE schemes from lattices, two improvements are available in the new scheme. First, the revocation mechanism for identity of user (or thing) is added in the new scheme to manage the dynamic user (or thing) identity in the system, and making the IBE scheme from lattice becomes more practical than ever before. Second, the security of the new scheme is based on the LWE assumption from lattice, so our construction has a solid secure foundation. The scheme is proved to be secured against adaptive-ID attacks under LWE assumption from lattice in the standard model.
Cloud computing offers abundant computing resources and scalable storage, but data leakage in the cloud storage environment is a common and critical concern due to inadequate protection measures. Revocable-attribute-based encryption (RABE) is introduced as an advanced form of identity-based encryption (IBE), which encrypts sensitive data while providing fine-grained access control and an effective user revocation mechanism. However, most existing RABE schemes are not resistant to quantum attacks and are limited in their application scenarios due to the revocation model. In this paper, we propose a RABE scheme constructed from lattices. Our scheme has several advantages, including a near-zero periodic workload for the key generation center (KGC), ensuring scalability as the number of users increases. Additionally, the encryptor is relieved from managing a revocation list. Moreover, our scheme guarantees the confidentiality and privacy of other ciphertexts even if the decryption key for a specific period is compromised. We validated the correctness of our scheme and demonstrated its security under the assumption of learning with errors (LWE), which is widely believed to be resistant to quantum attacks. Finally, we provide an application example of our RABE scheme in the electronic healthcare scenario.
Abstract. In view of the expiration or reveal of user’s private credential (or private key) in a real-istic scenario, identity-based encryption (IBE) schemes with an efficient key revocation mechanism, or for short, revocable identity-based encryption (RIBE) schemes, become prominently significant. In this paper, we present an RIBE scheme from lattices by combining two Agrawal et al.’s IBE schemes with the subset difference (SD) method. Our scheme is secure against adaptive identity-time attacks in the standard model under the learning with errors (LWE) assumption. In particular, our scheme serves as one solution to the challenge posed by Chen et al. (ACISP ’12). 1
Revocable identity-based encryption (RIBE) enables data encryption without certificates and allows for the revocation of users, thereby offering a more streamlined and secure approach to dynamic member management. However, the existing revocation models lack strong scalability, rendering the RIBE scheme unsuitable for scenarios where the key generation center (KGC) experiences high workloads and users face heavy storage burdens. Therefore, this paper introduces an integrated revocation model that maintains both the workload for the KGC and the size of the secret keys at a constant level, while also relieving the encryptor of the burden of handling revocation information. By combining online and offline encryption, we construct an OO-IRIBE-EnDKER scheme from lattices, which possesses properties such as anonymity, decryption key exposure resistance (DKER), resistance to quantum computing attacks, and selective security. Finally, the effectiveness of the OO-IRIBE-EnDKER scheme is demonstrated through experimental results.