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網際網路技術學刊

Lattice-based Fuzzy Conditional Proxy Re-encryption

Baohong Li, JieFei Xu, Yanzhi Liu

Published Sep 1, 2019• 1 citation
OpenAlex

Abstract

As an extension to conditional proxy re-encryption, fuzzy conditional proxy re-encryption allows for a proxy to re-encrypt a ciphertext only if it satisfies some t-out-of-d threshold condition. Therefore, it is more desirable in some applications where fine-grained control of the decryption delegation is required. In this paper, we construct the first lattice-based fuzzy conditional proxy re-encryption scheme as a post-quantum alternative to this primitive. In our construction, original ciphertexts and re-encryption ciphertexts have the same form, thus only one decryption algorithm is needed for both kinds of ciphertexts. We formalize its security model and prove that it is selective secure under the LWE assumption.

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Research on Non-interactive Construction based on Fuzzy Conditional Proxy Re-encryption

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In a conditional proxy re-encryption (C-PRE) scheme, a semi-trusted proxy can transform Alice's ciphertext into Bob's ciphertext without learning the underlying plaintext, if the ciphertext satisfies a certain condition.To achieve more fine-grained delegation on conditions, Fang, Wang and Ge introduced the notion of fuzzy conditional proxy re-encryption (FC-PRE), whereby the conditions is viewed a set of descriptive keywords.The proxy with a re-encryption key for a condition word set can convert a ciphertext encrypted with a condition word set , if and only if and are close to each other as measured by the "set overlap" distance metric.Nonetheless, they left an open problem on how to construct a non-interactive FC-PRE scheme.Furthermore, their scheme is only proved secure in the random oracle model.In this paper, we answer the above problems affirmatively by presenting a non-interactive fuzzy conditional proxy reencryption scheme.Moreover, our scheme is proved secure without random oracles.

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arXiv:2005.06741•May 14, 2020•1 citation
As an extension to conditional proxy re-encryption, fuzzy conditional proxy re-encryption allows for a proxy to re-encrypt a ciphertext only if it satisfies some t-out-of-d threshold condition. Therefore, it is more desirable in some applications where fine-grained control of the decryption delegation is required. In this paper, we construct the first lattice-based fuzzy conditional proxy re-encryption scheme as a post-quantum alternative to this primitive. In our construction, original ciphertexts and re-encryption ciphertexts have the same form, thus only one decryption algorithm is needed for both kinds of ciphertexts. We formalize its security model and prove that it is selective secure under the LWE assumption.
In a conditional proxy re-encryption (C-PRE) scheme, a semi-trusted proxy can transform Alice's ciphertext into Bob's ciphertext without learning the underlying plaintext, if the ciphertext satisfies a certain condition.To achieve more fine-grained delegation on conditions, Fang, Wang and Ge introduced the notion of fuzzy conditional proxy re-encryption (FC-PRE), whereby the conditions is viewed a set of descriptive keywords.The proxy with a re-encryption key for a condition word set can convert a ciphertext encrypted with a condition word set , if and only if and are close to each other as measured by the "set overlap" distance metric.Nonetheless, they left an open problem on how to construct a non-interactive FC-PRE scheme.Furthermore, their scheme is only proved secure in the random oracle model.In this paper, we answer the above problems affirmatively by presenting a non-interactive fuzzy conditional proxy reencryption scheme.Moreover, our scheme is proved secure without random oracles.
In a proxy re-encryption system, a semi-trusted proxy can convert a ciphertext originally intended for Alice into one encrypting the same plaintext for Bob without seeing the underlying plaintext.However, a fine-grained delegation is demanded in some scenarios.For this, Weng et al. introduce the notion of conditional proxy re-encryption (CPRE), and formalize its security model and propose an efficient CPRE scheme.This paper presents the notion of identity-based multi-condition proxy re-encryption, which is a variant of identity-based condition proxy re-encryption.In such system, ciphertexts are generated under specified conditions by Alice, and the proxy can translate the ciphertext if the relevant conditions are satisfied.We formalize its security model and construct a concrete multi-condition proxy re-encryption scheme, and prove its security in the standard model.
Proxy re-encryption allows a semi-trusted proxy to convert the ciphertext of the data owner into the ciphertext of the target user. The certificateless proxy re-encryption eliminates the need for public key certificate in traditional public-key cryptography and key-escrow problem in identity-based cryptography, which makes it more convenient to apply. However, the existing certificateless proxy re-encryption schemes cannot support one-to-many conversion and flexible control on convert conditions. In this paper, we propose a fine-grained certificateless conditional proxy broadcast re-encryption scheme without pairing. In our scheme, the data owner can delegate the decryption rights of the ciphertext that meets certain conditions to the target users, and the data owner can revoke the delegate rights. At the same time, no pairing is used, which makes the scheme more efficient. Finally, we show that the security of the scheme for chosen-ciphertext attacks in the random oracle model.
Proxy re-encryption (PRE) schemes, which nicely solve the problem of delegating decryption rights, enable a semi-trusted proxy to transform a ciphertext encrypted under one key into a ciphertext of the same message under another arbitrary key. Cohen first pointed out the insufficiency of the security under chosen-plaintext attacks (CPA) of PREs in PKC 2019, and proposed a strictly stronger security notion, named security under honest re-encryption attacks (HRA), of PREs. Surprisingly, a few PREs satisfy the stronger HRA security and almost all of them are paring-based till now. To the best of our knowledge, we present the first direct construction of HRA secure single-hop PREs based on standard LWE problems with comparably small and polynomially-bounded parameters in this paper. Combing known reductions, the HRA security of our PREs could also be guaranteed by the worst-case basic lattice problems (e.g. SIVPγ with γ=Õ(n3.5)). Our single-hop PRE schemes are key-private, which means that the implicit identities of a re-encryption key will not be revealed even in the case of a proxy colluding with some corrupted users. Meanwhile, our single-hop PRE schemes are also post-compromise (PCS) secure, ensuring that a re-encrypted ciphertext remains confidential even when the past key, potential old ciphertexts and the re-encryption key have been exposed. Some discussions about key-privacy of multi-hop PREs are also proposed, which indicates that several constructions of multi-hop PREs do not satisfy their key-privacy definitions.
Proxy re-encryption (PRE) securely enables the re-encryption of ciphertexts from one key to another, without relying on trusted parties, i.e., it offers delegation of decryption rights. PRE allows a semi-trusted third party termed as a "proxy" to securely divert encrypted files of user A (delegator) to user B (delegatee) without revealing any information about the underlying files to the proxy. To eliminate the necessity of having a costly certificate verification process, Green and Ateniese introduced an identity-based PRE (IB-PRE). The potential applicability of IB-PRE leads to intensive research from its first instantiation. Unfortunately, till today, there is no unidirectional IB-PRE secure in the standard model, which can withstand quantum attack. In this paper, we provide, for the first time, a concrete construction of unidirectional IB-PRE which is secure in standard model based on the hardness of learning with error problem. Our technique is to use the novel trapdoor delegation technique of Micciancio and Peikert. The way we use trapdoor delegation technique may prove useful for functionalities other than proxy re-encryption as well.