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IEEE Transactions on Cloud Computing

Achieving Multi-Hop PRE via Branching Program

Zengpeng Li, Chunguang Ma, Ding Wang

Published Oct 18, 2017• 21 citations
Publisher

Abstract

Proxy re-encryption (PRE) is a fundamental cryptographic primitive in secure data sharing and e-mail forwarding, etc. To our knowledge, most existing efficient lattice-based PRE schemes focus on the construction of single-hop, key-private, multi-bit and chosen-ciphertext attack (CCA), etc. Few works of literature discussed the detailed multi-hop construction over lattices. Very recently, Chandran et al. (PKC'14) proposed a lattice-based PRE scheme that builds upon the key switching mechanism of Brakerski (CRYPTO'12), and pointed out that their scheme can achieve multi-hop PRE scheme by the ideal circuit family for a directed graph G. In this paper, we are still working along this line and achieving multi-hop PRE via the branching program (BP), which is one type of NC1 circuit and can be used to compute encrypted data. To our knowledge, we proposed the first multi-hop PRE scheme via BP which supports homomorphic evaluation. We also analyze the security of our scheme under decisional learning with errors (LWE) assumption.

DOI
10.1109/tcc.2017.2764082

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Proxy re-encryption (PRE) is a fundamental cryptographic primitive in secure data sharing and e-mail forwarding, etc. To our knowledge, most existing efficient lattice-based PRE schemes focus on the construction of single-hop, key-private, multi-bit and chosen-ciphertext attack (CCA), etc. Few works of literature discussed the detailed multi-hop construction over lattices. Very recently, Chandran et al. (PKC'14) proposed a lattice-based PRE scheme that builds upon the key switching mechanism of Brakerski (CRYPTO'12), and pointed out that their scheme can achieve multi-hop PRE scheme by the ideal circuit family for a directed graph G. In this paper, we are still working along this line and achieving multi-hop PRE via the branching program (BP), which is one type of NC1 circuit and can be used to compute encrypted data. To our knowledge, we proposed the first multi-hop PRE scheme via BP which supports homomorphic evaluation. We also analyze the security of our scheme under decisional learning with errors (LWE) assumption.
Proxy re-encryption (PRE) is an important cryptographic primitive used for private information sharing. However, the recent advance in quantum computer has potentially crippled its security, as the traditional decisional Diffie-Hellman (DDH)-based PRE is venerable to the quantum attack. Thus, learning with errors (LWE)-based PRE schemes, as a kind of latticebased construction with the inherent quantum-resistant property, has attracted special research interest. Unfortunately, the main drawback of lattice-based public key encryption scheme is noise management after multiplication evaluation. Many cryptographers have been devoted to controlling the expansion of noise. In this line of work, Dagdelen-Gajek-G̈opfert (DGG) put forth the notion of learning with errors in the exponent (LWEE) which is based on lattice and group-theoretic assumption, meanwhile demonstrated a paradigm for constructing efficient quantum resistance public key schemes. In this paper, on top of DGG, we construct a single-bit, single-hop and unidirectional LWEE- based PRE scheme with indistinguishable chosen plaintext attack (IND-CPA) security. To the best of our knowledge, our scheme is the first LWEE-based PRE scheme.
Identity-based proxy re-encryption (IB-PRE) is a kind of public key cryptography that allows a proxy to convert the ciphertext based on Alice’s identity into another ciphertext of the same message for Bob. It has important applications in cloud computing, distributed systems and secure e-mail forwarding. So far, the existing lattice-based IB-PRE schemes are designed on the general lattice and their security is based on the learning with errors (LWE) assumption. In this paper, we propose an IB-PRE scheme over NTRU lattices with the desirable properties of anonymity, unidirectionality, backward collusion safeness and multi-hop. Our IB-PRE scheme is provable secure under adaptive chosen-plaintext and adaptive chosen-identity attacks. And, in the random oracle model, the security of our scheme is based on the decisional Ring-LWE assumption. Besides, the key and ciphertext sizes of our IB-PRE scheme are short, only one or two ring elements, and our scheme could encrypt n bits in each encryption process.
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) can be classified as single-hop PRE and multi-use PRE according to the times which the ciphertext is transformed. Finding a unidirectional, multi-use, and chosen ciphertext attack (CCA) secure PRE is presented as an open problem by Canetti et al. Wang claimed to resolve this problem by proposing the first multi-use CCAsecure unidirectional PRE scheme. But we found that different with single-hop PRE, multi-use PRE without randomize encrypt key in its re-encryption algorithm could be vulnerable to attack. A new type attack to multi-use CCA-secure PRE named proxy bypass attack is proposed with a concrete attacks on Wang-MultiUse-PRE scheme. This attack is also effective for other multi-use scheme. At last we propose an improvement for Multi-Use-PRE to resist proxy bypass attack by randomize re-encryption algorithm.
Abstract Proxy re‐encryption (PRE) is a cryptographic primitive that allows a proxy to turn an Alice's ciphertext into a Bob's ciphertext on the same plaintext. At present, there are many different PRE schemes that have been proposed with different properties. However, all of them are based on the logarithm assumption and the large integer factorization assumption except for a bidirectional PRE scheme over lattices. In this paper, we construct the first multi‐use unidirectional PRE scheme based on lattices. In addition, the generation of the PRE key does not interact with two users, and the scheme can resist collusion attacks. Moreover, it is proved chosen plaintext attack secure in the standard model based on the Learning With Errors assumption. Finally, an identity‐based PRE is obtained from the basic construction. Copyright © 2015 John Wiley & Sons, Ltd.
Proxy re-encryption (PRE) has recently become a hot topic in cryptography research field. PRE can be classified as single-hop PRE and multi-use PRE according to the times the cipher text can be transformed. Finding a unidirectional, multi-use, and chosen cipher text attack (CCA) secure PRE is presented as an open problem by Green et al. Wang claimed to resolve this problem by proposing the first multi-use CCA-secure unidirectional PRE scheme. But we found that different with single-hop PRE, multi-use PRE without randomize encrypt key in its encryption algorithm could be vulnerable to attack. A new type attack to multi-use CCA-secure PRE named proxy bypass attack is proposed with a concrete attacks on Wang-Multi-Use-IB-PRE scheme. This attack is also effective for other multi-use scheme. At last we propose an improvement for Multi-Use-IB-PRE to resist proxy bypass attack by randomize re-encryption algorithm.