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IEEE International Conference on Trust, Security and Privacy in Computing and Communications (TrustCom)

Toward Proxy Re-encryption From Learning with Errors in the Exponent

Zengpeng Li, Chunguang Ma, Ding Wang, Minghao Zhao, Qian Zhao, Lu Zhou

Published Aug 1, 2017• 1 citation
Publisher

Abstract

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.

DOI
10.1109/trustcom/bigdatase/icess.2017.300

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Learning with Errors in the Exponent.

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We initiate the study of a novel class of group-theoretic intractability problems. Inspired by the theory of learning in presence of errors [Regev, STOC’05] we ask if noise in the exponent amplifies intractability. We put forth the notion of Learning with Errors in the Exponent (LWEE) and rather surprisingly show that various attractive properties known to exclusively hold for lattices carry over. Most notably are worstcase hardness and post-quantum resistance. In fact, LWEE’s duality is due to the reducibility to two seemingly unrelated assumptions: learning with errors and the representation problem [Brands, Crypto’93] in finite groups. For suitable parameter choices LWEE superposes properties from each individual intractability problem. The argument holds in the classical and quantum model of computation. We give the very first construction of a semantically secure public-key encryption system in the standard model. The heart of our construction is an “error recovery” technique inspired by [Joye-Libert, Eurocrypt’13] to handle critical propagations of noise terms in the exponent.

•Jan 1, 2014•2 citations
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 plays an important role for data security in cloud computing and big data, but the traditional re-encryption scheme based on the classical number theory problem cannot resist quantum attack, and the lattice-based cryptosystem has been proved to have the ability to resist quantum attack, so the lattice-based re-encryption scheme has always been a research hotspot. In view of the problem that collusion-resistance and multi-hop cannot be satisfied at the same time in existing schemes, this paper proposes a new identity-based proxy re-encryption scheme on lattice. Firstly, the scheme uses trapdoors as private keys to achieve one-way anti-collusion. In addition, we construct a variant of Learning with Errors (LWE), which uses a convert algorithm to transform the user matrix and replace the vector with a uniform matrix, so that the scheme can meet the requirements of multi-hop and encrypt multiple bits of messages at one time. Theoretical analysis and experimental simulation prove that the security of the new scheme can be reduced to a decision LWE problem, which can reach the IND-sID-CPA security in the standard model and can improve the encryption efficiency while ensuring the security.
The proxy re-encryption allows an intermediate proxy to convert a ciphertext for Alice into a ciphertext for Bob without seeing the original message and leaking out relevant information.Unlike many prior identity based proxy re-encryption schemes which are based on the number theoretic assumptions such as large integer factorization and discrete logarithm problem.In this paper, we first propose a novel identity based proxy re-encryption scheme which is based on the hardness of standard Learning With Error(LWE) problem and is CPA secure in the standard model.This scheme can be reduced to the worst-case lattice hard problem that is able to resist attacks from quantum algorithm.The key step in our construction is that the challenger how to answer the private query under a known trapdoor matrix.Our scheme enjoys properties of the non-interactivity, unidirectionality, anonymous and so on.In this paper, we utilize primitives include G-trapdoor for lattice and sample algorithms to realize simple and efficient re-encryption.
Proxy re-encryption (PRE) can guarantee the security of data sharing in the cloud making it important in ciphertext sharing in the cloud computing environment. Plenty of the current PRE algorithms based on the learning with errors (LWE) problem are constructed under the random oracle model or have problems such as long public parameter size, large ciphertext expansion rate, etc. We propose an identity-based PRE (IB-PRE) scheme using the LWE problem with short public parameters which can solve the mentioned challenges. Our scheme uses the blocking operation to decrease the public parameter size and a more useful trapdoor generation algorithm to reduce the trapdoor size. These two technologies improve the computational efficiency of the public key. We think that when we divide the identity id into 16 blocks, without much increase in computational overhead, the public key size can be reduced by 88.34%, and the scheme’s security level can remain unchanged. Our scheme achieves adaptive IND-ID-CPA security. It is unidirectional, collusion-resistant, and constructed under the standard model.
Proxy re-encryption (PRE) is a momentous and widely used cryptographic technique. It enables a proxy to forward ciphertext without the need of decryption. PRE has received significant interest in applications like cloud computing, blockchain, and the Internet of Things. Despite its wide range of uses, PRE has also been subject to new security and privacy regulations. In PKC’19, Cohen et al.et~al.et al.~first drew attention to the weakness in PRE's security against chosen-plaintext attacks (CPA) and put up a more stringent security concept known as security against honest re-encryption attacks (HRA). Notably, Cohen provides a beneficial conclusion as well. It is proveded that PRE schemes with re-encryption simulatability property can be elevated from CPA to HRA security. It is also proved that CPA-secure PRE schemes with re-encryption simulatability property can be directly elevated to those satisfying HRA security. However, those PRE schemes with re-encryption simulatability are almost always based on pairings. In this study, to the best of our knowledge, we directly construct HRA-secure PRE with re-encryption simulatability for the first time based on the learning with errors (LWE) assumption, which was widely believed to be quantum-resistant. Based on the re-encryption key generation algorithm and the re-encryption algorithm construction method of the above scheme, we can modify attribute-based conditional proxy re-encryption (AB-CPRE) as well as the corresponding attribute-based proxy re-encryption (AB-PRE) algorithm to make them have re-encryption simulatability properties. Finally, by using this property, We boost the security of AB-CPRE scheme of ESORICS'21 from CPA to HRA and simplify the HRA-security proof for the AB-PRE of ESORICS'21.
We initiate the study of a novel class of group-theoretic intractability problems. Inspired by the theory of learning in presence of errors [Regev, STOC’05] we ask if noise in the exponent amplifies intractability. We put forth the notion of Learning with Errors in the Exponent (LWEE) and rather surprisingly show that various attractive properties known to exclusively hold for lattices carry over. Most notably are worstcase hardness and post-quantum resistance. In fact, LWEE’s duality is due to the reducibility to two seemingly unrelated assumptions: learning with errors and the representation problem [Brands, Crypto’93] in finite groups. For suitable parameter choices LWEE superposes properties from each individual intractability problem. The argument holds in the classical and quantum model of computation. We give the very first construction of a semantically secure public-key encryption system in the standard model. The heart of our construction is an “error recovery” technique inspired by [Joye-Libert, Eurocrypt’13] to handle critical propagations of noise terms in the exponent.