Proxy Re-encryption (PRE) is a useful cryptographic structure who enables a semi-trusted proxy to convert a ciphertext for Alice into a ciphertext for Bob without seeing the corresponding plaintext. Although there are many PRE schemes in recent years, few of them are set up based on lattice. Not only this, these lattice-based PRE schemes are all more complicated than the traditional PRE schemes. In this paper, through the study of the common lattice problems such as the Small integer solution (SIS) and the Learning with Errors (LWE), we analyze the feasibility of efficient lattice-based PRE scheme combined with the previous results. Finally, we propose an efficient lattice-based PRE scheme L-PRE without losing the hardness of lattice problems.
Proxy Re-encryption (PRE) is a useful cryptographic structure who enables a semi-trusted proxy to convert a ciphertext for Alice into a ciphertext for Bob without seeing the corresponding plaintext. Although there are many PRE schemes in recent years, few of them are set up based on lattice. Not only this, these lattice-based PRE schemes are all more complicated than the traditional PRE schemes. In this paper, through the study of the common lattice problems such as the Small integer solution (SIS) and the Learning with Errors (LWE), we analyze the feasibility of efficient lattice-based PRE scheme combined with the previous results. Finally, we propose an efficient lattice-based PRE scheme L-PRE without losing the hardness of lattice problems.
Proxy re‐encryption (PRE) is a promising cryptographic structure for pervasive data sharing in cloud‐based social networks, which enables a semi‐trusted proxy to convert a ciphertext for Alice into a ciphertext for Bob without seeing the corresponding plaintext. Since the proxy is semi‐trust, a PRE scheme which can resist the collusion attack will be of great practical value. Jiang et al . in 2015 and Kim and Jeong in 2016 have proposed collusion‐resistant PRE (CR‐PRE) schemes from the lattice by a similar technique, respectively. However, through the analysis of their schemes, the authors find that both of them have defects in the construction of the re‐encryption key, which will lead to the re‐encryption ciphertext cannot be decrypted or decrypted error with high probability. In this study, the authors first point out the defects in the work of Jiang et al . 's work and Kim and Jeong's work and propose an improved collusion‐resistant unidirectional PRE scheme from lattice, based on learning with errors problems. In addition to solving the defects, CR‐PRE still has many useful properties similar to the previous schemes, such as unidirectional, collusion resistant, chosen‐plaintext attack secure and so on.
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.
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) 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) allows a semi-trusted proxy to convert a ciphertext intended for Alice into a ciphertext for Bob without learning anything about the underlying plaintext. Chunbo Ma et al. have proposed a group based proxy re-encryption scheme to convert a ciphertext from one group to another. Any group member can independently decrypt the ciphertexts encrypted to its group. In their paper, the authors gave a security proof to say that the scheme is secure against adaptive chosen ciphertext attack. However, we highlight the aws in their scheme and show that their scheme is not secure against adaptive chosen ciphertext attack. In this direction, we construct an adversary who issues only one decryption oracle query and break the security of their scheme with non-negligible advantage.