We propose an unbounded fully homomorphic encryption scheme, i.e. a scheme that allows one to compute on encrypted data for any desired functions without needing to decrypt the data or knowing the decryption keys. Thi...We propose an unbounded fully homomorphic encryption scheme, i.e. a scheme that allows one to compute on encrypted data for any desired functions without needing to decrypt the data or knowing the decryption keys. This is a rational solution to an old problem proposed by Rivest, Adleman, and Dertouzos [1] in 1978, and to some new problems that appeared in Peikert [2] as open questions 10 and open questions 11 a few years ago. Our scheme is completely different from the breakthrough work [3] of Gentry in 2009. Gentry’s bootstrapping technique constructs a fully homomorphic encryption (FHE) scheme from a somewhat homomorphic one that is powerful enough to evaluate its own decryption function. To date, it remains the only known way of obtaining unbounded FHE. Our construction of an unbounded FHE scheme is straightforward and can handle unbounded homomorphic computation on any refreshed ciphertexts without bootstrapping transformation technique.展开更多
In this article, we introduce the discrete subgroup in ℝ<sup>n</sup> as preliminaries first. Then we provide some theories of cyclic lattices and ideal lattices. By regarding the cyclic lattices...In this article, we introduce the discrete subgroup in ℝ<sup>n</sup> as preliminaries first. Then we provide some theories of cyclic lattices and ideal lattices. By regarding the cyclic lattices and ideal lattices as the correspondences of finitely generated R-modules, we prove our main theorem, i.e. the correspondence between cyclic lattices in ℝ<sup>n</sup> and finitely generated R-modules is one-to-one. Finally, we give an explicit and countable upper bound for the smoothing parameter of cyclic lattices.展开更多
Under the standard model, an IND-slD-CPA secure IBE （Identity Based Encryption） scheme is proposed, which is based on an improved trapdoor generation function over ring and decisional R-LWE （ring-learning with err...Under the standard model, an IND-slD-CPA secure IBE （Identity Based Encryption） scheme is proposed, which is based on an improved trapdoor generation function over ring and decisional R-LWE （ring-learning with errors） assumption, thus the hardness of recovering system master key can be reduced to solve the Ideal-SIS （small integer solution） problem, and the attack to the ciphertext is equivalent to solving the SVP （the shortest vector problem） in the worst case on ideal lattice to within a fixed poly（n） factor. Moreover, the proposed scheme has advantages of high encrypfion and decryption speed and low encryption blowup factor compared with all known IBE scheme from the standard lattice under the standard model.展开更多
文摘We propose an unbounded fully homomorphic encryption scheme, i.e. a scheme that allows one to compute on encrypted data for any desired functions without needing to decrypt the data or knowing the decryption keys. This is a rational solution to an old problem proposed by Rivest, Adleman, and Dertouzos [1] in 1978, and to some new problems that appeared in Peikert [2] as open questions 10 and open questions 11 a few years ago. Our scheme is completely different from the breakthrough work [3] of Gentry in 2009. Gentry’s bootstrapping technique constructs a fully homomorphic encryption (FHE) scheme from a somewhat homomorphic one that is powerful enough to evaluate its own decryption function. To date, it remains the only known way of obtaining unbounded FHE. Our construction of an unbounded FHE scheme is straightforward and can handle unbounded homomorphic computation on any refreshed ciphertexts without bootstrapping transformation technique.
文摘In this article, we introduce the discrete subgroup in ℝ<sup>n</sup> as preliminaries first. Then we provide some theories of cyclic lattices and ideal lattices. By regarding the cyclic lattices and ideal lattices as the correspondences of finitely generated R-modules, we prove our main theorem, i.e. the correspondence between cyclic lattices in ℝ<sup>n</sup> and finitely generated R-modules is one-to-one. Finally, we give an explicit and countable upper bound for the smoothing parameter of cyclic lattices.
基金Supported by the National Natural Science Foundation of China (60573036)Funding Research Project of the Engineering College of Chinese Armed Police Force(wjy201023)
文摘Under the standard model, an IND-slD-CPA secure IBE （Identity Based Encryption） scheme is proposed, which is based on an improved trapdoor generation function over ring and decisional R-LWE （ring-learning with errors） assumption, thus the hardness of recovering system master key can be reduced to solve the Ideal-SIS （small integer solution） problem, and the attack to the ciphertext is equivalent to solving the SVP （the shortest vector problem） in the worst case on ideal lattice to within a fixed poly（n） factor. Moreover, the proposed scheme has advantages of high encrypfion and decryption speed and low encryption blowup factor compared with all known IBE scheme from the standard lattice under the standard model.
