Biblio

Data security and privacy have become an important problem while big data systems are growing dramatically fast in various application fields. Paillier additive homomorphic cryptosystem is widely used in information security fields such as big data security, communication security, cloud computing security, and artificial intelligence security. However, how to improve its computational performance is one of the most critical problems in practice. In this paper, we propose two modifications to improve the performance of the Paillier cryptosystem. Firstly, we introduce a key generation method to generate the private key with low Hamming weight, and this can be used to accelerate the decryption computation of the Paillier cryptosystem. Secondly, we propose an acceleration method based on Hensel lifting in the Paillier cryptosystem. This method can obtain a faster and improved decryption process by showing the mathematical analysis of the decryption algorithm.

Outsourcing the decryption of attribute-based encryption (ABE) ciphertext is a promising way to tackle the question of how users can perform decryption efficiently. However, existing solutions require the type of the target ciphertext to be determined at the setup of the outsourcing scheme. As such, making the target cryptosystems (or the clients) to be versatile becomes an issue that warrants investigations. In this paper, the problem we wish to tackle is to transform an ABE ciphertext to any client who is using the same, or possibly different, public-key encryption (PKE) system with the sender. The problem is of practical interest since it is hard to require all clients to use the same PKE, especially in the case of remote and cross-system data sharing. In addition, we also consider whether robust client-side decryption scheme can be adopted. This feature is not supported in the existing ABE with outsourcing. We introduce cross-system proxy re-encryptions (CS-PRE), a new re-encryption paradigm in which a semi-trusted proxy converts a ciphertext of a source cryptosystem (\$\textparagraphi\_0\$) into a ciphertext for a target cryptosystem (\$\textparagraphi\$). We formalize CS-PRE and present a construction that performs well in the following aspects. (1)Versatility: \$\textparagraphi\_0\$ can be any attribute-based encryption (ABE) within Attrapadung's pair encoding framework. \$\textparagraphi\$ can be any public-key encryption. Furthermore, the keys and public parameters can be generated independently. (2) Compatibility: CS-PRE does not modify the public parameters and keys of \$\textparagraphi\_0\$ and \$\textparagraphi\$. Besides, input for the conversion is an ordinary ciphertext of \$\textparagraphi\_0\$. (3) Efficiency: The computational cost for re-encryption and decryption of the re-encrypted ciphertext are roughly the same as a decryption in \$\textparagraphi\_0\$ and \$\textparagraphi\$ respectively. We prove that our construction is fully secure assuming \$\textparagraphi\_0\$ is secure in Attrapadung's framework and \$\textparagraphi\$ is IND-CPA secure. Furthermore, it remains secure when there are multiple target cryptosystems. As with other proxy re-encryption, CS-PRE enables flexible sharing of cloud data, as the owner can instruct the cloud server to re-encrypt his ciphertext to those for the intended recipient. In addition, it allows lightweight devices to enjoy access to remote data encrypted under powerful but possibly costly encryption, such as functional encryption, by utilizing the server's power in converting the ciphertext to a simpler encryption, such as RSA. Finally, instances of CS-PRE can be viewed as new proxy re-encryption schemes, such as a PRE supporting ABE for regular language to Hierarchical IBE or Doubly Spatial Encryption to lattice-based encryptions (e.g. NTRUCCA).