For efficiency improvement and public key size reduction, a new public key compression scheme is proposed for fully homomorphic encryption based on quadratic parameters with correction (QPC-PKC scheme). Compared with existing public key compression schemes, the size of the public key in the proposed scheme is reduced from $\tilde {\mathrm {O}}({\lambda }^{5})$ to $\tilde {\mathrm {O}}({\lambda }^{3.5})$ by reducing the number of subgroup public key elements and the element bit-lengths. Based on the construction mechanisms of the somewhat fully homomorphic encryption (SWHE), a QPC-PKC SWHE scheme is constructed and the parameter constraints are presented. The correctness and semantical security of the proposed QPC-PKC SWHE scheme are then proved based on the error-free approximate greatest common divisor assumption. Finally, the public key size performance of the QPC-PKC scheme is theoretically analyzed, while the public key sizes and running times of the QPC-PKC SWHE scheme are experimentally evaluated. The results show that the public key size of the proposed scheme is significantly reduced compared with the existing schemes, and the encryption efficiency of the QPC-PKC SWHE scheme is also improved as expected.

A Public Key Compression Scheme for Fully Homomorphic Encryption Based on Quadratic Parameters With Correction

In order to guarantee the user’s privacy and the integrity of data when retrieving ciphertext in an untrusted cloud environment, an improved ciphertext retrieval scheme was proposed based on full homomorphic encryption. This scheme can encrypt two bits one time and improve the efficiency of retrieval. Moreover, it has small key space and reduces the storage space. Meanwhile, the homomorphic property of this scheme was proved in detail. The experimental results and comparisons show that the proposed scheme is characterized by increased security, high efficiency and low cost.

An Improved Ciphertext Retrieval Scheme Based on Fully Homomorphic Encryption

This paper proposes a secure retrieval scheme based on homomorphic encryption for the server-side structured database. With the advantage of this scheme, ciphertext in server under unreliable storage circumstance can be efficiently retrieved without exposition of plaintext. Users can also have detailed access to their data. In this paper, a data encryption and decryption algorithm based on homomorphic encryption is proposed for character data in database. Server can calculate and operate the ciphertext data directly. An equivalent retrieval algorithm based on homomorphic encryption is proposed for equivalent retrieval of ciphertext data, which can effectively reduce the amount of data returned to the client and improve the retrieval efficiency. A counting joint index generation algorithm with upper limit based on dual encoding function is proposed for fuzzy retrieve of character data which can improve the efficiency of the server's filtering of the irrelevant data and reduce the waste of time and space.

Research on database ciphertext retrieval based on homomorphic encryption

Fully homomorphic encryption has important applications in cloud storage, the cipher text retrieval and other aspects. In order to get a better fully homomorphic encryption scheme for cloud storage, an improved fully homomorphic encryption (FHE) scheme based on DGHV scheme is proposed by analyzing and comparing the existing research situation of fully homomorphic encryption scheme. On the premise of guarantying scheme’s safety, the amount of single encrypted data is increased to 3 bit. Arguably, improving the single encrypted data volume at the same time, the public key, suitable for cloud storage platform, has smaller size, and reduces the computational complexity. Keywords-fully homomorphic encryption; cloud storage; cipher text retrieval

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Improved Fully Homomorphic Encryption Algorithm for Cloud Storage

In order to improve the efficiency of the homomorphic encryption scheme, an improved homomorphic encryption scheme based on integer is proposed. On the basis of the DGHV scheme, the size of the public key is first reduced to ( ) by using the public key element quadratic technique and the parameter offset technique. Then, by changing the modulo 2 operation to modulo operation, the improved scheme can encrypt the data of k bits at one time, which has smaller public key size and higher efficiency than the original DGHV scheme. Finally, the correctness and security of the scheme are proved by the theory, and the efficiency analysis of the scheme is given.

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A Fully Homomorphic Encryption Scheme With a Smaller Public Key

The efficiency of the present fully homomorphic encryption scheme is extra low and far from practical application.How to improve the efficiency and security of fully homomorphic encryption become the focus and pitfall of academic research.In order to improve the efficiency,this paper put forward an improved scheme of the base of Dijk's scheme using Gentry's fully homomorhpic technology.The improved scheme could encrypt 2 bit plaintext each time and reduce the public key size to(λ7),accordingly the improved scheme was more efficient than Dijk's scheme and had smaller public key size.The security of the proposed scheme was based on both the approximate GCD problem and the sparse-subset sum problem.

Du He

Papers

Improved fully homomorphic encryption over integers