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目前基于整数的全同态加密方案的效率较低,与实际应用仍有一定的距离.如何提高方案的效率和安全性是全同态加密技术研究的难点.本文首先分析了全同态加密方案的构造思想,总结了基于整数的全同态加密的研究现状以及相关技术.为了进一步提高方案的效率,本文在Dijk等人DGHV方案的基础上,通过利用Gentry的全同态加密构造基本思路,提出了一个具有较小公钥尺寸和更高效率的全同态加密新方案.新方案将明文空间由{0,1}扩展到{0,1}~l,并结合公钥元素的二次形式和密文压缩技术,有效地实现了DGHV方案的批量处理功能.再利用压缩解密电路的思路,引入SSSP假设,与加法或乘法门电路构造增强(扩展)解密电路,从而实现方案的全同态.本文对方案基于无错近似最大公约数问题(error-free GCD)的安全性规约做了较详细地分析,并从公、私钥尺寸等方面与DGHV、BDGHV方案进行了比较,新方案具有更短公钥尺寸等优点.
At present, the whole homomorphic encryption scheme based on integers is inefficient and still has a certain distance from the practical application.How to improve the efficiency and security of the scheme is a difficult point in the study of isomorphic encryption.In this paper, , And summarizes the research status and related technologies of integer-based homomorphic encryption.In order to further improve the efficiency of the scheme, based on the Dijk et al DGHV scheme, this paper constructs the basic idea by using Gentry’s homomorphic encryption, A new scheme of the homomorphic encryption with smaller size and higher efficiency is proposed. The new scheme expands the plaintext space from {0,1} to {0,1} ~ l and combines the secondary Form and ciphertext compression technology to effectively realize the batch processing function of DGHV scheme.And then use the idea of compression and decryption circuit, introduce the SSSP hypothesis, and construct the enhanced (extended) decryption circuit with addition or multiplication gate to achieve the same This paper analyzes the protocol based on the error-free GCD (GCD) security protocol in detail and compares it with the DGHV and BDGHV schemes in terms of public and private key dimensions Relatively new scheme has the advantages of a shorter dimension public key.