密码算法的同态计算

发布时间：2018-03-08 21:40

本文选题：FHE　切入点：同态调用　出处：《西安电子科技大学》2014年硕士论文　论文类型：学位论文

【摘要】：全同态加密,它是指在无需解密的情况下,允许对加密数据进行任意运算,将结果密文解密后得到的恰好是其明文对应的某种运算。这种同态性实现了在不可信终端对加密数据进行可信计算,从根本上解决了将数据及其操作委托给第三方时的保密问题。另外,全同态加密技术还在密文搜索、电子投票和多方计算等领域都有着重要的应用。自从09年Gentry提出第一个全同态加密方案至今,全同态加密机制不断得到发展和优化,构造出了基于不同安全假设的全同态加密体制。但其庞大的密钥尺寸和计算复杂度使得在实际应用中效率很低。通过引入混合加密技术可以提高全同态方案的效率。混合加密体制是指将一个普通的密码体制(对称密码或公钥密码等)和同态密码体制结合使用,初始信息的加密使用普通密码体制的加密算法,而解密以及对密文的运算使用同态加密体制,这样减小了同态运算时存储密文的代价和通信复杂度,但是这也引入了新的计算量和电路复杂度。本文在混合加密体制的背景下,研究了混合加密中同态调用普通密码算法解密电路时消耗的同态电路层数,这样有利于我们寻找更优的密码算法用于混合加密。主要的工作如下:首先,对全同态加密技术的研究背景、研究现状以及趋势作出了简单的介绍。然后,对全同态加密发展中出现的各种加密机制和关键技术进行了详细的介绍。主要分为两大部分:Gentry蓝本的全同态加密机制和基于LWE困难问题的全同态加密机制。它们分别对应的是Gentry09方案、DGHV方案和BV11方案、BGV换模方案、Bra12模不变方案、GSW13近似特征向量法。最后,介绍了混合加密技术。总结了当前文献中关于对称算法AES、hash函数SHA-256,以及公钥密码算法ElGamal的同态调用工作。为了寻找更优的密码体制用于混合计算,本文利用上述同态调用的分析思路,对其他对称算法进行了同态调用分析。主要对CLAFIA密码和KASUMI密码的同态计算进行了详细的分析,得出了它们在不同编码方式和不同的封装情况下各自消耗的同态电路层数。另外,在比特编码和比特封装下,对DES等12种对称密码算法的同态调用进行了简单的分析,将它们各自消耗的同态电路层数汇总成表。
[Abstract]:Full homomorphic encryption, which means that any operation of encrypted data is allowed without the need for decryption. After decrypting the result ciphertext, the result is exactly some kind of operation corresponding to its plaintext. This homomorphism realizes the trusted computation of encrypted data at untrusted terminals. It fundamentally solves the problem of confidentiality when entrusting the data and its operation to a third party. In addition, the full homomorphic encryption technology also searches the ciphertext. Electronic voting and multi-party computing have important applications. Since Gentry put forward the first full homomorphic encryption scheme in 2009, the mechanism of full homomorphic encryption has been continuously developed and optimized. A fully homomorphic encryption scheme based on different security assumptions is constructed. However, its huge key size and computational complexity make it inefficient in practical application. The effect of full homomorphism scheme can be improved by introducing mixed encryption technology. A hybrid cryptosystem is a combination of a common cryptosystem (symmetric cryptography, public key cryptography, etc.) and a homomorphic cryptosystem, The encryption of the initial information uses the common cipher encryption algorithm, while the decryption and the operation of the ciphertext use the homomorphic encryption system, which reduces the cost and communication complexity of storing the ciphertext in the homomorphic operation. However, it also introduces new computational complexity and circuit complexity. In this paper, we study the number of homomorphic circuit layers consumed when homomorphism calls the decryption circuit of common cipher algorithm in mixed encryption under the background of mixed encryption. The main work is as follows: firstly, the research background, research status and trend of the full homomorphism encryption technology are briefly introduced. Various encryption mechanisms and key technologies in the development of full homomorphic encryption are introduced in detail. They are mainly divided into two parts: one is the full homomorphic encryption mechanism of the Gentry blueprint and the other is the full homomorphic encryption mechanism based on the difficult problem of LWE. The corresponding schemes are Gentry09 scheme / DGHV scheme and BV11 scheme respectively. Bra12 mode invariant scheme / GSW13 approximate eigenvector method. This paper introduces the hybrid encryption technology, summarizes the homomorphic calls of the symmetric algorithm SHA-256 and the public key cryptosystem ElGamal in the literature. In order to find a better cryptosystem for hybrid computation, In this paper, the homomorphism call analysis of other symmetric algorithms is carried out by using the above homomorphism calls. The homomorphism calculation of CLAFIA cipher and KASUMI cipher is analyzed in detail. The number of homomorphic circuit layers consumed by them under different encoding modes and different encapsulation conditions is obtained. In addition, under bit coding and bit encapsulation, the homomorphism calls of 12 symmetric cryptographic algorithms such as DES are simply analyzed. Summarize the number of homomorphic circuit layers they consume into a table.
【学位授予单位】：西安电子科技大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TN918.4

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