格上公钥加密体制设计与分析

发布时间：2018-04-25 17:56

本文选题：公钥加密体制 + 格　；参考：《解放军信息工程大学》2014年硕士论文

【摘要】：随着互联网技术的蓬勃发展,网络通信的安全性受到了各界的高度重视。作为网络安全的基石,公钥密码在保障网络通信安全的过程中发挥了重要作用。但随着量子计算机研究的推进,传统公钥密码算法的安全性受到了越来越大的威胁。基于格上困难问题的公钥密码体制对量子攻击算法免疫,是后量子时代的重要密码技术之一,具有重要的研究意义和应用价值。本文围绕基于格的公钥加密体制的设计与分析展开研究,主要进行了以下三个方面的工作：1.提出基于格上带舍入学习问题(Learning with Rounding,LWR问题)的陷门单向函数,设计了三种基于LWR问题的公钥加密体制并给出安全性证明,和同类现有体制相比,本文中的体制具有密文扩张较小、计算复杂度较低等优点。在此基础上,进一步研究了多比特加密的情况,给出了所设计体制的密文和明文尺寸比值的下限。在判断性LWR问题难解的假设下,上述体制满足选择明文攻击下不可区分(IND-CPA)安全性。2.对于公钥加密体制而言,适应性选择密文攻击下不可区分(IND-CCA2)安全性是更高的安全级别。本文在IND-CPA安全的体制基础上,研究了IND-CCA2安全的新体制设计,提出了两种随机谕示模型下和一种标准模型下IND-CCA2安全的体制,并基于判断性LWR问题给出了安全性证明。和IND-CPA安全的体制相比,算法效率有所降低,但安全级别得到有效提升。3.近年来,内存泄露攻击给公钥加密的应用安全性提出了更高的要求,如何提高体制的抗泄露性成为公钥加密研究中需要注意的问题之一。本文对基于LWR问题的陷门函数和文中提出的加密体制进行抗泄露性分析,给出了在一般泄露模型和有限泄露模型下保证安全的最大泄漏量。在此基础上,本文通过对陷门函数和加密体制进行改进,设计了一种具有较强抗泄露性的公钥加密体制。对一般泄露模型而言,该体制可以抵抗1-log β/log q的泄漏量,其中β,q为体制参数。
[Abstract]:With the rapid development of Internet technology, the security of network communication has been attached great importance. As the cornerstone of network security, public key cryptography plays an important role in the process of ensuring the security of network communication. However, with the development of quantum computer, the security of traditional public key cryptography is threatened more and more. The public-key cryptosystem based on the difficult problem on lattice is immune to quantum attack algorithm, which is one of the important cryptographic techniques in the post-quantum era, and has important research significance and application value. This paper focuses on the design and analysis of lattice-based public key cryptosystem, mainly in the following three aspects: 1. In this paper, a trapdoor one-way function based on rounding learning problem with rounding learning is proposed. Three public-key encryption schemes based on LWR problem are designed, and the security proof is given. The scheme in this paper has the advantages of small expansion of ciphertext and low computational complexity. On this basis, the case of multi-bit encryption is further studied, and the lower limit of the ciphertext and plaintext size ratio of the designed scheme is given. Under the assumption that the judging LWR problem is difficult to solve, the proposed scheme satisfies the security of indistinguishable IND-CPA under selective plaintext attack. For public key cryptosystem, indistinguishable IND-CCA2 is a higher security level under adaptive ciphertext attack. Based on the IND-CPA security system, this paper studies the new architecture design of IND-CCA2 security, proposes two kinds of IND-CCA2 security systems under random oracle model and one standard model, and gives the security proof based on the judging LWR problem. Compared with the IND-CPA security system, the efficiency of the algorithm is reduced, but the security level is effectively improved. 3. 3. In recent years, memory leak attacks have put forward higher requirements for the application security of public key encryption. How to improve the anti-disclosure of the system has become one of the important problems in the research of public key encryption. In this paper, the trapdoor function based on LWR problem and the encryption scheme proposed in this paper are analyzed against leakage, and the maximum leakage quantity to ensure safety under the general leakage model and the finite leakage model is given. On this basis, a public-key cryptosystem with strong anti-leakage is designed by improving the trapdoor function and encryption system. For the general leakage model, the system can resist the leakage of 1-log 尾 / log Q, where 尾 Q is the system parameter.
【学位授予单位】：解放军信息工程大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TN918.4

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