全同態(tài)密碼理論研究
發(fā)布時間：2018-07-26 17:50
【摘要】：公鑰密碼學(xué)已經(jīng)走過了36個年頭,歷史上誕生的公鑰密碼體制大都具有同態(tài)特性,但是構(gòu)造“完美”的全同態(tài)密碼體制也一直是密碼學(xué)上的難題。云計算關(guān)鍵技術(shù),密文檢索技術(shù),安全多方計算以及遠程數(shù)據(jù)完整性校驗對密碼學(xué)發(fā)展提出了新的要求,設(shè)計安全高效的全同態(tài)密碼體制變得很必要。因此,研究全同態(tài)密碼相關(guān)理論,設(shè)計實用的全同態(tài)密碼體制成了學(xué)者們關(guān)注的熱點。本文的工作正是基于此展開,主要包括以下幾個方面:首先,為了對全同態(tài)密碼有一個全面而深入的分析,本文對具有代表性的同態(tài)密碼體制進行了研究。歷史上的經(jīng)典體制如RSA密碼體制,Paillier密碼體制和ElGamal密碼體制的同態(tài)性產(chǎn)生都有各自不同的特點,本文重點剖析了這些公鑰密碼體制同態(tài)特性的產(chǎn)生方法,對同態(tài)密碼體制進行分類,歸納了多種同態(tài)特性。在此基礎(chǔ)上,設(shè)計了一種語義安全的靶向全同態(tài)密碼體制,并利用上述密碼體制,設(shè)計了一種安全兩方點積計算協(xié)議。其次,為了把握全同態(tài)密碼體制的設(shè)計方法,本文對基于Gentry思想設(shè)計的、兩個經(jīng)典的全同態(tài)密碼體制—基于整數(shù)的(又名DGHV密碼體制)和基于理想格的全同態(tài)密碼體制進行了研究和分析。在分析理想格的密碼學(xué)特性及其局限性和DGHV全同態(tài)密碼體制的基礎(chǔ)上,對經(jīng)典的DGHV全同態(tài)密碼體制進行了改進,設(shè)計了一種公鑰尺寸小、效率更高的Somewhat同態(tài)密碼體制。再次,為了構(gòu)造格上全同態(tài)密碼體制,本文設(shè)計了一種基于后量子安全假設(shè)LWE的全同態(tài)密碼體制。在文中,首先以LWE為載體,研究并給出了全同態(tài)密碼體制設(shè)計的關(guān)鍵技術(shù),結(jié)合矩陣運算的特點,設(shè)計了一種基于密文展縮的全同態(tài)密碼體制,該體制避開了經(jīng)典全同態(tài)設(shè)計中引入額外的安全假設(shè)的環(huán)節(jié),安全性更加明確。其公私鑰尺寸為O(n2l),而明密文擴展為O(n2l),這兩點和之前的全同態(tài)密碼體制相比,都有很大改善。最后,全同態(tài)密碼體制的研究和設(shè)計給同態(tài)數(shù)字簽名和同態(tài)消息認證帶來了新的思路,本文在研究全同態(tài)密碼體制的基礎(chǔ)上,對消息認證過程進行分析,設(shè)計了一種改進的全同態(tài)消息認證算法。該同態(tài)消息認證碼的安全性是基于偽隨機函數(shù)的設(shè)計,本文的改進算法保證了明文的不泄露性和兩類不可偽造性,給部分數(shù)據(jù)的完整性認證提供了新的思路和方法。在本文的結(jié)尾,對全文的工作進行總結(jié),并給出了下一步的工作計劃。
[Abstract]:Public key cryptography has gone through 36 years. Most of the public key cryptosystems in history have homomorphic characteristics, but the construction of "perfect" homomorphic cryptosystem has always been a difficult problem in cryptography. With new requirements, it is necessary to design a safe and efficient all homomorphic cryptosystem. Therefore, it is a hot topic for scholars to study the whole homomorphic cipher theory and design a practical homomorphic cryptosystem. The work of this paper is based on the following aspects: first, there is a comprehensive analysis of all homomorphic ciphers. In depth analysis, a representative homomorphic cryptosystem has been studied in this paper. The classical system in history, such as the RSA cryptosystem, the Paillier cryptosystem and the homomorphism of the ElGamal cryptosystem, has its own characteristics. This paper focuses on the analysis of the homomorphic characteristics of the public key cryptosystems, and the homomorphic ciphers. The system is classified and generalizes a variety of homomorphism characteristics. On this basis, a semantic security target full homomorphic cryptosystem is designed, and a secure two party point product calculation protocol is designed by using the above cryptosystem. Secondly, in order to grasp the design method of the whole homomorphic cryptosystem, this paper designs two classics based on Gentry thought. The whole homomorphism cryptosystem, an integer based (also called DGHV cryptosystem) and an all homomorphic cryptosystem based on ideal lattice, is studied and analyzed. On the basis of the analysis of the cryptology characteristics and limitations of the ideal lattice and the DGHV homomorphism cryptosystem, the classical DGHV homomorphism cryptosystem is improved and a kind of public cryptosystem is designed. Somewhat homomorphic Cryptosystem with small key size and higher efficiency. Again, in order to construct the whole homomorphic cryptosystem on the lattice, this paper designs a all homomorphic cryptosystem based on the post quantum security hypothesis LWE. In this paper, the key technology of the whole homomorphic cryptosystem is studied and given the key technology of the whole homomorphic cryptosystem, and the characteristic of the matrix operation is combined with the LWE as the carrier. An all homomorphism cryptosystem based on ciphertext expansion is designed, which avoids the additional security hypothesis in the classical homomorphism design. The security is more explicit. The public key size is O (n2l), and the plaintext is extended to O (n2l). The research and design of cryptosystem bring new ideas to homomorphic digital signature and homomorphic message authentication. On the basis of studying the whole homomorphism cryptosystem, this paper analyzes the message authentication process and designs an improved whole homomorphic message authentication algorithm. The security of the homomorphic message identification code is based on the design of pseudo random function. The improved algorithm in this paper ensures the non leaking and two kinds of non forgery of the plaintext, and provides new ideas and methods for the integrity authentication of some data. At the end of this paper, the work of the full text is summarized, and the next work plan is given.
【學(xué)位授予單位】：西安電子科技大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2014
【分類號】：TN918.4
[Abstract]:Public key cryptography has gone through 36 years. Most of the public key cryptosystems in history have homomorphic characteristics, but the construction of "perfect" homomorphic cryptosystem has always been a difficult problem in cryptography. With new requirements, it is necessary to design a safe and efficient all homomorphic cryptosystem. Therefore, it is a hot topic for scholars to study the whole homomorphic cipher theory and design a practical homomorphic cryptosystem. The work of this paper is based on the following aspects: first, there is a comprehensive analysis of all homomorphic ciphers. In depth analysis, a representative homomorphic cryptosystem has been studied in this paper. The classical system in history, such as the RSA cryptosystem, the Paillier cryptosystem and the homomorphism of the ElGamal cryptosystem, has its own characteristics. This paper focuses on the analysis of the homomorphic characteristics of the public key cryptosystems, and the homomorphic ciphers. The system is classified and generalizes a variety of homomorphism characteristics. On this basis, a semantic security target full homomorphic cryptosystem is designed, and a secure two party point product calculation protocol is designed by using the above cryptosystem. Secondly, in order to grasp the design method of the whole homomorphic cryptosystem, this paper designs two classics based on Gentry thought. The whole homomorphism cryptosystem, an integer based (also called DGHV cryptosystem) and an all homomorphic cryptosystem based on ideal lattice, is studied and analyzed. On the basis of the analysis of the cryptology characteristics and limitations of the ideal lattice and the DGHV homomorphism cryptosystem, the classical DGHV homomorphism cryptosystem is improved and a kind of public cryptosystem is designed. Somewhat homomorphic Cryptosystem with small key size and higher efficiency. Again, in order to construct the whole homomorphic cryptosystem on the lattice, this paper designs a all homomorphic cryptosystem based on the post quantum security hypothesis LWE. In this paper, the key technology of the whole homomorphic cryptosystem is studied and given the key technology of the whole homomorphic cryptosystem, and the characteristic of the matrix operation is combined with the LWE as the carrier. An all homomorphism cryptosystem based on ciphertext expansion is designed, which avoids the additional security hypothesis in the classical homomorphism design. The security is more explicit. The public key size is O (n2l), and the plaintext is extended to O (n2l). The research and design of cryptosystem bring new ideas to homomorphic digital signature and homomorphic message authentication. On the basis of studying the whole homomorphism cryptosystem, this paper analyzes the message authentication process and designs an improved whole homomorphic message authentication algorithm. The security of the homomorphic message identification code is based on the design of pseudo random function. The improved algorithm in this paper ensures the non leaking and two kinds of non forgery of the plaintext, and provides new ideas and methods for the integrity authentication of some data. At the end of this paper, the work of the full text is summarized, and the next work plan is given.
【學(xué)位授予單位】：西安電子科技大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2014
【分類號】：TN918.4
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