本文選題：RSA加密算法　切入點(diǎn)：三個(gè)素?cái)?shù)因子　出處：《安徽大學(xué)》2014年碩士論文

【摘要】：隨著網(wǎng)絡(luò)信息技術(shù)的高速發(fā)展,其安全問題越來越凸顯出來。而網(wǎng)絡(luò)信息安全重要理論基礎(chǔ)是密碼學(xué)。其中,RSA加密算法是被應(yīng)用最廣泛的公鑰加密算法,它既可以實(shí)現(xiàn)數(shù)據(jù)加密中,又可以實(shí)現(xiàn)數(shù)字簽名。但是近些年來,隨著因子分解技術(shù)的不斷提高(即對(duì)大數(shù)分解能力的提高),它的安全性受到了威脅。為了保證RSA加密算法的安全性,人們將算法中密鑰的位數(shù)不斷地增加。例如,在2009年12月,研究人員完成了768位RSA算法(即232數(shù)位數(shù)字的RSA-768密鑰)的因式分解,同時(shí)研究人員也表示現(xiàn)在普遍使用的1024位密鑰預(yù)計(jì)也將會(huì)在10年內(nèi)攻破,在未來幾年中需要將RSA算法中的1024位密鑰過渡到2048位密鑰。 雖然密鑰位數(shù)的增加確保了其安全性,但是也導(dǎo)致了算法效率大大的下降,主要表現(xiàn)在選擇密鑰的困難性上和加解密計(jì)算的復(fù)雜性上,這大大限制了它的應(yīng)用范圍。為了提高RSA加密算法的效率,本文首先介紹和分析了RSA加密算法,并對(duì)RSA加密算法做出了改進(jìn),內(nèi)容大致如下： 1)介紹了傳統(tǒng)的RSA加密算法,對(duì)于密鑰位數(shù)的增加所帶來的問題,本文采用了三個(gè)素?cái)?shù)因子的RSA加密算法,這樣雖然增加了素?cái)?shù)因子的個(gè)數(shù)但是減少了素?cái)?shù)因子的位數(shù),從而降低了選擇大素?cái)?shù)因子的困難性,同時(shí)也提高了其選擇的效率。 2)在加密過程中介紹了常用的加密算法：傳統(tǒng)的平方乘算法、基于乘同余對(duì)稱性的SMM算法、2K進(jìn)制算法以及擴(kuò)展2K進(jìn)制算法,然后分析了這些算法的優(yōu)缺點(diǎn),最后在加密算法過程中將SMM算法和擴(kuò)展的2K進(jìn)制算法進(jìn)行組合,這樣可以將它們的優(yōu)點(diǎn)進(jìn)行結(jié)合形成一種新的組合算法。 3)在解密過程中介紹了基于中國剩余定理的解密算法,與以前算法不同點(diǎn)是在本文中采用了三個(gè)素?cái)?shù)因子,分析了其解密過程,將解密算法中的取模運(yùn)算轉(zhuǎn)化為對(duì)三個(gè)較小素?cái)?shù)因子的取模運(yùn)算,減少了解密算法的計(jì)算量。 4)設(shè)計(jì)并實(shí)現(xiàn)了RSA加解密軟件,軟件中可以選擇不同的算法進(jìn)行加密和解密并測試出其所需的時(shí)間,將改進(jìn)后的算法與傳統(tǒng)的算法從效率上進(jìn)行比較, 最后得出改進(jìn)后的算法在效率上有了一定程度的提高。
[Abstract]:With the rapid development of network information technology, its security problems become more and more prominent.The important theoretical foundation of network information security is cryptography.Among them, RSA encryption algorithm is the most widely used public key encryption algorithm, it can not only realize data encryption, but also realize digital signature.However, in recent years, with the constant improvement of factorization technology (that is, the ability to decompose large numbers), its security is threatened.In order to ensure the security of RSA encryption algorithm, people increase the number of keys in the algorithm.For example, in December 2009, researchers completed factorization of the 768 bit RSA algorithm, or the 232-digit RSA-768 key, while researchers said that the now widely used 1024 bit key is also expected to break through within 10 years.In the next few years, the 1024 bit key in RSA algorithm needs to be transferred to 2048 bit key.Although the increase in the number of key bits ensures its security, it also leads to a great decrease in the efficiency of the algorithm, which is mainly reflected in the difficulty of selecting the key and the complexity of encryption and decryption computation, which greatly limits its application scope.In order to improve the efficiency of RSA encryption algorithm, this paper first introduces and analyzes the RSA encryption algorithm, and RSA encryption algorithm has been improved, the content is as follows:1) the traditional RSA encryption algorithm is introduced. For the problem of increasing the number of key bits, the RSA encryption algorithm with three prime factors is adopted in this paper, which increases the number of prime factors but reduces the number of prime factors.Therefore, the difficulty of selecting large prime factor is reduced, and the efficiency of selection is also improved.2) in the process of encryption, the common encryption algorithms are introduced: the traditional square multiplication algorithm, the SMM algorithm based on multiplicative congruence symmetry and the extended 2K-ary algorithm. Then, the advantages and disadvantages of these algorithms are analyzed.Finally, the SMM algorithm and the extended 2K binary algorithm are combined in the process of encryption, which can combine their advantages to form a new combination algorithm.3) in the process of decryption, the decryption algorithm based on the Chinese residue theorem is introduced. Different from the previous algorithm, three prime factors are used in this paper, and the decryption process is analyzed.In order to reduce the computation of decryption algorithm, the modulo operation in decryption algorithm is transformed into that of three smaller prime number factors.4) the RSA encryption and decryption software is designed and implemented. The software can choose different algorithms to encrypt and decrypt and test the time required. The improved algorithm is compared with the traditional algorithm in terms of efficiency.Finally, it is concluded that the efficiency of the improved algorithm has been improved to a certain extent.
【學(xué)位授予單位】：安徽大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2014
【分類號(hào)】：TN918.4

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