本文關(guān)鍵詞： SM2 數(shù)字簽名 Dickson乘法器　出處：《哈爾濱工業(yè)大學(xué)》2014年碩士論文　論文類型：學(xué)位論文

【摘要】：SM2是使用橢圓曲線加密(ECC)的一種密碼學(xué)標(biāo)準(zhǔn),而ECC是1985年提出的一種公鑰密碼算法。與主流加密算法如RSA算法相比,ECC算法具有安全性能高、計算量小、處理速度快等特點。然而為充分保證系統(tǒng)的安全性,目前的數(shù)字簽名系統(tǒng)的公鑰和私鑰倍數(shù)一般都在256位以上,即密鑰生成和驗證過程進(jìn)行都需要大數(shù)運(yùn)算,因此即使采用ECC算法,無論是軟件還是硬件實現(xiàn),速度較慢仍然是數(shù)字簽名算法的一個缺陷。由于在實時性要求較高的場合,需要進(jìn)行高速運(yùn)算,因此,提高ECC算法的運(yùn)算速度是非常重要的。在ECC算法中,需要執(zhí)行大量的加法與乘法運(yùn)算。在加法運(yùn)算可以通過XOR門實現(xiàn),而乘法運(yùn)算則需要很多的AND和XOR門以及很長的延時。其他二位元擴(kuò)域上的復(fù)雜運(yùn)算如指數(shù)和點加運(yùn)算等都可以通過調(diào)用乘法運(yùn)算來實現(xiàn)。為了滿足數(shù)字簽名運(yùn)算中數(shù)據(jù)快速處理的要求,需要設(shè)計出一種能夠快速完成二位元有限域上乘法運(yùn)算的高效結(jié)構(gòu)。本文的目標(biāo)就是設(shè)計出一種能夠有效縮短乘法運(yùn)算時間,提高數(shù)字簽名效率的乘法器。為此,本文提出了一種基于Dickson原理實現(xiàn)的新型乘法器,它利用Dickson多項式的獨(dú)特性質(zhì),將Dickson基底與傳統(tǒng)的GNB基底(Gaussian normal basis)聯(lián)系起來,并使用Dickson基底替代GNB基底。通過有限域上加減法相同的特性,使用Karatsuba分解方法對多項式進(jìn)行分解,在付出增加三個加法的代價之下,減少一個乘法。接著利用Dickson多項式的性質(zhì),實現(xiàn)分解后多項式的重構(gòu),之后采用遞歸方法將一個長度為m的多項式分解成長度為2的多項式再進(jìn)行基本的乘法運(yùn)算,在遞歸返回之后,再利用基底轉(zhuǎn)換將Dickson基底轉(zhuǎn)換回GNB基底,最終實現(xiàn)整個乘法器的結(jié)構(gòu)。本文一共提出了使用Karatsuba分解的二分法和三分法兩種乘法器結(jié)構(gòu),實驗結(jié)果表明,本文提出的新型Dickson乘法器與傳統(tǒng)乘法器以及同類改進(jìn)的2型和4型GNB乘法器相比,二分法可以減少約50%的乘法運(yùn)算,而三分法則可以減少約三分之二的乘法運(yùn)算,并相應(yīng)地減少一點加法運(yùn)算。因此可知,使用本文提出的新型乘法器,可以優(yōu)化二位元有限域上的乘法結(jié)構(gòu),并提升數(shù)字簽名的效率。
[Abstract]:SM2 is a cryptographic standard using elliptic curve encryption (ECC), while ECC is a public key cryptographic algorithm proposed in 1985, which is compared with the mainstream encryption algorithms such as RSA. The ECC algorithm has the advantages of high security, small computation and fast processing speed. However, in order to fully guarantee the security of the system, the public and private key multiples of the current digital signature systems are generally more than 256-bit. That is, the key generation and verification process all need large number operation, so even if we use ECC algorithm, whether it is software or hardware implementation. The slow speed is still a defect of the digital signature algorithm. It is very important to improve the operation speed of ECC algorithm. In ECC algorithm, a large number of addition and multiplication operations need to be performed. In addition, the addition operation can be implemented by XOR gate. Multiplication requires a lot of AND and XOR gates and a long delay. Complex operations such as exponent and point addition on other binary extension fields can be implemented by calling multiplication operations. The requirement of fast data processing in signature operation. It is necessary to design an efficient structure which can quickly complete multiplication operations over binary finite fields. The goal of this paper is to design a new structure that can effectively shorten the time of multiplication operations. To improve the efficiency of digital signature, a new multiplier based on Dickson principle is proposed in this paper, which makes use of the unique properties of Dickson polynomials. The Dickson substrate is associated with the traditional GNB substrate Gaussian normal basis. The Dickson base is used to replace the GNB substrate. The polynomial is decomposed by using the Karatsuba decomposition method through the same properties of addition and subtraction over finite fields. At the cost of adding three additions, we reduce one multiplication. Then we use the properties of Dickson polynomials to reconstruct the decomposed polynomials. Then a polynomial whose length is m is decomposed into two polynomials by recursive method, and then the basic multiplication operation is carried out. After recursion returns, a polynomial with a length of m is decomposed into a polynomial with a growth degree of 2. Then the Dickson base is converted back to the GNB base using the base transformation. Finally, the structure of the whole multiplier is realized. In this paper, the dichotomy using Karatsuba decomposition and the three-point multiplier structure are proposed, and the experimental results show that. Compared with the traditional multiplier and the similar improved type 2 and 4 GNB multipliers, the new Dickson multiplier proposed in this paper can reduce the multiplication operation by about 50%. The three-point rule can reduce the multiplication operation by about 2/3, and reduce the addition operation by a little bit. Therefore, using the new multiplier proposed in this paper, we can optimize the multiplication structure on the binary finite field. And improve the efficiency of digital signatures.
【學(xué)位授予單位】：哈爾濱工業(yè)大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2014
【分類號】：TN918.91

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中國碩士學(xué)位論文全文數(shù)據(jù)庫 前1條

1 李瑤;基于Dickson乘法器的SM2數(shù)字簽名算法研究與實現(xiàn)[D];哈爾濱工業(yè)大學(xué);2014年

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本文編號：1457388