本文選題：橢圓曲線 + Montgomery算法��； 參考：《計(jì)算機(jī)學(xué)報(bào)》2017年05期

【摘要】：橢圓曲線公鑰密碼是公鑰密碼體制的主流方向之一.由于密鑰短、計(jì)算速度快,該體制在智能卡和手機(jī)存儲(chǔ)卡等受限的環(huán)境中得到了廣泛的應(yīng)用.橢圓曲線密碼體系中最耗時(shí)的運(yùn)算是標(biāo)量乘.標(biāo)量乘需要安全、有效、快速的實(shí)現(xiàn)算法.Montgomery算法是計(jì)算橢圓曲線標(biāo)量乘的算法之一,它能夠有效地抵抗簡(jiǎn)單能量分析.在Montgomery算法結(jié)構(gòu)的基礎(chǔ)上,文中首次利用統(tǒng)一Z坐標(biāo)技巧和循環(huán)中間階段不計(jì)算Y坐標(biāo)的技巧,改進(jìn)了有限域GF(3~m)上橢圓曲線的點(diǎn)加和倍點(diǎn)公式,構(gòu)造了抵抗簡(jiǎn)單能量攻擊的co-Z Montgomery算法.設(shè)I,M,C分別表示有限域上的求逆、乘法、立方.當(dāng)域上的平方和乘法使用相同的算法時(shí),理論分析表明每輪循環(huán)中,co-Z Montgomery算法比仿射Montgomery算法快I+C-5 M,比射影Montgomery算法快C+2 M,比使用"Selected Areas in Cryptography"2012上快速點(diǎn)加、倍點(diǎn)公式的Montgomery算法快2C+M.在文章"特征3有限域上橢圓曲線的Montgomery算法"的模擬實(shí)驗(yàn)環(huán)境下,結(jié)果表明該算法比上述算法分別快26.3%、19.0%、20.6%;Sage云平臺(tái)的實(shí)驗(yàn)結(jié)果表明該算法比上述算法分別快24.1%、20.1%、23.1%.
[Abstract]:Elliptic curve public key cryptosystem is one of the main directions of public key cryptosystem. Because of the short key and fast computing speed, this scheme has been widely used in the limited environment such as smart card and mobile phone memory card. The most time-consuming operation in elliptic curve cryptosystem is scalar multiplication. Scalar multiplication needs to be implemented safely, efficiently and quickly. Montgomery algorithm is one of the algorithms to calculate scalar multiplication of elliptic curves, which can effectively resist simple energy analysis. On the basis of the structure of Montgomery algorithm, the technique of unified Z-coordinate and the technique of not calculating Y-coordinate in the middle stage of the cycle are used for the first time to improve the formula of point addition and point doubling of elliptic curve on the finite field GFN 3m. The co-Z Montgomery algorithm to resist simple energy attack is constructed. Let I _ M _ M _ (C) denote the inverse, multiplication, and cubic of finite fields, respectively. When the square sum multiplication in the domain uses the same algorithm, the theoretical analysis shows that the co-Z Montgomery algorithm in each cycle is faster than the affine Montgomery algorithm I C-5 M, the projective Montgomery algorithm C 2 M, and the Montgomery algorithm which uses the "Selected Areas in Cryptography" 2012 fast point addition and double point formula is faster than the Montgomery algorithm. In this paper, the Montgomery algorithm of elliptic curve on the finite field of feature 3 is simulated. The results show that the algorithm is 26.3and 19.019.019.020.6Sage cloud platform faster than the above algorithm, respectively. The experimental results show that the algorithm is 24.1and 20.1and 23.1faster than the above algorithm, respectively.
【作者單位】： 中國(guó)科學(xué)院信息工程研究所;中國(guó)科學(xué)院DCS中心;
【基金】：國(guó)家自然科學(xué)基金(61502487,61272040) 國(guó)家“九七三”重點(diǎn)基礎(chǔ)研究發(fā)展規(guī)劃項(xiàng)目基金(2013CB338001)資助
【分類(lèi)號(hào)】：TN918.1

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本文編號(hào)：1895995