Efficiency Analysis of Arithmetic for Public-Key Cryptosystems and its Applications

(1)为了对抗Koblitz曲线密码体制的侧信道攻击，我们提出了虚二次域上给定元素的固定模式的tau展开式。(2)PKC中标量乘法的秘密比特对应于乘法或平方。实验表明，两个相同输入的乘法具有不同的功耗。(3)XTR是最高效的公钥密码体制之一。提出了一种在固定模式下进行乘法运算的算法，该算法可以有效地抵抗旁路攻击。(4)RSA-CRT是提高RSA密码系统运算速度的有效方法。给出了RSA-CRT的概况和一些抗旁路攻击的方法。(5)将特征为3的有限域上超奇异椭圆曲线对的最终指数运算提高了50%。E(6)CDSA在验证过程中需要多标量乘法。在这项研究中，我们利用Shamir技巧给出了一个窗方法的最小联合Hamming重量类。(7)我们提出了GF(3^6m)上的一个变种XTR，它的密文可以压缩1/6。我们还给出了一个使用最优正规基(ONB)的有效实现。(8)我们用Koblitz曲线的Frobenius映射给出了一个有效的标量表示，(9)提出了一种基于随机坐标安全的ETAT配对的高效实现方案。(10)我们发表了首届基于配对的密码学会议论文集《配对2007》，内容涉及与配对相关的基本数学、密码协议、实现和应用安全。

We have investigated the following research topics.(1) For a countermeasure against side channel attacks on Koblitz curve cryptosystem, we proposed a tau expansion with a fixed pattern for a give element in an imaginary quadratic filed.(2) A secret bit of a scalar multiplication in PKC corresponds to either a multiplication or a squaring. We experimented that a multiplication with two same input has a different power consumption.(3) XTR is one of the most efficient public-key cryptosystems. We presented an algorithm that computes an exponentiation with a fixed pattern secure against side channel attacks.(4) RSA-CRT is an efficient method to enhance the speed of RSA cryptosystem. We gave a survey of RSA-CRT and some countermeasures against side channel attacks.(5) The final exponentiation of pairing on supersingular elliptic curve over finite field with characteristic three was improved by 50% using the torus over GF (3^m).E(6) CDSA requires a multi-scalar multiplication in the verification step. In this research we presented a minimal joint Hamming weight class for a window method using Shamir's trick.(7) We proposed a variant of XTR over GF (3^6m) whose ciphertexts can be compressed by 1/6. We also presented an efficient implementation using the optimal normal basis (ONB).(8) We have presented an efficient representation of scalar by the Frobenius map of Koblitz curve, which is able to reduce the number of pre-computed table only to two in TNAF5.(9) We proposed an efficient implementation of EtaT pairing using the random coordinate secure against side channel attacks.(10) We published a proceedings of the first conference on pairing-based cryptography "Pairing 2007", which deals basic mathematics, cryptographic protocols, implementation, and applied security, related to pairing.