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

我们调查了以下研究课题。(1)针对Koblitz曲线密码系统的侧信道攻击，提出了虚二次域中给定元素的固定模式的tau展开。(2) PKC中标量乘法的秘密位对应于乘法或平方。我们实验了两个相同输入的乘法有不同的功耗。(3) XTR是最有效的公钥密码体制之一。我们提出了一种算法，该算法以固定的模式计算幂次，以防止侧信道攻击。(4) RSA- crt是提高RSA密码系统速度的有效方法。对RSA-CRT进行了综述，并提出了一些应对侧信道攻击的措施。(5)利用GF （3^m）上的环面，具有特征3的有限域上的超奇异椭圆曲线上的配对最终幂提高了50%。E(6) CDSA需要在验证步骤中进行多标量乘法。在这项研究中，我们提出了一个最小的关节汉明权重类的窗口方法使用沙米尔的技巧。(7)我们提出了一种基于GF （3^6m）的XTR变体，其密文可以被压缩1/6。我们还提出了一种使用最优正态基（ONB）的有效实现方法。(8)我们提出了一种用Koblitz曲线的Frobenius映射表示标量的有效方法，该方法能够将TNAF5中预计算表的数量减少到2个。(9)提出了一种利用随机坐标安全抵御侧信道攻击的EtaT配对的有效实现方法。（10）我们发表了第一届基于配对的密码学会议论文集“配对2007”，讨论了与配对相关的基础数学、密码协议、实现和应用安全性。

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.