Edwards曲线上抗SPA快速标量乘算法

针对Edwards曲线上标量乘法的效率及安全性,提出了马尔科夫点加-倍点链(Markov Addition-Double Chain,MADC)。基于MADC的椭圆曲线标量乘算法每次循环都固定执行"点加-倍点"运算,从而能够天然抵抗简单能量攻击。此外,倍点运算占总运算量的一半,由于Edwards曲线的倍点公式相对点加公式所需的运算量极少,新算法的运算量将大大减少。实验结果表明,MADC的最佳链长为160,MADC-160相对于EAC-320、SAC-260和GRAC-258,效率分别提高了27%、10.4%和9.7%。

一种抵抗Montgomery错误攻击的检错算法

针对Montgomery椭圆曲线标量乘算法,通过构建检错点形成规则的检错体制,提出了在错误攻击下有效抵抗Montgomery算法的检错方法。实验分析结果表明此方法的运算复杂度低、时间花销小、漏检率可达到最小,检错有效性相比于传统的检错方法提高了57.1%,能够有效抵抗Montgomery错误攻击。

Efficient and Provably Secure Multi-Recipient Signcryption from Bilinear Pairings

Signcryption is a cryptographic primitive that performs signature and encryption simultaneously, at lower computational costs and communication overheads than the signature-then- encryption approach. In this paper, we propose an efficient multi-recipient signcryption scheme based on the bilinear pairings, which broadcasts a message to multiple users in a secure and authenticated manner. We prove its semantic security and unforgeability under the Gap Diffie-Hellman problem assumption in the random oracle model. The proposed scheme is more efficient than re-signcrypting a message n times using a signcryption scheme in terms of computational costs and communication overheads.

基于Pell型序列的快速安全标量乘算法

提出了一种新的椭圆曲线快速安全的标量乘算法。利用佩尔序列前后项分割比产生新的佩尔型点加-倍点链(Pell Type Double-and-Add Chain,PTDAC),其循环固定的"倍点-点加"操作可天然抵抗简单能量分析(Simple Power Analysis,SPA)攻击。PTDAC算法结合Edwards椭圆曲线可从底层域减少运算时间,进一步优化算法。经过理论分析和仿真实验表明,PTDAC算法在最优情况下比EAC-270和GRAC-258算法在时间效率上分别提高了2.6%和22.8%。

An Improved Simple Power Attack against Camellia's Key Schedule

This paper presents an improved simple power attack against the key schedule of Camellia. While the original attack required an exact determination of the Hamming weight of intermediate data values based on power measurements, in this paper, two types of the simple power attack are presented and shown to be tolerant of errors that might occur in the Hamming weight determinations. In practical applications of the attack, such errors are likely to occur due to noise and distortion in the power measurements and their mapping to the Hamming weights of the data. To resist these attacks, the required design rationale of key schedules and several practical countermeasures are suggested.

New Weak Keys in RSA

The security of the RSA system with the prime pairs of some special form is investigated. A new special-purpose algorithm for factoring RSA numbers is proposed. The basic idea of the method is to factor RSA numbers by factoring a well-chosen quadratic polynomial with integral coefficients. When viewed as a general-purpose algorithm, the new algorithm has a high computational complexity. It is shown thai the RSA number n = pq can be easily factored if p and q have the special form of p = as＋b, q=cs＋d, where a, b, c, d are relatively small numbers. Such prime pairs （p, q） are the weak keys of RSA, so when we generate RSA modulus, we should avoid using such prime pairs （p, q）.

An Efficient Method against Side-Channel Attacks on ECC

Side-channel attacks （SCA） may exploit leakage information to break cryptosystems. In this paper we present a new SCA resistant Elliptic Curve scalar multiplication algorithm. The proposed algorithm, builds a sequence of bit-strings representing the scalar k, characterized by the fact that all bit-strings are different from zero; this property will ensure a uniform computation behavior for the algorithm, and thus will make it secure against simple power analysis attacks （SPA）. With other randomization techniques, the proposed countermeasures do not penalize the computation time. The proposed scheme is more efficient than MOEller＇s one, its cost being about 5% to 10% smaller than MOEller＇s one.

GF(2^(m))椭圆曲线上的Co＿Z点加算法

基于统一Z坐标,提出了有限域GF(2~m)上两种射影坐标下的Co_Z点加运算公式。通过对椭圆曲线上有理点的Z坐标统一化处理,使得其运算量分别为10M+3S和8M+3S(M,S分别表示有限域上的乘法和平方),相比已有的计算公式,运算量分别减少了2S和2M。另外,提出了一种Jacobian坐标下的3P运算公式,运算量减少了1M+4S。将新提出的点加、3P运算公式与对称三进制标量乘相结合,改进了标量乘算法的运算效率,使得标量乘算法的效率提高了13%。