Improved differential fault attack on scalar multiplication algorithm in elliptic curve cryptosystem

doi:10.11772/j.issn.1001-9081.2016.12.3328

Journal of Computer Applications ›› 2016, Vol. 36 ›› Issue (12): 3328-3332.DOI: 10.11772/j.issn.1001-9081.2016.12.3328

Previous Articles Next Articles

Improved differential fault attack on scalar multiplication algorithm in elliptic curve cryptosystem

XU Shengwei^1,2, CHEN Cheng^1,2, WANG Rongrong^1,2

1. Beijing Electronic Science & Technology Institute, Beijing 100070, China;
2. School of Telecommunications Engineering, Xidian University, Xi'an Shaanxi 710071, China

Received:2016-05-11 Revised:2016-06-23 Online:2016-12-08 Published:2016-12-10

针对椭圆曲线密码系统点乘算法的改进差分故障攻击

许盛伟^1,2, 陈诚^1,2, 王荣荣^1,2

1. 北京电子科技学院, 北京 100070;
2. 西安电子科技大学通信工程学院, 西安 710071

通讯作者: 陈诚
作者简介:许盛伟(1976-),男,江西吉安人,副教授,博士,主要研究方向:保密通信、信息安全、公钥密码应用;陈诚(1990-),女,湖北随州人,硕士研究生,主要研究方向:保密通信、信息安全、商用密码算法、商用密码应用;王荣荣(1991-),女,山东临沂人,硕士研究生,主要研究方向:保密通信、信息安全、公钥密码应用。

Abstract

Abstract: Concerning the failure problem of fault attack on elliptic curve scalar multiplication algorithm, an improved algorithm of differential fault attack was proposed. The nonzero assumption was eliminated, and an authentication mechanism was imported against the failure threat of "fault detection". Using the elliptic curve provided by SM2 algorithm, the binary scalar multiplication algorithm, binary Non-Adjacent Form (NAF) scalar multiplication algorithm and Montgomery scalar multiplication algorithm were successfully attacked with software simulation. The 256-bit private key was restored in three hours. The attacking process of binary NAF scalar multiplication algorithm was optimized, so the attack time was reduced to one fifth of the original one. The experimental results show that the proposed algorithm can improve the effectiveness of the attack.

Key words: Elliptic Curve Cryptosystem (ECC), scalar multiplication algorithm, differential fault attack, zero block failure, fault detection

摘要： 针对故障攻击椭圆曲线点乘算法失效问题，提出一种改进的差分故障攻击算法。该算法消除了非零块的假设，并引入验证机制抵抗了“故障检测”失效威胁。以SM2算法提供的椭圆曲线为例，通过软件仿真成功攻击了二进制点乘算法、二进制非相邻型（NAF）点乘算法和蒙哥马利点乘算法，3小时内恢复出了256比特私钥。针对二进制NAF点乘算法攻击过程进行了优化，将攻击时间缩短至原来的五分之一。实验结果表明，所提算法能够提高攻击的有效性。

关键词: 椭圆曲线密码系统, 点乘算法, 差分故障攻击, 零块失效, 故障检测

CLC Number:

TP301.5

XU Shengwei, CHEN Cheng, WANG Rongrong. Improved differential fault attack on scalar multiplication algorithm in elliptic curve cryptosystem[J]. Journal of Computer Applications, 2016, 36(12): 3328-3332.

许盛伟, 陈诚, 王荣荣. 针对椭圆曲线密码系统点乘算法的改进差分故障攻击[J]. 计算机应用, 2016, 36(12): 3328-3332.

References

[1] 李浪,李仁发,童元满,等.嵌入式加密芯片功耗分析攻击与防御研究进展[J].计算机研究与发展,2010,47(4):595-604.(LI L, LI R F, TONG Y M, et al. Development on power analysis attack and defense of embedded cipher chip[J]. Journal of Computer Research and Development, 2010, 47(4):595-604.)
[2] 李浪,杨柳,李肯立,等.一种椭圆曲线密码算法ECC旁路攻击方法研究[J].计算机应用研究,2013,30(3):889-890.(LI L, YANG L, LI K L, et al. Research on side-channel attack methods of ECC[J]. Application Research of Computers, 2013, 30(3):889-890.)
[3] BIEHL I, MEYER B, MVLLER V. Differential fault attacks on elliptic curve cryptosystems[C]//CRYPTO'00:Proceedings of the 20th Annual International Cryptology Conference on Advances in Cryptology, LNCS 1880. Berlin:Springer, 2000:131-146.
[4] EBEID N, LAMBERT R. Securing the elliptic curve Montgomery ladder against fault attacks[C]//FDTC'09:Proceedings of the 2009 Workshop on Fault Diagnosis and Tolerance in Cryptography. Washington, DC:IEEE Computer Society, 2009:46-50.
[5] 张金中,寇应展,王韬,等.针对滑动窗口算法的椭圆曲线密码故障分析[J].通信学报,2012,33(1):71-78.(ZHANG J Z, KOU Y Z, WANG T, et al. Fault analysis on elliptic curve cryptosystems with sliding window method[J]. Journal on Communications, 2012, 33(1):71-78.)
[6] ANDREAS E.椭圆曲线及其在密码学中的应用——导引[M].吴铤,董军武,王明强,译.北京:科学出版社,2007:11-20.(ANDREAS E. Elliptic curves and their applications to cryptography:an introduction[M]. WU T, DONG J W, WANG M Q, translated. Beijing:Science Press, 2007:11-20.)
[7] 赵前进.椭圆曲线密码点乘算法的并行调度研究[D].郑州:信息工程大学,2010:19-23.(ZHAO Q J. Research on parallel schedule of scalar multiplication of elliptic curve cryptography[D]. Zhengzhou:Information Engineering University, 2010:19-23.)
[8] 刘红明.公钥密码的抗边信道攻击研究与实现[D].上海:上海交通大学,2014:72-78.(LIU H M. Research and implementation of countermeasures against side channel attacks for public key[D]. Shanghai:Shanghai Jiao Tong University, 2014:72-78.)
[9] BLÖMER J, OTTO M, SEIFERT J P. Sign change fault attacks on elliptic curve cryptosystems[C]//FDTC 2006:Proceedings of the Third International Workshop on Fault Diagnosis and Tolerance in Cryptography, LNCS 4236. Berlin:Springer, 2006:36-52.
[10] 肖攸安. 椭圆曲线密码体系研究[M].武汉:华中科技大学出版社,2006:41-46.(XIAO Y A. Research on Elliptic Curves Cryptography[M]. Wuhan:Huazhong University of Science and Technology Press, 2006:41-46.)

[1]	YANG Xian, ZHAO Jisheng, QIANG Baohua, MI Luzhong, PENG Bo, TANG Chenghua, LI Baolian. Wind turbine fault sampling algorithm based on improved BSMOTE and sequential characteristics [J]. Journal of Computer Applications, 2021, 41(6): 1673-1678.
[2]	ZHANG Chenxi, TANG Shu, TANG Ke. Strategies of parameter fault detection for rocket engines based on transfer learning [J]. Journal of Computer Applications, 2020, 40(9): 2774-2780.
[3]	HUANG Gong, ZHAO Yongping, XIE Yunlong. Fault detection for turboshaft engine based on local density weighted one-class SVM algorithm [J]. Journal of Computer Applications, 2020, 40(3): 917-924.
[4]	MAO Wentao, YANG Chao, LIU Yamin, TIAN Siyu. Deep domain adaptation model with multi-scale residual attention for incipient fault detection of bearings [J]. Journal of Computer Applications, 2020, 40(10): 2890-2898.
[5]	WANG Shuo, WANG Peiliang. Fault detection method for batch process based on deep long short-term memory network and batch normalization [J]. Journal of Computer Applications, 2019, 39(2): 370-375.
[6]	ZHANG Cheng, GUO Qingxiu, FENG Liwei, LI Yuan. Fault detection strategy based on local neighbor standardization and dynamic principal component analysis [J]. Journal of Computer Applications, 2018, 38(9): 2730-2734.
[7]	ZHANG Cheng, GUO Qingxiu, LI Yuan. Batch process monitoring based on k nearest neighbors in discriminated kernel principle component space [J]. Journal of Computer Applications, 2018, 38(8): 2185-2191.
[8]	FENG Liwei, ZHANG Cheng, LI Yuan, XIE Yanhong. Fault detection for multistage process based on improved local neighborhood standardization and kNN [J]. Journal of Computer Applications, 2018, 38(7): 2130-2135.
[9]	LI Yuan, WU Haoyu, ZHANG Cheng, FENG Liwei. Multi-modal process fault detection method based on improved partial least squares [J]. Journal of Computer Applications, 2018, 38(12): 3601-3606.
[10]	LIU Yong, SHEN Xuanfan, LIAO Yong, ZHAO Ming. Fault detection filter design based on genetic algorithm in wireless sensor and actuator network [J]. Journal of Computer Applications, 2016, 36(3): 616-619.
[11]	XIN Xiaoxia, WANG Yi, LI Renfa. FPGA-based implementation for fault detection of SMS4 [J]. Journal of Computer Applications, 2015, 35(2): 420-423.
[12]	TANG Liu HUANG Zhangqin HOU Yibin FANG Fengcai ZHANG Huibing. Fault detection approach for MPSoC by redundancy core [J]. Journal of Computer Applications, 2014, 34(1): 41-45.
[13]	HU Jichen HUANG Guoyong SHAO Zongkai WANG Xiaodong ZOU Jinhui. Small fault detection method of instruments based on independent component subspace algorithm and ensemble strategy [J]. Journal of Computer Applications, 2013, 33(07): 2063-2066.
[14]	TIAN Ning FAN Yugang WU Jiande HUANG Guoyong WANG Xiaodong. Check valve's fault detection with wavelet packet's kernel principal component analysis [J]. Journal of Computer Applications, 2013, 33(01): 291-294.
[15]	BAO Jian WEI Li-na ZHAO Jian-yong. Fault diagnostic method of elevator control system based on finite state machine [J]. Journal of Computer Applications, 2012, 32(06): 1692-1695.

Improved differential fault attack on scalar multiplication algorithm in elliptic curve cryptosystem

针对椭圆曲线密码系统点乘算法的改进差分故障攻击

PDF

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 15

Recommended Articles

Metrics