基于枚举错误向量的McEliece公钥密码体制攻击方法

doi:10.3969/j.issn.1000-436x.2014.05.009

Journal on Communications ›› 2014, Vol. 35 ›› Issue (5): 65-69.doi: 10.3969/j.issn.1000-436x.2014.05.009

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McEliece public key cryptosystem attack algorithm based on enumeration error vector

Jing-mei LIU¹,Yan-li WANG¹,Bin LIANG¹,Lin-sen ZHAO²

¹ National Key Laboratory of Integrated Service Networks, Xidian University, Xi'an 710071, China
² College of Electronic Engineering, Xi'an University of Post ＆ Telecommunications, Xi'an 710061, China

Online:2014-05-25 Published:2017-07-24
Supported by:
Foundation Items: The National Natural Science Foundation of China;The 111 Project;The Fundamental Research Funds for the Central Universities

Abstract

Abstract:

The research on the security of McEliece (M) public key cryptosystem was presented. The Hamming weight of error vector is less than the code length, and M public key cryptosystem based on Goppa code possesses low weight public code words. Considering the above analysis, an attack algorithm based on enumeration error vector was proposed. The effect on probability of correct decryption by the numbers of error flipping bits and algorithm iteration was focused on. And the security of (1 024,524,101) Goppa-based M public key cryptosystem was analyzed. Performance analysis of the proposed algorithm from probability of correct decryption and work factor was simulated, and the experimental results show that the proposed algorithm has a good performance when the code weight is low.

Key words: Goppa code;, McEliece, low weight code word, enumeration error vector

Jing-mei LIU,Yan-li WANG,Bin LIANG,Lin-sen ZHAO. McEliece public key cryptosystem attack algorithm based on enumeration error vector[J]. Journal on Communications, 2014, 35(5): 65-69.

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References 12

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				g
w	i
w	i
		10	1 000		10 000	100 000
	20	6.0×10^-8	6.0×10^-6		6.0×10^-5	0.000 6
101	30	0.006 7	0.493		0.998 8	—
	40	0.047 3	0.992		—	—
	20	6.6×10^-11	6.6×10^-9		6.6×10^-8	6.6×10^-7
131	30	0.000 16	0.016 4		0.152 5	0.809
	40	0.008 3	0.569 4		0.999 7	—
	20	1.3×10^-13	1.3×10^-11		1.3×10^-10	1.3×10^-9
161	30	3.6×10^-6	0.000 36		0.003 6	0.035 8
	40	0.001 2	0.117 1		0.712	1.0

				g
w	i
w	i
		10	1 000		10 000	100 000
	20	132.4	139.0		142.3	145.6
101	30	149.7	156.3		159.7	—
	40	152.7	159.4		—	—
	20	140.5	147.1		150.5	153.8
131	30	162.3	169		172.3	175.6
	40	168.3	174.9		178.3	—
	20	146.8	153.5		156.8	160.1
161	30	172.1	178.8		182.1	185.4
	40	180.9	187.5		190.8	194.2

McEliece public key cryptosystem attack algorithm based on enumeration error vector

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