基于耦合帐篷映射的时空混沌单向Hash函数构造

doi:1000-436X(2007)06-0030-09

摘要/Abstract

摘要：

提出一种基于耦合帐篷映射的时空混沌单向 Hash 函数构造方案。与帐篷映射相比，该方案所采用的离散耦合帐篷时空混沌模型避免了有限精度实现产生的短周期行为，产生的时间序列近似服从均匀分布，具有更为理想的扩散与混乱特性。利用该模型实现了任意长度明文序列单向Hash为128位Hash值的算法。时空混沌系统的初态作为密钥，具有很大的密钥空间。Hash值与相应的明文消息及密钥有着敏感、复杂的非线性强耦合关系。理论分析与仿真实验结果表明，该方案与现有混沌 Hash 算法相比，既有好的安全性，又有高的执行效率，满足单向Hash函数的各项性能要求。

关键词: Hash函数, 帐篷映射, 时空混沌, 耦合映像格子

Abstract:

A novel coupled tent maps-based spatiotemporal chaotic cryptographic Hash function was proposed. Compared with the discrete tent map, the coupled discrete tent spatiotemporal chaotic maps have longer computer-realization-period, nearly uniform distribution and desired diffusion and confusion properties. Based on the coupled discrete tent spatiotemporal chaotic maps, a cryptographic Hashing function is constructed to generate 128-bit Hash value from a message with arbitrary length. The approach uses the initial value of coupled discrete tent chaotic dynamical system iteration as the secret key. The key space is very large. There is a high sensitivity and complex and strongly nonlinear coupling relation between the Hash value and the corresponding message and secret key. Theoretic analysis and simulation results are shown that the approach possess not only extremely high security in comparison with earlier chaotic Hash functions, but also the high execution speed. Therefore, the approach can satisfy all the performance requirements of Hash function, such as one-way, key sensitivity and collision resistance.

Key words: Hash function, tent map, spatiotemporal chaos, coupled map lattice

刘建东,付秀丽. 基于耦合帐篷映射的时空混沌单向Hash函数构造[J]. 通信学报, 2007, 28(6): 34-43.

Jian-dong LIU,Xiu-li FU. Spatiotemporal chaotic one-way Hash function construction based on coupled tent maps[J]. Journal on Communications, 2007, 28(6): 34-43.

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文本改变情况	Hash结果
文本1:1M 字节文本文件	23A49A84502C4C117CD7986BAE8D39C7
文本1中首字母改为小写	CF2703D6902F3017E45D36EA412FD30E
文本1最后的句号改成逗号	9880FC950DC8F4408F3CB19D636B517C
文本1中最后加一个空格	156CB24B26601D8203BF4174AA1D590D
文中间一字符a改为b	56F464640B2CA3C03F1A4698BB4B3923
文本2 10M字节文本文件	C26B2718E3989B6964F934ABFA7E18BB
文本2中首字母改为小写	F73F91B366F93499F8ED77A672CEA326
文本2最后的句号改成逗号	BCEBC026767EFBE3D343631FB0627957
文本2中最后加一个空格	55287E246273E715AEEFEF188EED6EDC
文中间一字符a改为b	7ECAD963A0AC8B2B814C9643734E2B5C

统计值	N=256	N=512	N=1 024	N=2 048	平均
B	64.687	64.406	64.278	64.075	64.361
?B	5.098	5.355	5.725	5.682	5.465
P/%	50.53	50.31	50.21	50.05	50.275
?P/ %	3.982	4.183	4.439	4.564	4.292

统计值	N=256	N=512	N=1024	N=2048	平均
B	63.875	64.258	63.685	63.973	63.948
?B	5.672	5.384	5.732	5.173	5.490
P/%	49.90	50.20	49.75	49.97	49.95
?P/ %	4.824	4.367	4.682	4.183	4.514

中间结果	x_i(1)	x_i(2)	x_i(3)	x_i(4)	x_i(5)	x_i(6)	x_i(7)	x_i(8)	x_i(9)	x_i(10)	x_i(11)	x_i(12)	x_i(13)	x_i(14)	x_i(15)	x_i(16)	∑
B	19	18	17	11	23	22	22	12	24	25	23	21	23	21	16	18	315