Collision Analysis and Improvement of a Parallel Hash Function based ...
International Journal of Digital Crime and Forensics, 5(2), 23-34, April-June 2013 23
Collision Analysis and Improvement of a Parallel Hash Function based on Chaotic Maps with Changeable Parameters Min Long, School of Computer and Communication Engineering, Changsha University of Science and Technology, Changsha, China Hao Wang, School of Computer and Communication Engineering, Changsha University of Science and Technology, Changsha, China
ABSTRACT Recently, a parallel hash function based on chaotic maps with changeable parameters was proposed by Li et al (2011, pp.1305-1312). In this paper, the security of it is analyzed and the weakness of the architecture is pointed out. It is found that the main limitations are the error using of floor, round and exclusive OR operations in the algorithm. In order to counterstrike these, some improvements are done to strength its security. Theoretical analysis and experimental results illustrate that the improved Hash function is more secure and practical than the original one. Keywords:
Changeable Parameters, Chaos, Collision, Hash Function, Security Analysis
1. INTRODUCTION One-way hash function is a fundamental technique for information security, and it is usually applied for integrity protection, digital signatures and message authentication. In the past few years, chaos has been found that it has great potential to be used in the construction of hash function due to its sensitivity to initial conditions and system parameters, ergodicity and random like behavior. Thus, many works
have been done on the chaos-based hash functions (Akhavan & Samsudin, 2009; Ren & Wang, 2009; Xiao & Liao, 2008; Zhang &Wang, 2007). Among them, wide attention has been paid to parallel hash function, where the sub-blocks of a message are processed in a parallel mode with high efficiency (Xiao & Liao, 2008). However, cryptanalysis of chaosbased hash functions is also developed very fast. Some chaos-based hash functions also been ben proved to be insecure (Li & Li 2006;
DOI: 10.4018/jdcf.2013040102 Copyright © 2013, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited.
24 International Journal of Digital Crime and Forensics, 5(2), 23-34, April-June 2013
Guo & Wang, 2009; Wang & Li, 2012; Wang & Wang, 2008; Wang & Xu, 2010; Wang & Zhao, 2010). Collisions and flaws exist if two or more distinct messages or keys are found to obtain a same hash value, which can be implemented by adversary to fabricate fake messages. For this reason, collision resistance is a basic requirement for a secure hash function. Recently, a parallel hash function based on chaotic maps with changeable parameters is proposed by Li et al. (2011). Detailed analysis is performed to it, and it is found that it is vulnerable to collision attacks, thus, some measurements of how to improve its security are proposed in this paper. The rest of the paper is organized as follows. The original algorithm is described and analyzed in the second Section 2, and some improvements are made in Section 3. In Section 4, the experiments and analysis are performed to evaluate the performance of the improved hash function. Finally, some conclusions are drawn in the Section 5.
2. ORIGINAL HASH FUNCTION AND ITS SECURITY ANALYSIS 2.1. Description of the ChaosBased Parallel Hash Function In the parallel hash function, two chaotic maps are used. One is tent map defined in Equation (1), where 0 < α < 1 , and 0 ≤ x i ≤ 1 . The
other is piecewise linear maps defined in Equation (2) (Box 1), where 0 < P < 0.5 , and 0 ≤ X (t ) ≤ 1 :
x i +1
x i , = α 1 − x i , 1 − α
if (0 ≤ x i ≤ α)
(1)
if (α < x i ≤ 1)
The hash function is composed of the following three steps: Step 1: Message expansion. The message is first padded with 64 bits, which represents the length of the original message, and then padded another s bits (1010…10)2 so that the padded message can be partitioned into n blocks. Each block consists of 1016 bits, and the padded message can be expressed by a matrix M:
m m1,2 m1,127 r2 1,1 m m2,2 m2,127 r3 2,1 M = m m m r n −1,1 n −1,2 n −1,127 n c126 c1 r1 c127
(3)
Box 1. X (t ) / P, (X (t ) − P ) / (0.5 − P ), X (t + 1) = FP (X (t )) = (1 − X (t ) − P ) / (0.5 − P ), (1 − X (t )) / P,
0 ≤ X (t ) < P P ≤ X (t ) < 0.5 0.5 ≤ X (t ) < 1 − P 1 − P ≤ X (t ) ≤ 1
(2)
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Collision Analysis and Improvement of a Parallel Hash Function based on Chaotic Maps with Changeable Parameters Min Long, School of Computer and Communication Engineering, Changsha University of Science and Technology, Changsha, China Hao Wang, School of Computer and Communication Engineering, Changsha University of Science and Technology, Changsha, China
ABSTRACT Recently, a parallel hash function based on chaotic maps with changeable parameters was proposed by Li et al (2011, pp.1305-1312). In this paper, the security of it is analyzed and the weakness of the architecture is pointed out. It is found that the main limitations are the error using of floor, round and exclusive OR operations in the algorithm. In order to counterstrike these, some improvements are done to strength its security. Theoretical analysis and experimental results illustrate that the improved Hash function is more secure and practical than the original one. Keywords:
Changeable Parameters, Chaos, Collision, Hash Function, Security Analysis
1. INTRODUCTION One-way hash function is a fundamental technique for information security, and it is usually applied for integrity protection, digital signatures and message authentication. In the past few years, chaos has been found that it has great potential to be used in the construction of hash function due to its sensitivity to initial conditions and system parameters, ergodicity and random like behavior. Thus, many works
have been done on the chaos-based hash functions (Akhavan & Samsudin, 2009; Ren & Wang, 2009; Xiao & Liao, 2008; Zhang &Wang, 2007). Among them, wide attention has been paid to parallel hash function, where the sub-blocks of a message are processed in a parallel mode with high efficiency (Xiao & Liao, 2008). However, cryptanalysis of chaosbased hash functions is also developed very fast. Some chaos-based hash functions also been ben proved to be insecure (Li & Li 2006;
DOI: 10.4018/jdcf.2013040102 Copyright © 2013, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited.
24 International Journal of Digital Crime and Forensics, 5(2), 23-34, April-June 2013
Guo & Wang, 2009; Wang & Li, 2012; Wang & Wang, 2008; Wang & Xu, 2010; Wang & Zhao, 2010). Collisions and flaws exist if two or more distinct messages or keys are found to obtain a same hash value, which can be implemented by adversary to fabricate fake messages. For this reason, collision resistance is a basic requirement for a secure hash function. Recently, a parallel hash function based on chaotic maps with changeable parameters is proposed by Li et al. (2011). Detailed analysis is performed to it, and it is found that it is vulnerable to collision attacks, thus, some measurements of how to improve its security are proposed in this paper. The rest of the paper is organized as follows. The original algorithm is described and analyzed in the second Section 2, and some improvements are made in Section 3. In Section 4, the experiments and analysis are performed to evaluate the performance of the improved hash function. Finally, some conclusions are drawn in the Section 5.
2. ORIGINAL HASH FUNCTION AND ITS SECURITY ANALYSIS 2.1. Description of the ChaosBased Parallel Hash Function In the parallel hash function, two chaotic maps are used. One is tent map defined in Equation (1), where 0 < α < 1 , and 0 ≤ x i ≤ 1 . The
other is piecewise linear maps defined in Equation (2) (Box 1), where 0 < P < 0.5 , and 0 ≤ X (t ) ≤ 1 :
x i +1
x i , = α 1 − x i , 1 − α
if (0 ≤ x i ≤ α)
(1)
if (α < x i ≤ 1)
The hash function is composed of the following three steps: Step 1: Message expansion. The message is first padded with 64 bits, which represents the length of the original message, and then padded another s bits (1010…10)2 so that the padded message can be partitioned into n blocks. Each block consists of 1016 bits, and the padded message can be expressed by a matrix M:
m m1,2 m1,127 r2 1,1 m m2,2 m2,127 r3 2,1 M = m m m r n −1,1 n −1,2 n −1,127 n c126 c1 r1 c127
(3)
Box 1. X (t ) / P, (X (t ) − P ) / (0.5 − P ), X (t + 1) = FP (X (t )) = (1 − X (t ) − P ) / (0.5 − P ), (1 − X (t )) / P,
0 ≤ X (t ) < P P ≤ X (t ) < 0.5 0.5 ≤ X (t ) < 1 − P 1 − P ≤ X (t ) ≤ 1
(2)
Copyright © 2013, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited.
10 more pages are available in the full version of this document, which may be purchased using the "Add to Cart" button on the product's webpage: www.igi-global.com/article/collision-analysis-andimprovement-of-a-parallel-hash-function-based-on-chaoticmaps-with-changeable-parameters/83487?camid=4v1
This title is available in InfoSci-Journals, InfoSci-Journal Disciplines Computer Science, Security, and Information Technology. Recommend this product to your librarian: www.igi-global.com/e-resources/libraryrecommendation/?id=2
Related Content A Framework for the Forensic Analysis of User Interaction with Social Media John Haggerty, Mark C. Casson, Sheryllynne Haggerty and Mark J. Taylor (2013). Emerging Digital Forensics Applications for Crime Detection, Prevention, and Security (pp. 195-210).
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www.igi-global.com/article/the-state-of-the-art-forensic-techniques-in-mobilecloud-environment/132965?camid=4v1a Indirect Attribution in Cyberspace Robert Layton and Paul A. Watters (2015). Handbook of Research on Digital Crime, Cyberspace Security, and Information Assurance (pp. 246-262).
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A Game Theoretic Approach for Sensitive Information Sharing in Supply Chain Xiaofeng Zhang, William K. Cheung, ZongWei Luo and Frank Tong (2012). Cyber Crime: Concepts, Methodologies, Tools and Applications (pp. 1265-1275).
www.igi-global.com/chapter/game-theoretic-approach-sensitiveinformation/61007?camid=4v1a
