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چكيده انگليسي :

Study of Hash Functions Based on Chaotic Maps Zahra Hajibabaei z hajibabaei@ec iut ac ir Date of Submission 2012 02 23 Department of Electrical and Computer Engineering Isfahan University of Technology Isfahan 84156 83111 Iran Degree M Sc Language FarsiSupervisor Mohammad Dakhilalian mdalian@cc iut ac irAbstractCryptographic hash functions are a vital part of our current computer systems They are a core componentof digital signature message authentication codes file checksums and many other protocols and securityschems A hash function takes a message of any length as input and produces a fixed length string as outputwhich is called hash value In addition it satisfies the following properties a it is easy to compute hashvalue for any message b it should be pre image resistance which means it is computationally infeasible tofind any input which its hash value equals to a specified output c it should be second preimage resistancewhich means it is computationally infeasible to find any second input which has the same output as anyspecified input d the hash function should be collision resistance which means it is computationallyinfeasible to find any two distinct inputs which have the same hash value The most widely used hashfunctions are dedicated hash functions such as RIPEMD MD5 and SHA1 which are derived from MD4 Recently some attacks based on differential attack have been done on these algorithms and it has beenshown that these algorithms are not collision resistance Because of these attacks researchers have beenworking to develop new and more secure hash functions One direction is development of chaos based hashfunction Chaos based hash function is attracting more and more interest due to the characteristics of chaossuch as sensitivity to initial value random like behavior and ergodicity Because of these characteristics some hash functions based on chaotic maps such as tent map logistic map cat map and other chaotic mapshave been proposed As the subject of this thesis study of hash functions based on chaotic maps weintroduce hash function and its application review the general structure of hash functions and differenttypes of hash functions Then some hash functions based on chaotic map are reviewed Moreover weintroduce a composite map based hash function and show that this algorithm is not collision resistance Finally we express another hash function based on cat map It has been shown that this algorithm has lowconfusion and diffusion property In addition this algorithm has low sensitivity to least significant bits Therefore this algorithm has a high probability of collision and based on its weaknesses the secondversion of the algorithm has been proposed It has been shown that in this vesion each bit of the final hashvalue is closely related to all the bits of the message or key and a single bit change in message or key resultsin great changes in the final hash value As a result the second version of the algorithm has good confusionand diffusion property We show that both algorithms the basic algorithm and the second version of thealgorithm have the same weaknesses and they are not preimage resistance Then based on its weaknesse we improve the second version of the algorithm and show that the proposed algorithm has the sameconfusion and diffusion property as the second version of the algorithm Keywords Hash function collision resistance chaotic map cat map

حاجي بابايي نجف آبادي، زهرا

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