Differential Analysis Of REESSE3+

With the rapid development of computer technology and network technology,information sharing becomes more and more easy,but it also makes the information more and more insecure.Information security relates to the stability of the state and society.To protect the information security of our country is an important standard to measure the comprehensive national strength.Cryptography is the core technology of information security,which can provide confidentiality,integrity and non-repudiation of information.Block cipher is an important part of cryptography,which has the characteristics of fast encryption speed,easy standardization and easy realization on hardware and software.It is usually the key part of realizing data encryption,authentication and key management.Therefore,the research on block cipher can not be slack.REESSE3+ is a block cipher proposed in 2014.When the algorithm is proposed,the author of the original algorithm only makes a theoretical analysis on the 1 round of iteration of the cipher,and he does not analyze the 8 rounds of iteration,and also he does not analyze the situation of facing differential analysis.We verify the correctness of the algorithm and make a differential analysis of the algorithm in this paper.The main works are as follows:1)Verify the correctness of REESSE3+.We analyze the old version of REESSE3+ and find out some problems.In order to solve these problems,we point out the reasons and give an amendment.We are also involved in the work of verifing the correctness of current version of REESSE3+.The current version of REESSE3+ does not use our amendment,but use the new amendment proposed by the author of the original algorithm.The following REESSE3+ we mentioned is the revised version of the original author.2)Make a differential analysis of REESSE3+ based on Markov theory.In order to analyze REESSE3+,we first give the definition of REESSE3+(m).Then we prove that REESSE3+(m)belongs to the Markov cipher.We also show the algorithm of generating the probability transfer matrix of REESSE3+(16).Through the probability transfer matrix of REESSE3+(16),we prove that REESSE3+(16)needs 16 rounds of iteration to resist differential analysis.Because REESSE3+ only has 8 rounds,so when the block length is 16 bits,the algorithm can't resist differential analysis.Then we also prove that the probability transfer matrix of REESSE3+ is asymmetric and the Markov chain it corresponding is non-periodic.Combined with the proof of IDEA,we speculate that REES SE3+ is sufficient to resist differential analysis after 16 rounds of iteration.3)Make an improvement to improve the security of facing differential analysis based on REESSE3+.We propose an improved REESSE3+.We prove that in the case of the 16 bits input,the improved algorithm needs only 8 rounds of iteration to achieve safety requirements.We also prove that the probability transfer matrix of the improved algorithm is non-symmetric,and the Markov chain it corresponding is non-periodic.Combined with the proof of IDEA,we speculate that the improved algorithm is able to resist differential analysis after 8 rounds of iteration.