The Cryptanalysis Of The Even-Mansour Scheme

Nowadays,most of the block cipher is iterated block cipher,and the security of the iterated block cipher is ensured by the round function and the number of rounds.A common design structure for the wheel function is the SP(Substitution-Permutation)structure,known as the AES(Advanced encryption Standard),which is designed using this structure.One of the most primitive cryptographic schemes for this structure is the Even-Mansour cipher proposed by Even and Mansour.The Even-mansour cipher is not only very simple in structure,but also has a clear lower bound for guaranteeing its security.For this reason,the structure is often used as the basic component of the block cipher design.In recent years,the Even-Mansour cipher has always been a very popular research point in the direction of block cipher,and it has related papers in many important cryptographic meetings.Firstly,this paper expounds the research background and significance of the Even-Mansour cipher,and explains its current main attack.Then,the key problems in the original attack are explained,the existing problems are analyzed by the experiment,and the experimental results are explained by the mathematical theory.Subsequently,this paper presents an advanced attack on the original attack against this problem.In the study,the main use of provable security theory,and the expansion of birthday con-jecture,as well as some basic knowledge of probability theory.The specific research content is described as follows:1.The cryptanalysis of the original attack on the Even-Mansour cipher.The author describes two kinds of sliding attacks on the Even-Mansour cipher,namely the textitslide with a twist attack and the Slidex attack.The second attack was the advanced version of the first attack.These two attacks are the most important known plaintext attacks on Even-Mansour cipher today.Based on the simple proof in the original at-tack,this paper gives the complete security proof of these two attacks,and analyzes its complexity.2.The special instances of the original attack.In view of the above two kinds of slide attacks,the author constructs some corresponding instances respectively.Through mathematical analysis,it is not difficult to calculate that the attack case of attack success rate is close to 0.This result and the original attack feasibility analysis of the theoretical results are not very consistent.Through the analysis of the experiment,the author finds that one of the hypotheses in the original proof is inconsistent with the reality,which leads to the difference between theoretical analysis and experimental results.3.Advanced attacks.In order to solve the problem of 2,this paper puts forward a technique of the slide attack,which makes the probability of the advaced attacks is a non-negligible constant in the case of any instance that satisfies the input requirement.In turn,the author uses this technique on the sliding attack of the variant system of Even-Mansour cipher.The attack success rate of the advanced attack is significantly higher than that of the original attack.4.The attack of key leakage.The attack on the Even-Mansour cipher of key leakage have been neglected in previous studies.In the study of the advanced attacks of the aforementioned slide attacks,it is found that by constructing the clear text,in the case of known partial key,the number of the use of plaintext and the permutation can be greatly reduced.Thus,the space complexity and time complexity of the attack can be greatly reduced.The same technique applies to many variants of the Even-Mansour cipher,but requires some modification.In this part,we first put forward the key-leakage attack of the corresponding cipher,then give the proof of the feasibility of the attack,and briefly explain the space and time complexity of the attack.Finally,the author sums up the research methods of the whole thesis,and puts forward the future research direction and the problems that need to be solved in the future research.