Research On Algebraic Attack Based On Stream Cipher

In the continuous research and development of crypt,ography,many meaning-ful achievements have been made.The Boolean function is widely used in the con-struction of various cryptosystems.Its cryptological properties directly affect the security of the cryptosystem and cryptographic protocol,and it has a far-reaching influence on the construction and deciphering of the cryptosystem.Algebraic at-tacks have been widely used in the analysis of various cryptosystems and algo-rithms since the algebraic attacks made by the French cryptography expert N.Courtois in 2003,which makes the algebraic immunity of the Boolean function a judge of the goodness of the Boolean function an important criterion.Many of the articles on the algebraic attacks on the contents of a lot of research,research results are rich,mainly around the annihilator and algebraic immunity in the optimal algebraic immunity Boolean function of the structure and other aspects of the content to expand,Conducted an in-depth study.At present,in the stream cipher system,the most successful example of algebraic attack is the attack of Toyocrypt and LI LI-128 for the cryptosystem.In 2003,N.Courtois and W.Meierusing the low-order annihilator denominator of the nonlinear Boolean function in these two algorithms,Sub-equations,successfully decipher the two algorithms.Therefore,for the security based on the nonlinear Boolean function of the cryptosystem,to find its low-order annihilator to become the key to the use of algebraic attack deciphering cryptography.Based on the relationship between the Boolean function support set and its zero set of annihilator,a new method to calculate the annihilator of the Boolean function is obtained on the basis of the algorithm about annihilator given by many scholars before the combination.And analyze the feasibility of these algo-rithms through attacking the LILI-128.In addition,this paper also analyzes the various properties of the annihilator and algebraic immunity.In the study of the nature of algebraic immunity,we mainly study the relationship between it and other cryptological properties,hoping to find how to design a good cryptographic performance of the Boolean function,through the relationship between them.The construction of the new annihilator algorithm in the LI LI-128 attack reflects the higher efficiency of the existing annihilator algorithm,but there are still possible to promote the various types of cryptosystem algebra attacks,But also need to continue to study the direction of the next;Secondly,the relation-ship between algebraic immunity of combine Boolean functions and the algebraic immunity of the sub-function is discussed.Which contributes to the study of an-nihilator algorithm and the study of algebraic immunity of higher order Boolean function.But there is a problem that the combination function type is not com-prehensive enough,we still need to further study.