Integral Analysis Of Block Ciphers Based On MILP

The Internet of Things technology maintains an irresistible momentum of development since it was invented,and its influence on daily life is also very significant.The hidden danger of information security in the communication can not be underestimated,while it brings convenience to life.How to ensure that the data is transmitted safely and reliably has become an important point of network security.Block cipher algorithm is widely used in Internet of Things communication due to its high efficiency of encryption and decryption and relatively simple hardware implementation.The design and analysis of block cipher complement each other.Various analysis methods become more and more mature while the design method of block cipher is improved.Integral analysis is one of the important methods to judge the security of block cipher algorithm.The integral distinguisher is constructed according to a integral property of some positions in the ciphertext corresponding choosen plaintext,which used to attack the cipher by key recovery attack.Bit-based division property is an extension of integral property in integral analysis.The construction process of the integral distinguisher can be transformed into the solution process of corresponding mathematical model.Mixed integer linear programming(MILP)is one of programming problem in operational research to find the optimal solution.In this paper,integral analysis of three block ciphers with different structures was given using MILP,which is based on bit-based division property.The specific research contents are as follows.1.The SPN structure cipher DoT was attacked against integral analysis.Firstly,a simplified equivalent structure is proposed according to the characteristics of the round function.Then the equivalent structure of cipher was modelled based on MILP,and multiple integral distinguishers with different rounds were obtained.Among them,the longest round of distinguisher is 19-round one.Then,a 16-round integral distinguisher was selected to construct 21-round integral analysis of DoT cipher based on bit-based division property.Finally,a full round attack was given,which is combined with key schedule algorithm of DoT cipher.The time complexity of DoT's 80 bit and 128 bit key length is 2^59.24 and 2⁷¹ full-round encryption,respectively.The data complexity is 2^40.62 choice plaintext and the storage complexity is 2⁹⁶.This is the best result in the integral analysis which are known of DoT so far.2.The Feistel structure cipher ANU was attacked against integral analysis.Firstly,the MILP model of ANU cipher was constructed,and many different integral distinguishers were obtained.The 9-round one was the longest distinguisher among them.Then,one 8-round integral distinguisher was selected to attack 13-round ANU cipher against integral analysis.The time complexity is 2^88.46 13-round encryption,data complexity is 2^63.32,storage complexity is 2⁷⁶.Because the time complexity of the attack is too high to 80-bit key length ANU cipher,a 7-round integral distinguish was selected to attack 12-round one.The time complexity is 2^51.17 12-round encryption,data complexity is 2^76.58,storage complexity is 2⁷².This is the best result in the integral analysis of ANU so far.3.The Feistel structure cipher VAYU was attacked against integral analysis.Firstly,the MILP model of VAYU cipher was constructed,and many different integral distinguishers were obtained.The 8-round one was the longest distinguisher among them.Then,one 7-round integral distinguisher was selected to attack 9-round VAYU cipher against integral analysis.The time complexity is 2^74.41 13-round encryption,data complexity is 2⁶⁴,storage complexity is 2²².Then,a 12-round integral analysis against 128-bit key length VAYU cipher was given.The time complexity is 2^88.42 12-round encryption,data complexity is 2^62.58,storage complexity is 2⁸².This is the best result in the integral analysis of VAYU so far.