Computer Science

Computer Science ›› 2023, Vol. 50 ›› Issue (11A): 220900231-8.doi: 10.11896/jsjkx.220900231

• Information Security • Previous Articles     Next Articles

Search and Optimization of GIFT Integral Distinguisher Based on MILP

ZU Jinyuan1, LIU Jie1,2, SHI Yipeng1, ZHANG Tao1, ZHANG Guoqun3   

  1. 1 College of Software,Northwestern Polytechnical University,Xi'an 710000,China
    2 Yangtze River Delta Research Institute,Nerthwestern Polytechnical University,Taicang,Jiangsu 215400,China
    3 Shanghai Institute of Mechanical and Electrical Engineering,Shanghai 200000,China
  • Published:2023-11-09
  • About author:ZU Jinyuan,born in 2001.His main research interests include information security and cryptography.
    LIU Jie,born in 1985,Ph.D,associate professor,is a member of China Computer Federation.His main research interests include cryptography and network security.
  • Supported by:
    Shanghai Aerospace Science and Technology Innovation Fund(SAST2021-054),Taicang City Basic Research Program on Project Fund(TC2021JC32) and Fundamental Research Funds for the Central Universities(D5000210638).

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Abstract: The lightweight block cipher GIFT algorithm proposed by Banik et al.has been selected for the final round of the NIST standardization competition for international lightweight cryptographic algorithms.At present,there have been linear analysis,difference analysis and other related studies,but the integral analysis of GIFT still needs to be further studied.Aiming at the problem of division trails expression redundancy in the process of integral cryptanalysis of GIFT,an integral dividers solution and search optimization algorithm based on mixed integer linear programming model(MILP) is proposed.Firstly,the linear layer and the nonlinear layer of the GIFT algorithm are respectively described according to their bit division property.The linear layer is expressed by the propagation rule,the greedy algorithm is used to simplify the expression for the nonlinear S-box based on the propagation rule,and 15 inequalities are obtained as constraint conditions.64 9-round integral discriminators are found after the MILP solution.On this basis,in order to solve the problem of insufficient accuracy of the MILP solution model based on the greedy algorithm,the MILP model is introduced to reconstruct the bit division property of the S-box.Design a MILP-based reduction algorithm to optimize the GIFT integral dividers search,and re-solve the MILP model,then obtain two 13-round integral discriminators.Therefore,the MILP-based S-box new reduction algorithm can optimize the expression of the S-box division property,and can effectively increase the number of rounds of the integral dividers attack on the GIFT algorithm,and improve the integral attack effect.

Key words: Integral cryptanalysis, Mixed integer linear programming(MILP), GIFT, Division property, SPN network structure

CLC Number: 

  • TN918.1
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