Many cryptanalytic techniques for sym-metric-key primitives rely on specific statistical analysis to extract some secrete key information from a large num-ber of known or chosen plaintext-ciphertext pairs.For ex-ample,there is a standard statistical model for differen-tial cryptanalysis that determines the success probability and complexity of the attack given some predefined con-figurations of the attack.In this work,we investigate the differential attack proposed by Guo et al.at Fast Soft-ware Encryption Conference 2020 and find that in this at-tack,the statistical behavior of the counters for key can-didates deviate from standard scenarios,where both the correctkey and the correct key xor specific difference are expected to receive the largest number of votes.Based on this bimodal behavior,we give three different statistical models for truncated differential distinguisher on CRAFT(a cryptographic algorithm name)for bimodal phenom-ena.Then,we provide the formulas about the success probability and data complexity for different models un-der the condition of a fixed threshold value.Also,we veri-fy the validity of our models for bimodal phenomena by experiments on round-reduced of the versions distinguish-ers on CRAFT.We find that the success probability of theory and experiment are close when we fix the data complexity and threshold value.Finally,we compare the three models using the mathematical tool Matlab and conclude that Model 3 has better performance.

WANG Caibing;GUO Hao;YE Dingfeng;WANG Ping

State Key Laboratory of Information Security,Institute of Information Engineering,Chinese Academy of Sciences,Beijing 100195,China;School of Cyber Security,University of Chinese Academy of Sciences,Beijing 100049,China;Tianjin Aerospace Zhongwei Data System Technology Co.,Ltd.,Tianjin 300301,China

电子学报（英文）

[1]WANG Caibing;GUO Hao;YE Dingfeng;WANG Ping-.Statistical Model on CRAFT)[J].电子学报（英文）,2022(04):698-712

cryptanalytic,tack,correctkey,xor,distinguisher

Statistical,Model,CRAFT,Many,techniques,sym,metric,primitives,rely,specific,statistical,extract,some,secrete,information,from,known,chosen,plaintext,ciphertext,pairs,For,ample,there,standard,cryptanalysis,that,determines,success,probability,complexity,attack,given,predefined,figurations,In,this,work,we,investigate,differential,proposed,by,Guo,Fast,Soft,ware,Encryption,Conference,find,behavior,counters,can,didates,deviate,scenarios,where,both,difference,expected,receive,largest,number,votes,Based,bimodal,three,models,truncated,cryptographic,algorithm,name,Then,provide,formulas,about,data,der,condition,fixed,threshold,value,Also,veri,fy,validity,our,phenomena,experiments,round,reduced,versions,We,theory,close,when,Finally,compare,using,mathematical,tool,Matlab,conclude,has,better,performance

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