The MILP/CP models for the paper "A Holistic Framework for Impossible Boomerang Attacks"

How to use this tool

v_1,2,3 (MILP)

Environment needed: Gurobi + Python

"__main__" can be modified (example):

''' 10-r Deoxys-BC-256 (v1,2) '''
DeoxysBC256_10r = IB_DandJ(key_size, rEb, rEu, rEm, rEl, rEf, SetX, Construct_pairs_in_Eb)
DeoxysBC256_10r.ib_model()

''' 10-r Deoxys-BC-256 (v3)'''
DeoxysBC256_10r = IB_DandJ(key_size, rEb, rEd, rEf, SetX, Construct_pairs_in_Eb)
DeoxysBC256_10r.ib_model()

v_4 (CP)

Environment needed: Minizinc + Gurobi

We only tried 11-round IB on Deoxys-BC-256. (detail refer v4_4trails)

Modify "bashSolve.bat" like:

minizinc --solver THESOLVER -p #THREADS MODEL -D "rEb; rDis; rEf; setX" > OUTPUTFILE

Example:

minizinc --solver Gurobi -p 4 .\IB_cp_Deoxys-Joltik.mzn -D "rEb=2; rDis=7; rEf=2; setX=24" > .\res_IBDJ_2_7_2_24.txt

Discussion about multi-objective optimization

Thanks to the comments of the reviewer, we discuss the comparison between "Linear weighted multi-objectives" and "Stage multi-objectives" in the following context.

• Linear weighted multi-objectives are an approximation of a Pareto frontier; that is, the optimization of one target will affect the optimization of all other targets, which may cause other goals to be non-optimized (although their weight is greater;

$$ \alpha * Tc + \beta * Dc + \gamma * Mc, \text{ where } \alpha + \beta + \gamma = 1 $$

• Stage multi-objective optimization in MILP (which we implement using the Python interface) will optimize other parts based on the already optimized maximum weighted target. The optimal value of the target with the maximum weight is fixed when optimizing other targets.

ModelSense = GRB.MINIMIZE
setObjectiveN(Tc, index = 0, priority = 3)
setObjectiveN(Dc, index = 1, priority = 2)
setObjectiveN(Mc, index = 2, priority = 1)

In our model, time complexity is related to the maximum weight, and we want to maintain the optimal time complexity while optimizing data and memory complexity.

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Code for paper A Holistic Framework for Impossible Boomerang Attacks

*Author: Yincen Chen, Qinggan Fu, Ning Zhao, Jiahao Zhao, Ling Song, Qianqian Yang

*Affiliation: 暨南大学网络空间安全学院（College of Cyber Security, Jinan University）