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### Differential and Linear Cryptanalysis Using Mixed-Integer Linear Programming [chapter]

Nicky Mouha, Qingju Wang, Dawu Gu, Bart Preneel
2012 Lecture Notes in Computer Science
We use mixedinteger linear programming (MILP), a method that is frequently used in business and economics to solve optimization problems.  ...  Differential and linear cryptanalysis are two of the most powerful techniques to analyze symmetric-key primitives.  ...  We present our problem as a mixed-integer linear programming (MILP) problem, and use CPLEX [17] to solve it.  ...

### Towards Finding Active Number of S-Boxes in Block Ciphers using Mixed Integer Linear Programming

Vikas Tiwari, Neelima Jampala, Appala Naidu Tentu, Ashutosh Saxena
2021 Informatica (Ljubljana, Tiskana izd.)
Two of the most important attacks on block ciphers are differential cryptanalysis [1] and linear cryptanalysis [2] .  ...  We utilized the method proposed in [9] , where calculation of the minimum number of active S-boxes is formulated as a Mixed Integer Linear Programming (MILP) problem.  ...  The method which is used to construct as well as solve such problems is called Mixed Integer Linear Programming(MILP).  ...

### Mixed Integer Programming Models for Finite Automaton and Its Application to Additive Differential Patterns of Exclusive-Or [article]

Siwei Sun, Lei Hu, Peng Wang, Meiqin Wang, Danping Shi, Xiaoshuang Ma, Qianqian Yang, Kai Fu
2016 IACR Cryptology ePrint Archive
be formulated as an mixed-integer programming model.  ...  Using this method, we show how to construct a mixed integer programming model whose feasible region is the set of all differential patterns (α, β, γ)'s, such that adp ⊕ (α, β → γ) = Prx,y[((x + α) ⊕ (y  ...  automatic differential and linear cryptanalysis.  ...

### New automatic tool for finding impossible differentials and zero-correlation linear approximations

Tingting Cui, Shiyao Chen, Kai Fu, Meiqin Wang, Keting Jia
2020 Science China Information Sciences
Similar to the idea of using mixed-integer linear programming (MILP) models for differential cryptanalysis in [1], we first use linear inequalities to describe all the target cipher's components exactly  ...  Dear editor, Impossible differential cryptanalysis and zero-correlation linear cryptanalysis are two powerful methods in the block cipher field.  ...  Supporting information Appendixes A and B. The supporting information is available online at info.scichina.com and link.springer.com.  ...

### Automatic Security Evaluation of Block Ciphers with S-bP Structures Against Related-Key Differential Attacks [chapter]

Siwei Sun, Lei Hu, Ling Song, Yonghong Xie, Peng Wang
2014 Lecture Notes in Computer Science
Based on Mixed Integer Linear Programming (MILP), Mouha et al proposed a method to accomplish this task automatically for word-oriented symmetric-key ciphers with SPN structures.  ...  Moreover, the MILP constrains presented in Mouha et al's method are not enough to describe the differential propagation behaviour of a linear diffusion layer constructed from a non-MDS code, even an almost  ...  In Section 2 we recall the Mixed Integer Linear Programming and its applications to analysing word-oriented block ciphers.  ...

### A cautionary note on the use of Gurobi for cryptanalysis [article]

Muhammad ElSheikh, Amr M. Youssef
2020 IACR Cryptology ePrint Archive
Mixed Integer Linear Programming (MILP) is a powerful tool that helps to automate several cryptanalysis techniques for symmetric key primitives.  ...  Gurobi is one of the most popular solvers used by researchers to obtain useful results from the MILP models corresponding to these cryptanalysis techniques.  ...  Introduction Since Mouha et al. introduced the concept of using Mixed Integer Linear Programming (MILP) to count of the minimum number of active S-boxes in differential cryptanalysis [5] , MILP has attracted  ...

### Differential Cryptanalysis on Block Cipher Skinny with MILP Program

Pei Zhang, Wenying Zhang
2018 Security and Communication Networks
The method is called mixed-integer linear programming (MILP) which can characterize precisely the linear operation and nonlinear operation in a round function.  ...  In recent years, lightweight block ciphers have emerged and are widely used, and their security is also crucial.  ...  Mixed-integer linear programming (MILP) [14, 15] is a mathematical optimization or feasibility scheme, where some or all variables are limited to integers.  ...

### CASCADA: Characteristic Automated Search of Cryptographic Algorithms for Distinguishing Attacks [article]

Adrián Ranea, Vincent Rijmen
2022 IACR Cryptology ePrint Archive
, rotational-XOR, impossible-differential, impossible-rotational-XOR, related-key impossibledifferential, linear and zero-correlation cryptanalysis.  ...  The tool CASCADA implements the bit-vector property framework herein proposed and several SMT-based automated search methods to evaluate the security of ciphers against differential, related-key differential  ...  Theories) or MILP (Mixed Integer Linear Programming) [MP13; Mou+11] .  ...

### Functional Cryptanalysis: Application to reduced-round Xoodoo [article]

Emanuele Bellini, Rusydi H. Makarim
2022 IACR Cryptology ePrint Archive
To the best of our knowledge, this is the first time the SMT model is used to construct a valid differential while previous approaches rely on Mixed-Integer Linear Programming (MILP) model.  ...  Lastly, we remark that the use of non-translation functionals shares analogous advantages and limitations with the use of nonlinear approximations in linear cryptanalysis.  ...  In a separate trend, there have been multiple works that utilizes constraint-based solving such as Mixed-Integer Linear Programming (MILP) [MWGP11] , SAT [MP13] , and Satisfiability Modulo Theory (SMT  ...

### Automatic Search of Linear Trails in ARX with Applications to SPECK and Chaskey [chapter]

Yunwen Liu, Qingju Wang, Vincent Rijmen
2016 Lecture Notes in Computer Science
In addition, our method can be used to enumerate the trails in a linear hull, and we present two linear hulls with the distributions of trails for round-reduced SPECK32.  ...  Our work provides designers with more accurate evaluation against linear cryptanalysis on ARX designs, especially for primitives with large block sizes and many rounds.  ...  Qingju Wang is in part sponsored by National Natural Science Foundation of China (61472250, U1536103) and Major State Basic Research Development Program (973 Plan) of China (2013CB338004).  ...

### Chaotic block ciphers: from theory to practical algorithms

N. Masuda, G. Jakimoski, K. Aihara, L. Kocarev
2006 IEEE Transactions on Circuits and Systems I Fundamental Theory and Applications
We propose a chaotic Feistel cipher and a chaotic uniform cipher.  ...  However, their overall performance in terms of the tradeoff between security and speed, as well as the connection between chaos and cryptography, has not been sufficiently addressed.  ...  From a cryptographical viewpoint, however, they must be chosen so that the generated S-boxes are strong against differential cryptanalysis and linear cryptanalysis [7] , [10] .  ...

### MILP-Based Automatic Differential Searches for LEA and HIGHT [article]

Elnaz Bagherzadeh, Zahra Ahmadian
2018 IACR Cryptology ePrint Archive
In this paper we use MILP technique for automatic search for differential characteristics of ARX ciphers LEA and HIGHT.  ...  For LEA block cipher, we found more efficient 12 and 13-round differentials whose probabilities are better than the best previous 12 and 13-round differentials for a factor of about 2 6 and 2 7 , respectively  ...  [16] [17] [18] , and the method based on mixed integer linear programming problems [26, 27] .  ...

### Improved linear (hull) cryptanalysis of round-reduced versions of SIMON

Danping Shi, Lei Hu, Siwei Sun, Ling Song, Kexin Qiao, Xiaoshuang Ma
2016 Science China Information Sciences
By using a Mixed-integer Linear Programming based technique presented in Aasicrypt 2014 for automatic search for characteristics, we obtain improved linear characteristics for several versions of the SIMON  ...  Moreover, by employing a recently published method for automatic enumeration of differential and linear characteristics by Sun et. al., we present an improved linear hull analysis of some versions of the  ...  Description of automatic enumeration of characteristics with MILP Automatic search of differential characteristic for bit-oriented block ciphers by Mixed-integer Linear Programming (MILP) modelling was  ...

### Battery power optimized encryption

S. Bapatla, R. Chandramouli
2004 2004 IEEE International Conference on Communications (IEEE Cat. No.04CH37577)
A new measure called "vulnerability" that quantifies the success of linear cryptanalysis attack is proposed and its relationship with the power consumption is explored.  ...  A closed form solution to the the first problem is derived while the second optimization formulation is posed as an integer program and solved numerically. Several numerical results are also provided.  ...  ACKNOWLEDGEMENTS This work was partially supported by NSF DAS 0242417 and NSF CAREER 0133761.  ...

### Rotational-XOR Cryptanalysis of Reduced-round SPECK

Yunwen Liu, Glenn De Witte, Adrián Ranea, Tomer Ashur
2017 IACR Transactions on Symmetric Cryptology
In particular, we present distinguishers for 10, 11 and 12 rounds for Speck32/64 which have better probabilities than the previously known 9-round differential characteristic, for a certain weak key class  ...  In this paper we formulate a SAT/SMT model for Rotational-XOR (RX) cryptanalysis in ARX primitives for the first time.  ...  Right: Key schedule BV14, BVLC16, YZW15, AB16]; • Mixed integer linear programming, cf.  ...
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