2016
DOI: 10.1007/978-3-319-39555-5_26
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Automatic Search of Linear Trails in ARX with Applications to SPECK and Chaskey

Abstract: Abstract. In this paper, we study linear cryptanalysis of the ARX structure by means of automatic search. To evaluate the security of ARX designs against linear cryptanalysis, it is crucial to find (round-reduced) linear trails with maximum correlation. We model the problem of finding optimal linear trails by the boolean satisfiability problem (SAT), translate the propagation of masks through ARX operations into bitwise expressions and constraints, and then solve the problem using a SAT solver. We apply the me… Show more

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Cited by 51 publications
(50 citation statements)
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“…Finally, we do not know how to apply our method to ARX based constructions. (15,2,13,4,11,6,3,8,1,10,5,0,7,12,9,14) 7 (7,2,13,4,15,6,1,8,5,10,3,0,11,12,9,14) 2 (15,2,9,4,1,6,11,8,3,10,13,0,7,12,5,14) 8 (7,2,11,4,9,…”
Section: Conclusion and Discussionmentioning
confidence: 99%
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“…Finally, we do not know how to apply our method to ARX based constructions. (15,2,13,4,11,6,3,8,1,10,5,0,7,12,9,14) 7 (7,2,13,4,15,6,1,8,5,10,3,0,11,12,9,14) 2 (15,2,9,4,1,6,11,8,3,10,13,0,7,12,5,14) 8 (7,2,11,4,9,…”
Section: Conclusion and Discussionmentioning
confidence: 99%
“…One paradigm for automatic symmetric-key cryptanalysis getting increasing popularity in recent years is to model the problem by means of constraints, which includes the methods based on SAT/SMT (satisfiability modulo theory) [6][7][8], MILP (mixed-integer linear programming) [9][10][11][12][13], and classical constraint programming [14,15]. In this paper, these methods are collectively referred to as the general constraint programming (CP) based approach, or just CP based approach for short.…”
Section: Introductionmentioning
confidence: 99%
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“…In 2013, Schulte-Geers used CCZ equivalence to improve the explicit formula for the calculation of linear correlation of modular addition [17]. Based on the improved formula and SAT solver model, Liu et al obtained better linear characteristics for SPECK [18], the optimal linear trails for SPECK32/48/64 with correlation close to the security boundary (2 − n/2 ) were obtained, and the 9/10-round linear hull with a potential of 2 − 29.1 /2 − 32.1 for SPECK32 was obtained.…”
Section: Introductionmentioning
confidence: 99%
“…The main target of ShiftBits is to avoid trivial propagations of differences through the MixColumns operation where the modular additions are not effectively activated. The difference propagation through modular addition can be efficiently modelled with a SAT/SMT language similar to the techniques in [11,12]. As a result, we track the propagation of the differences through the round function, and obtain that when the rotational offset r is 3, an optimal differential characteristic of 4 rounds has a probability 2 −42 .…”
Section: Nonlinear Diffusion Function ρ and ψmentioning
confidence: 99%