Cartesian Genetic Programming Approach for Generating Substitution Boxes of Different Sizes

Picek, Stjepan; Miller, Julian F.; Jakobović, Domagoj; Batina, Lejla

doi:10.1145/2739482.2764698

Cited by 15 publications

(9 citation statements)

References 10 publications

(9 reference statements)

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“…With their approach, they were able to generate a number of S-boxes of appropriate sizes that satisfy all the requirements placed on a MARS S-box. Picek et al used Cartesian Genetic Programming and Genetic Programming to evolve S-boxes and discussed how to obtain permutation based encoding with those algorithms [31]. Picek et al presented an improved fitness function with which EC is able to find higher nonlinearity values for a number of S-box sizes [28].…”

Section: Related Workmentioning

confidence: 99%

Cellular automata based S-boxes

et al. 2018

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Section: Related Workmentioning

confidence: 99%

Cellular automata based S-boxes

et al. 2018

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“…Picek et al used CGP and GP to evolve 3×3 and 4×4 S-boxes and discussed how to obtain permutation-based encoding with those algorithms [21]. The authors used the single-objective optimization where both nonlinearity and differential uniformity are used.…”

Section: Related Workmentioning

confidence: 99%

One property to rule them all?

Djurasevic

Jakobović

Picek

2020

Proceedings of the 2020 Genetic and Evolutionary Computation Conference

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Substitution boxes (S-boxes) are nonlinear mappings that represent one of the core parts of many cryptographic algorithms (ciphers). If S-box does not possess good properties, a cipher would be susceptible to attacks. To design suitable S-boxes, we can use heuristics as it allows significant freedom in the selection of required cryptographic properties. Unfortunately, with heuristics, one is seldom sure how good a trade-off between cryptographic properties is reached or if optimizing for one property optimizes implicitly for another property. In this paper, we consider what is to the best of our knowledge, the most detailed analysis of tradeoffs among S-box cryptographic properties. More precisely, we ask questions if one property is optimized, what is the worst possible value for some other property, and what happens if all properties are optimized. Our results show that while it is possible to reach a large variety of possible solutions, optimizing for a certain property would commonly result in good values for other properties. In turn, this suggests that a single-objective approach should be a method of choice unless some precise values for multiple properties are needed. CCS CONCEPTS • Security and privacy → Block and stream ciphers; • Computing methodologies → Discrete space search;

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“…When considering the lack of the information to guide the search, we need to first decide how to represent the S-box. A trivial choice would be to represent it as a number of Boolean functions (since an S-box is a vectorial Boolean function) but the results in literature suggest this approach is not adequate for obtaining bijective S-boxes for sizes larger than 4 × 4 [31]. To alleviate this problem, a common choice is to use permutation encoding where bijectivity is inherently preserved.…”

Section: Introductionmentioning

confidence: 99%

A characterisation of S-box fitness landscapes in cryptography

Jakobović

Picek

Martins

et al. 2019

Proceedings of the Genetic and Evolutionary Computation Conference

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Substitution Boxes (S-boxes) are nonlinear objects often used in the design of cryptographic algorithms. The design of high quality S-boxes is an interesting problem that attracts a lot of attention. Many attempts have been made in recent years to use heuristics to design S-boxes, but the results were often far from the previously known best obtained ones. Unfortunately, most of the effort went into exploring different algorithms and fitness functions while little attention has been given to the understanding why this problem is so difficult for heuristics. In this paper, we conduct a fitness landscape analysis to better understand why this problem can be difficult. Among other, we find that almost each initial starting point has its own local optimum, even though the networks are highly interconnected. CCS CONCEPTS• Software and its engineering → Software notations and tools; Search-based software engineering;

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Cartesian Genetic Programming Approach for Generating Substitution Boxes of Different Sizes

Cited by 15 publications

References 10 publications

Cellular automata based S-boxes

Cellular automata based S-boxes

One property to rule them all?

A characterisation of S-box fitness landscapes in cryptography

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