Optimizing S-Box Implementations for Several Criteria Using SAT Solvers

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9783)


We explore the feasibility of applying SAT solvers to optimizing implementations of small functions such as S-boxes for multiple optimization criteria, e.g., the number of nonlinear gates and the number of gates. We provide optimized implementations for the S-boxes used in Ascon, ICEPOLE, Joltik/Piccolo, Keccak/Ketje/Keyak, LAC, Minalpher, PRIMATEs, Prøst, and RECTANGLE, most of which are candidates in the secound round of the CAESAR competition. We then suggest a new method to optimize for circuit depth and we make tooling publicly available to find efficient implementations for several criteria. Furthermore, we illustrate with the 5-bit S-box of PRIMATEs how multiple optimization criteria can be combined.


S-box SAT solvers Implementation optimization Multiplicative complexity Circuit depth complexity Shortest linear straight-line program 

Supplementary material


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Copyright information

© International Association for Cryptologic Research 2016

Authors and Affiliations

  1. 1.Digital SecurityRadboud UniversityNijmegenThe Netherlands

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