Search-Space Reduction for S-Boxes Resilient to Power Attacks

Applied Sciences

Omar Rojas¹  Guillermo Sosa-Gómez¹  Yasser Bardaji-López²  Dianne Miyares-Moreno²  Ricardo Sánchez-Muiña²  Ismel Martínez-Díaz³  CarlosMiguel Legón-Pérez³ 

[1] Facultad de Ciencias Económicas y Empresariales, Universidad Panamericana, Álvaro del Portillo 49, Zapopan, Jalisco 45010, Mexico;Faculty of Computer Science, Technologic University of Havana, Havana 19390, Cuba;Institute of Cryptography, University of Havana, Havana 10400, Cuba;

关键词: power attacks;    cryptology;    confusion coefficient variance;    S-boxes;    equivalence classes;   

DOI  :  10.3390/app11114815

来源: DOAJ

【 摘 要 】

The search of bijective $n\times n$ S-boxes resilient to power attacks in the space of dimension $\left(2^n\right)!$ is a controversial topic in the cryptology community nowadays. This paper proposes partitioning the space of $\left(2^n\right)!$ S-boxes into equivalence classes using the hypothetical power leakage according to the Hamming weights model, which ensures a homogeneous theoretical resistance within the class against power attacks. We developed a fast algorithm to generate these S-boxes by class. It was mathematically demonstrated that the theoretical metric confusion coefficient variance takes constant values within each class. A new search strategy—jumping over the class space—is justified to find S-boxes with high confusion coefficient variance in the space partitioned by Hamming weight classes. In addition, a decision criterion is proposed to move quickly between or within classes. The number of classes and the number of S-boxes within each class are calculated, showing that, as n increases, the class space dimension is an ever-smaller fraction of the space of S-boxes, which significantly reduces the space of search of S-boxes resilient to power attacks, when the search is performed from class to class.

【 授权许可】

Unknown