On the search of non-complete set coverings for the design of protected substitution layers
The security of digital information systems relies on the use of cryptographic algorithms implemented within communicating devices. Attacks to such algorithms may rely not only on their mathematical properties, but also on those related to the physical implementing device. First described in the lat...
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| Tipo de recurso: | tesis de maestría |
| Fecha de publicación: | 2025 |
| País: | España |
| Institución: | Universitat Oberta de Catalunya (UOC) |
| Repositorio: | O2, repositorio institucional de la UOC |
| OAI Identifier: | oai:openaccess.uoc.edu:10609/152825 |
| Acceso en línea: | https://hdl.handle.net/10609/152825 |
| Access Level: | acceso embargado |
| Palabra clave: | side channel attacks threshold Implementations non-complete set covering Cryptography -- FMDP Criptografia -- TFM |
| Sumario: | The security of digital information systems relies on the use of cryptographic algorithms implemented within communicating devices. Attacks to such algorithms may rely not only on their mathematical properties, but also on those related to the physical implementing device. First described in the late 1990s, side-channel attacks (SCA) are an important threat in this sense. These attacks exploit the physical magnitudes of hardware devices. Otherwise secure algorithms are considered vulnerable under this adversarial model. Threshold Implementations aim to mitigate SCAs by using a modified algorithm that runs over randomized shares of its input and intermediate values. They rely on the possibility of splitting the algorithm into sub-functions that satisfy certain properties about their dependence structure on the randomized shares. Non-complete set coverings, first defined in 2019, are mathematical objects that represent this desired dependence structure and can be used to guide the design of Threshold Implementations. Fixed some target level (order) of security and degree of the functions to be implemented, for a non-complete set covering to be useful, it is necessary that it leads to a small and similar number of randomized shares and sub-functions. As such, the search for useful non-complete set coverings is a current research area. To date, some practical coverings have been found, although their optimality has not been established in most cases. This work contributes by proving the optimality of some of the already known non-complete set coverings and also finding and analyzing the optimality of new ones. In particular, for coverings of third degree, (i) the optimality of the known ones of order two is confirmed, and (ii) new coverings of order three have been found and proven to be not far from optimal. Additionally, coverings of degree four and order two are also found and shown to be close to optimality. In this process, new properties of non-complete set coverings have been formulated. |
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