Abstract
Substitution boxes (S-boxes) are an important part of the design of block ciphers. They provide nonlinearity and so the security of the cipher depends strongly on them. Some block ciphers use S-boxes given by lookup tables (e.g., DES) where as others use S-boxes obtained from finite field operations (e.g., AES). As a generalization of the latter, finite semifields (i.e., finite nonassociative division rings) have been suggested as algebraic structures from which S-boxes with good cryptographic properties might be obtained. In this paper we present the results of experiments on the construction of S-boxes from finite semifields of orders 256 and 64, using the left and right inverses of these rings.
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Notes
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Incidentally, let us mention that we had the privilege of learning the basic aspects of Probability, Statistics and Information Theory from Pedro himself, in two courses delivered at University of Oviedo some twenty years ago.
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Acknowledgements
I.F. Rúa is partially supported by MINECO-13-MTM2013-45588-C3-1-P, and Principado de Asturias Grant GRUPIN14-142. E.F. Combarro is partially supported by MINECO-16-TEC2015-67387-C4-3-R.
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Rúa, I.F., Combarro, E.F. (2018). Cryptographic Uncertainness: Some Experiments on Finite Semifield Based Substitution Boxes. In: Gil, E., Gil, E., Gil, J., Gil, M. (eds) The Mathematics of the Uncertain. Studies in Systems, Decision and Control, vol 142. Springer, Cham. https://doi.org/10.1007/978-3-319-73848-2_45
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DOI: https://doi.org/10.1007/978-3-319-73848-2_45
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