In Inscrypt 2016, Chang et al. proposed a new family of substitution-permutation (SPN) based format preserving encryption algorithms in which a non-MDS (Maximum Distance Separable) matrix was used in its diffusion layer. In the same year in Indocrypt 2016 Gupta et al., in their attempt to provide a reason for choosing non-MDS over MDS matrices, introduced an algebraic structure called format preserving sets (FPS). They formalised the notion of this structure with respect to a matrix both of whose elements are coming from some finite field F q . Many interesting properties of format preserving sets (FPS). with respect to a matrix M(F q ) were derived. Nevertheless, a complete characterisation of such sets could not be derived. In this paper, we fill that gap and give a complete characterisation of format preserving sets when the underlying algebraic structure is a finite field. Our results not only generalise and subsume those of Gupta et al., but also obtain some of these results over a more generic algebraic structure viz. ring R. We obtain a complete characterisation of format preserving sets over rings when the sets are closed under addition. Finally, we provide examples of format preserving sets of cardinalities 10 3 and 26 3 with respect to 4 × 4 MDS matrices over some rings which are not possible over any finite field.
CITATION STYLE
Barua, R., Gupta, K. C., Pandey, S. K., & Ray, I. G. (2018). On diffusion layers of spn based format preserving encryption schemes: Format preserving sets revisited. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 11356 LNCS, pp. 91–104). Springer Verlag. https://doi.org/10.1007/978-3-030-05378-9_5
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