Geodesic
XS-circuits: hiding round oracles
Prikladnaya Diskretnaya Matematika. Supplement, no. 14 (2021), pp. 59-61.

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XS-circuits describe block ciphers that utilize 2 operations on binary words of fixed length: X — bitwise modulo 2 addition and S — substitution. In this paper, we develop a model of XS-circuits according to which several instances of a simple round circuit containing only one S operation are linked together and form a compound circuit called a cascade. S operations of a cascade are interpreted as independent round oracles. Determining some input/output pair of some round oracle from an input/output of the cascade is considered a security breach. We introduce the notion of hiding round oracles when such determining is hard. We show that a cascade based on a regular round circuit hides round oracles when the number of rounds is at least twice its dimension (the number of words in the processed data blocks).
Keywords: block cipher, round oracle, linear recurrence sequence.
Mots-clés : XS-circuit 
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     author = {S. V. Agievich},
     title = {XS-circuits: hiding round oracles},
     journal = {Prikladnaya Diskretnaya Matematika. Supplement},
     pages = {59--61},
     publisher = {mathdoc},
     number = {14},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDMA_2021_14_a12/}
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S. V. Agievich. XS-circuits: hiding round oracles. Prikladnaya Diskretnaya Matematika. Supplement, no. 14 (2021), pp. 59-61. http://geodesic.mathdoc.fr/item/PDMA_2021_14_a12/

[1] Agievich S., “XS-circuits in block ciphers”, Matem. vopr. kriptogr., 10:2 (2019), 7–30 | MR