Geodesic
On explicit constructions for solving the problem “A secret sharing”
Prikladnaya Diskretnaya Matematika. Supplement, no. 10 (2017), pp. 68-70 Cet article a éte moissonné depuis la source Math-Net.Ru

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“A secret sharing” problem was suggested to the participants of the second round competition in cryptography NSUCRYPTO-2015. The problem is to construct a subset $M\subset\mathbb F_2^n$ satisfying the following conditions: 1) any $u\in M$ can be represented as $u=x\oplus y\oplus z$, where $x,y,z$ are different elements of $\overline M=\mathbb F_2^n\setminus M$; 2) $x\oplus y\oplus z\in M$ for all different $x,y,z\in\overline M$. The paper presents some approaches to solving this problem. In particular, for even $n$, an explicit construction of the required set $M$ on the basis of a cubic parabola is proposed.
Mots-clés : NSUCRYPTO-2015, parabola curve.
Keywords: Galois field, secret sharing 
@article{PDMA_2017_10_a28,
     author = {K. L. Geut and K. A. Kirienko and P. O. Sadkov and R. I. Taskin and S. S. Titov},
     title = {On explicit constructions for solving the problem {{\textquotedblleft}A~secret} sharing{\textquotedblright}},
     journal = {Prikladnaya Diskretnaya Matematika. Supplement},
     pages = {68--70},
     year = {2017},
     number = {10},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDMA_2017_10_a28/}
}
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K. L. Geut; K. A. Kirienko; P. O. Sadkov; R. I. Taskin; S. S. Titov. On explicit constructions for solving the problem “A secret sharing”. Prikladnaya Diskretnaya Matematika. Supplement, no. 10 (2017), pp. 68-70. http://geodesic.mathdoc.fr/item/PDMA_2017_10_a28/

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