Geodesic
Faulty share detection in Shamir’s secret sharing
Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 15 (2019) no. 2, pp. 274-282
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For Shamir's secret key sharing algorithm, we develop the procedure for detection of faulty shares. This procedure consists of the error locator polynomial construction for the data set $ \{ (x_j,y_j)\}_{j=1}^N $ with $ y $ values generated from $ x $ ones by a polynomial interpolant of a degree $ n < N-1 $ with possible occurrence of some errors. The error locator polynomial is sought out in the form of an appropriate Hankel polynomial $$ \mathcal H_{L}(x;\{ \tau \}) := \left| \begin{array}{lllll} \tau_0 & \tau_1 & \tau_2 & \ldots & \tau_{L} \\ \tau_1 & \tau_2 & \tau_3 &\ldots & \tau_{L+1} \\ \vdots & \vdots & \vdots & & \vdots \\ \tau_{L-1} & \tau_{L} & \tau_{L+1} & \ldots & \tau_{2L-1} \\ 1 & x & x^2 & \ldots & x^{L} \end{array} \right| \, , $$ where $ \tau_{\ell} := \displaystyle \sum_{j=1}^{N} y_j \frac{x_j^{\ell}}{W^{\prime}(x_j)} $; $ \displaystyle W(x):=\prod_{j=1}^N (x- x_j) $.
Keywords: Shamir’s secret sharing, Hankel polynomials
Mots-clés : polynomial interpolation, error correction. 
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     title = {Faulty share detection in {Shamir{\textquoteright}s} secret sharing},
     journal = {Vestnik Sankt-Peterburgskogo universiteta. Prikladna\^a matematika, informatika, processy upravleni\^a},
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A. Yu. Uteshev; A. V. Marov. Faulty share detection in Shamir’s secret sharing. Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 15 (2019) no. 2, pp. 274-282. http://geodesic.mathdoc.fr/item/VSPUI_2019_15_2_a9/

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