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Comments on "Efficient Group Key Management for Resilient Operation of LoRaWAN-Based Smart Grid Applications"
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DOI：10.1109/TCST.2026.3682777.png)
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Abstract
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We show that Hanna et al.'s group key management cannot be practically implemented, because its group key renewal falsely requires that the control center (CC) uses <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> random points to construct a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$t{\,}-{\,}1$ </tex-math></inline-formula> degree polynomial by Lagrange interpolation, where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$t{\,}\lt {\,}n$ </tex-math></inline-formula>. Actually, the interpolated polynomial is of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$n{\,}-{\,}1$ </tex-math></inline-formula> degree, not of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$t{\,}-{\,}1$ </tex-math></inline-formula> degree.
Keywords:
Group key management
group key renewal
Lagrange interpolation
Shamir’s secret share
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