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Pré-Publication, Document De Travail Année : 2024

Subfield attack: leveraging composite-degree extensions in the Quotient Ring transform

Pierre Pébereau
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Résumé

In this note, we show that some of the parameters of the Quotient-Ring transform proposed for VOX are vulnerable. More precisely, they were chosen to defeat an attack in the field extension F q l obtained by quotienting Fq[X] by an irreducible polynomial of degree l. We observe that we may use a smaller extension F q l ′ for any l ′ |l, in which case the attacks apply again. We also introduce a simple algebraic attack without the use of the MinRank problem to attack the scheme. These attacks concern a subset of the parameter sets proposed for VOX: I, Ic, III, IIIa, V, Vb. We estimate the cost of our attack on these parameter sets and find costs of at most 2 67 gates, and significantly lower in most cases. In practice, our attack requires 0.3s, 1.35s, 0.56s for parameter sets I,III,V for VOX [1], and 56.7s, 6.11s for parameter sets IIIa, Vb [2].
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Dates et versions

hal-04453298 , version 1 (12-02-2024)

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  • HAL Id : hal-04453298 , version 1

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Pierre Pébereau. Subfield attack: leveraging composite-degree extensions in the Quotient Ring transform. 2024. ⟨hal-04453298⟩
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