On Polynomial Systems Arising from a Weil Descent

@article{Petit2012OnPS,
  title={On Polynomial Systems Arising from a Weil Descent},
  author={Christophe Petit and Jean-Jacques Quisquater},
  journal={IACR Cryptology ePrint Archive},
  year={2012},
  volume={2012},
  pages={146}
}
In the last two decades, many computational problems arising in cryptography have been successfully reduced to various systems of polynomial equations. In this paper, we revisit a class of polynomial systems introduced by Faugère, Perret, Petit and Renault. Based on new experimental results and heuristic evidence, we conjecture that their degrees of regularity are only slightly larger than the original degrees of the equations, resulting in a very low complexity compared to generic systems. We… CONTINUE READING

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References

Publications referenced by this paper.
Showing 1-10 of 52 references

Inverting HFE Is Quasipolynomial

View 10 Excerpts
Highly Influenced

Ein Algorithmus zum Auffinden der Basiselemente des Restklassenringes nach einem nulldimensionalen Polynomideal

Bruno Buchberger
PhD thesis, Universitt Innsbruck, • 1965
View 5 Excerpts
Highly Influenced

Degree of regularity for HFE-

IACR Cryptology ePrint Archive • 2011
View 4 Excerpts
Highly Influenced

The Degree of Regularity of HFE Systems

ASIACRYPT • 2010
View 4 Excerpts
Highly Influenced

Improving the complexity of index calculus algorithms in elliptic curves over binary fields

N. Thériault
Accepted at EUROCRYPT • 2012

On polynomial systems arising from a weil descent

Christophe Petit, Jean-Jacques Quisquater
Cryptology ePrint Archive, Report 2012/146, • 2012
View 1 Excerpt

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