An Algorithm for NTRU Problems and Cryptanalysis of the GGH Multilinear Map without an encoding of zero

@article{Cheon2016AnAF,
  title={An Algorithm for NTRU Problems and Cryptanalysis of the GGH Multilinear Map without an encoding of zero},
  author={Jung Hee Cheon and Jinhyuck Jeong and Changmin Lee},
  journal={IACR Cryptology ePrint Archive},
  year={2016},
  volume={2016},
  pages={139}
}
Let h and g be polynomials of bounded Euclidean norm in the ring Z[X]/⟨X+1⟩. Given polynomial [h/g]q ∈ Zq[X]/⟨X+1⟩, the NTRU problem is to find a, b ∈ Z[X]/⟨X + 1⟩ with small Euclidean norm such that [a/b]q = [h/g]q. We propose an algorithm to solve the NTRU problem which runs in 2 2 q) time when ∥g∥, ∥h∥ and ∥g−1∥ are in some range. The main technique of our algorithm is to reduce a problem on a field to one in a subfield. Recently, the GGH scheme, the first candidate of a (approximate… CONTINUE READING
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