Discrete Logarithm Problems with Auxiliary Inputs

@article{Cheon2009DiscreteLP,
  title={Discrete Logarithm Problems with Auxiliary Inputs},
  author={Jung Hee Cheon},
  journal={Journal of Cryptology},
  year={2009},
  volume={23},
  pages={457-476}
}
Let g be an element of prime order p in an abelian group, and let α∈ℤ p . We show that if g,g α , and $g^{\alpha^{d}}$ are given for a positive divisor d of p−1, the secret key α can be computed deterministically in $O(\sqrt{p/d}+\sqrt{d})$ exponentiations by using $O(\max\{\sqrt{p/d},\sqrt{d}\})$ storage. If $g^{\alpha^{i}}$ (i=0,1,2,…,2d) is given for a positive divisor d of p+1, α can be computed in $O(\sqrt{p/d}+d)$ exponentiations by using $O(\max\{\sqrt{p/d},\sqrt{d}\})$ storage. We also… CONTINUE READING
Highly Cited
This paper has 29 citations. REVIEW CITATIONS
20 Citations
34 References
Similar Papers

Citations

Publications citing this paper.
Showing 1-10 of 20 extracted citations

References

Publications referenced by this paper.
Showing 1-10 of 34 references

Complexity of a Deterministic Algorithm for the Discrete Logarithm

  • V. Nechaev
  • Math. Zametki,
  • 1994
Highly Influential
12 Excerpts

The Distribution of Integers with a Divisor in a given Interval

  • K. Ford
  • To appear in Annals of Mathematics,
  • 2008
1 Excerpt

Similar Papers

Loading similar papers…