On the vector decomposition problem for m-torsion points on an elliptic curve

Negar Kiyavash, Iwan M Duursma

Research output: Contribution to journalConference article

Abstract

The vector decomposition problem for m-torsion points on an elliptic curve was discussed. The study proves sufficient conditions for which vector decomposition (VDP) on a two-dimensional vector space was at least as hard as the computational Diffie-Hellman Problem (CDHP) on a one-dimensional subspace. It was proved that any elliptic curve for which sufficient conditions hold was bound to be supersingular. In addition to this, a study gives family of hyperelliptic curves of genus two that were suitable for the VDP.

Original languageEnglish (US)
Number of pages1
JournalIEEE International Symposium on Information Theory - Proceedings
StatePublished - Oct 20 2004
EventProceedings - 2004 IEEE International Symposium on Information Theory - Chicago, IL, United States
Duration: Jun 27 2004Jul 2 2004

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Torsion Points
Problem Decomposition
Torsional stress
Elliptic Curves
Decomposition
Decompose
Hyperelliptic Curves
Sufficient Conditions
Diffie-Hellman
Vector spaces
Vector space
Genus
Subspace

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Information Systems
  • Modeling and Simulation
  • Applied Mathematics

Cite this

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title = "On the vector decomposition problem for m-torsion points on an elliptic curve",
abstract = "The vector decomposition problem for m-torsion points on an elliptic curve was discussed. The study proves sufficient conditions for which vector decomposition (VDP) on a two-dimensional vector space was at least as hard as the computational Diffie-Hellman Problem (CDHP) on a one-dimensional subspace. It was proved that any elliptic curve for which sufficient conditions hold was bound to be supersingular. In addition to this, a study gives family of hyperelliptic curves of genus two that were suitable for the VDP.",
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N2 - The vector decomposition problem for m-torsion points on an elliptic curve was discussed. The study proves sufficient conditions for which vector decomposition (VDP) on a two-dimensional vector space was at least as hard as the computational Diffie-Hellman Problem (CDHP) on a one-dimensional subspace. It was proved that any elliptic curve for which sufficient conditions hold was bound to be supersingular. In addition to this, a study gives family of hyperelliptic curves of genus two that were suitable for the VDP.

AB - The vector decomposition problem for m-torsion points on an elliptic curve was discussed. The study proves sufficient conditions for which vector decomposition (VDP) on a two-dimensional vector space was at least as hard as the computational Diffie-Hellman Problem (CDHP) on a one-dimensional subspace. It was proved that any elliptic curve for which sufficient conditions hold was bound to be supersingular. In addition to this, a study gives family of hyperelliptic curves of genus two that were suitable for the VDP.

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