### 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 language | English (US) |
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Number of pages | 1 |

Journal | IEEE International Symposium on Information Theory - Proceedings |

State | Published - Oct 20 2004 |

Event | Proceedings - 2004 IEEE International Symposium on Information Theory - Chicago, IL, United States Duration: Jun 27 2004 → Jul 2 2004 |

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### ASJC Scopus subject areas

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

### Cite this

**On the vector decomposition problem for m-torsion points on an elliptic curve.** / Kiyavash, Negar; Duursma, Iwan M.

Research output: Contribution to journal › Conference article

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TY - JOUR

T1 - On the vector decomposition problem for m-torsion points on an elliptic curve

AU - Kiyavash, Negar

AU - Duursma, Iwan M

PY - 2004/10/20

Y1 - 2004/10/20

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.

UR - http://www.scopus.com/inward/record.url?scp=5044251832&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=5044251832&partnerID=8YFLogxK

M3 - Conference article

AN - SCOPUS:5044251832

JO - IEEE International Symposium on Information Theory - Proceedings

JF - IEEE International Symposium on Information Theory - Proceedings

SN - 2157-8095

ER -