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ISAAC

2004

Springer

2004

Springer

It has been suggested that a major obstacle in ﬁnding an index calculus attack on the elliptic curve discrete logarithm problem lies in the diﬃculty of lifting points from elliptic curves over ﬁnite ﬁelds to global ﬁelds. We explore the possibility of circumventing the problem of explicitly lifting points by investigating whether partial information about the lifting would be suﬃcient for solving the elliptic curve discrete logarithm problem. Along this line, we show that the elliptic curve discrete logarithm problem can be reduced to three partial lifting problems. Our reductions run in random polynomial time assuming certain conjectures, which are based on some well-known and widely accepted conjectures concerning the expected ranks of elliptic curves over the rationals. Should the elliptic curve discrete logarithm problem admit no subexponential time attack, then our results suggest that gaining partial information about lifting would be at least as hard. Keyword: Ellipt...

Related Content

Added |
02 Jul 2010 |

Updated |
02 Jul 2010 |

Type |
Conference |

Year |
2004 |

Where |
ISAAC |

Authors |
Qi Cheng, Ming-Deh A. Huang |

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