Contact Info
Combinatorics & Optimization
University of Waterloo
Waterloo, Ontario
Canada N2L 3G1
Phone: 519-888-4567, ext 33038
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Speaker: | Dimitar Jetchev |
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Affiliation: | Institut des Hautes Études Scientifiques |
Room: | Mathematics & Computer Building (MC) 5158 |
We show that if one can predict the least significant bit of the Diffie-Hellman secret keys for elliptic curves with non-negligible advantage on a polynomial fraction of all curves over a given finite field $\mathbb{F}_p$, then one can compute the entire Diffie-Hellman secret on a polynomial fraction of all curves over the same finite field. Our method combines rapid mixing properties of certain isogeny graphs, results due to Boneh and Shparlinski and a new refinement of H. Lenstra's lower bounds on the size of the isogeny classes corresponding to certain traces of Frobenius.
This is joint work with Ramarathnam Venkatesan.
Combinatorics & Optimization
University of Waterloo
Waterloo, Ontario
Canada N2L 3G1
Phone: 519-888-4567, ext 33038
PDF files require Adobe Acrobat Reader.
The University of Waterloo acknowledges that much of our work takes place on the traditional territory of the Neutral, Anishinaabeg and Haudenosaunee peoples. Our main campus is situated on the Haldimand Tract, the land granted to the Six Nations that includes six miles on each side of the Grand River. Our active work toward reconciliation takes place across our campuses through research, learning, teaching, and community building, and is centralized within our Office of Indigenous Relations.