Tutte seminar - Dimitar Jetchev

Friday, August 22, 2008 — 3:30 PM to 4:30 PM EDT

Bit Security of Elliptic Curve Diffie-Hellman Secret Keys

Speaker: Dimitar Jetchev Institut des Hautes Études Scientifiques Mathematics & Computer Building (MC) 5158

Abstract:

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.

Location
MC - Mathematics & Computer Building
5158
200 University Avenue West

Waterloo, ON N2L 3G1

March 2023

S M T W T F S
26
27
28
1
2
4
5
8
11
12
14
15
18
19
21
22
25
26
28
31
1
1. 2023 (36)
1. April (1)
2. March (17)
3. February (10)
4. January (8)
2. 2022 (150)
1. December (8)
2. November (18)
3. October (15)
4. September (11)
5. August (2)
6. July (17)
7. June (17)
8. May (10)
9. April (12)
10. March (18)
11. February (10)
12. January (13)
3. 2021 (103)
4. 2020 (119)
5. 2019 (167)
6. 2018 (136)
7. 2017 (103)
8. 2016 (137)
9. 2015 (136)
10. 2014 (88)
11. 2013 (48)
12. 2012 (39)
13. 2011 (36)
14. 2010 (40)
15. 2009 (40)
16. 2008 (39)
17. 2007 (15)