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Tutte seminar - David JaoExport this event to calendar

Friday, July 8, 2011 — 3:30 PM to 4:30 PM EDT

Quantum-resistant public-key cryptosystems from supersingular elliptic curve isogenies

Speaker: David Jao
Affiliation: University of Waterloo
Room: Mathematics & Computer Building (MC) 5158

Abstract:

We present a new construction of quantum-resistant public-key cryptosystems based on the conjectured difficulty of finding isogenies between supersingular elliptic curves. The main technical idea in our scheme is that we transmit the images of torsion bases under the isogeny in order to allow the two parties to arrive at a common shared key despite the noncommutativity of the endomorphism ring. Our work is motivated by the recent development of a subexponential-time quantum algorithm for constructing isogenies between ordinary elliptic curves. In the supersingular case, by contrast, the fastest known quantum attack remains exponential, since the noncommutativity of the endomorphism ring means that the approach used in the ordinary case does not apply. We give a precise formulation of the necessary computational assumption along with a discussion of its validity, and prove the security of our protocols under this assumption. In addition, we present implementation results showing that our protocols are multiple orders of magnitude faster than previous isogeny-based cryptosystems over ordinary curves.

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

Waterloo, ON N2L 3G1
Canada

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