1. Implementing a feasible
attack against ECC2K-130
with use of grid computing
Ahmad Lavasani
<sahosse@math.ucalgary.ca>
Reza Mohammadi <reza@teeleh.ir>
Sunday, May 17, 2009 @ CC of SUT
2. Certicom Challenges
Elliptic Curves
Employed in Cryptography (1980s)
Certicom
$ 20,000 for ECC2K-130
ECC2K-108 (Apr 4, 2000 - After 166000 Machine Days)
3. Large Scale Computing [SC]
Using multi-processing is NOT the easiest way!
SuperComputer
Does not necessarily use multi-processing
Penultimate easiest way because of integration
So costly
4. Large Scale Computing [Cluster]
Cluster
Many CPUs
Requires fast networking equipment (costly)
Not applicable on so sequential algorithms
Standardized infrastructure
Message Passing Interface
5. Large Scale Computing [Grid]
No special equipment (cheaper)
For algorithms with minimum message passing
LHC Computing Grid
Berkeley Open Infrastructure for Network
Computing
6. ECC2K-130 Challenge
Underlying Field: GF(2 131)
Irreducible Polynomial: f(t) = t131 + t13 + t2 + t + 1
The Curve: y2 + xy = x3 +1
Special definition of add operation
The Problem: Knowing P and Q , find n such that
Q = nP over the curve.