The document discusses implementing an attack against the elliptic curve cryptosystem ECC2K-130 using grid computing. Grid computing involves using idle processing power from multiple computers or devices connected through a network. The document proposes using the BOINC (Berkeley Open Infrastructure for Network Computing) platform to distribute the Pollard's Rho algorithm for finding collisions to solve the discrete logarithm problem underlying ECC2K-130. A 4-step process is outlined for setting up the BOINC server and clients to generate and distribute work units for the algorithm.

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.

7. Attack against ECC2K-130
Effectiveness with relatively short key length
Pollard’s Rho
Birthday attack
Walk until collision
Minimum message passing

8. Implementation
BOINC
Since 2002
Open Source
Communication over HTTP
Multi-platform
Utilities & UIs

9. Steps
1. Setup & configuration of BOINC server
2. Client(s)
3. Assimilator
4. Work generator

10. http://boinc.math.ucalgary.ca/sheti/
Any Question?