ECC2K-130

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  • ECC2K-130

    1. 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. 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. 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. 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. 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. 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. 7. Attack against ECC2K-130 Effectiveness with relatively short key length Pollard’s Rho Birthday attack Walk until collision Minimum message passing
    8. 8. Implementation BOINC Since 2002 Open Source Communication over HTTP Multi-platform Utilities & UIs
    9. 9. Steps 1. Setup & configuration of BOINC server 2. Client(s) 3. Assimilator 4. Work generator
    10. 10. http://boinc.math.ucalgary.ca/sheti/ Any Question?

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