### Abstract

[Updated version of paper at Indocrypt 2010]
A major cryptanalytic computation is currently underway on multiple platforms, including standard CPUs, FPGAs, PlayStations and GPUs, to break the Certicom ECC2K-130 challenge. This challenge is to compute an elliptic-curve discrete logarithm on a Koblitz curve over F_2^131 . Optimizations have reduced the cost of the computation to approximately 2^77 bit operations in 2^61 iterations.
GPUs are not designed for fast binary-field arithmetic; they are designed for highly vectorizable floating-point computations that fit into very small amounts of static RAM. This paper explains how to optimize the ECC2K-130 computation for this unusual platform. The resulting GPU software performs more than 63 million iterations per second, including 320 million F_2^131 multiplications per second, on a $500 NVIDIA GTX 295 graphics card. The same techniques for finite-field arithmetic and elliptic-curve arithmetic can be reused in implementations of larger systems that are secure against similar attacks, making GPUs an interesting option as coprocessors when a busy Internet server has many elliptic-curve operations to perform in parallel.

Original language | English |
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Publisher | IACR |

Number of pages | 19 |

Publication status | Published - 2012 |

### Publication series

Name | Cryptology ePrint Archive |
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Volume | 2012/002 |

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## Cite this

Bernstein, D. J., Chen, H-C., Cheng, C. M., Lange, T., Niederhagen, R. F., Schwabe, P., & Yang, B. Y. (2012).

*ECC2K-130 on NVIDIA GPUs*. (Cryptology ePrint Archive; Vol. 2012/002). IACR.