@inproceedings{6c84a356e07245aeb37090fac0b2e37c,

title = "ECC2K-130 on NVIDIA GPUs",

abstract = "A major cryptanalytic computation is currently underway on multiple platforms, including standard CPUs, FPGAs, PlayStations and Graphics Processing Units (GPUs), to break the Certicom ECC2K-130 challenge. This challenge is to compute an elliptic-curve discrete logarithm on a Koblitz curve over $\rm F_{2^{131}}$ . Optimizations have reduced the cost of the computation to approximately 277 bit operations in 261 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 $\rm F_{2^{131}}$ 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.",

author = "D.J. Bernstein and H.-C. Chen and C.M. Cheng and T. Lange and R.F. Niederhagen and P. Schwabe and B.Y. Yang",

year = "2010",

doi = "10.1007/978-3-642-17401-8_23",

language = "English",

isbn = "978-3-642-17400-1",

series = "Lecture Notes in Computer Science",

publisher = "Springer",

pages = "328--346",

editor = "G. Gong and K.C. Gupta",

booktitle = "Progress in Cryptology - INDOCRYPT 2010 (11th International Conference on Cryptology in India, Hyderabad, India, December 12-15, 2010. Proceedings)",

address = "Germany",

}