## Abstract

This paper presents the Graphics Processing Unit (GPU) accelerated version of the LSB Invariant scalar point multiplication for binary elliptic curves. This method was implemented using the CUDA programming language for nVidia graphics cards. With a parallel factor of (length+1) and Ĺopez- Dahab projective coordinate P_{i'}s, on an nVidia GTX 285 graphics card precomputation takes 190.203995 ms while the actual scalar point multiplication takes 173.121002 ms for GF(2^{163}). With a parallel factor of (length+1)*(length) and Ĺopez-Dahab projective coordinate P _{i'}s, on an nVidia GTX 285 graphics card precomputation of 2 ^{i}P points takes 9.545 ms while the actual scalar point multiplication takes 10.743 ms (∼93.0839 kP/s) for GF(2163). With a parallel factor of (length+1)*(length) and affine coordinate P_{i'}s, on an nVidia GTX 285 graphics card precomputation takes 140.078003 ms for GF(2^{163}) while the actual scalar point multiplication takes 10.363000 ms (∼96.4972 kP/s) for GF(2^{163}).

Original language | English (US) |
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Title of host publication | 2010 IEEE International 53rd Midwest Symposium on Circuits and Systems, MWSCAS 2010 |

Pages | 57-60 |

Number of pages | 4 |

DOIs | |

State | Published - 2010 |

Event | 53rd IEEE International Midwest Symposium on Circuits and Systems, MWSCAS 2010 - Seattle, WA, United States Duration: Aug 1 2010 → Aug 4 2010 |

### Publication series

Name | Midwest Symposium on Circuits and Systems |
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ISSN (Print) | 1548-3746 |

### Other

Other | 53rd IEEE International Midwest Symposium on Circuits and Systems, MWSCAS 2010 |
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Country/Territory | United States |

City | Seattle, WA |

Period | 8/1/10 → 8/4/10 |

## Keywords

- Cryptography
- Elliptic Curves
- GPU
- Multicore

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