## Abstract

Vercauteren introduced the concept of optimal pairing, which by definition can be computed by using at most (log_{2} r)/φ(k) + log_{2} k basic Miller iterations, where r is the order of the groups involved and k is the embedding degree Vercauteren (IEEE Trans Inf Theory 56(1):455-461, 2010). Freeman et al. summarized and proposed all of the new constructions of pairing-friendly elliptic curves that currently exist Freeman et al. (J Cryptol 23(2):224-280, 2010). In this paper, we give an optimal pairing for each family of pairing-friendly curves in Freeman et al. (J Cryptol 23(2):224-280, 2010) by taking the Ate or R-ate pairing approach.

Original language | English |
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Pages (from-to) | 235-248 |

Number of pages | 14 |

Journal | Applicable Algebra in Engineering, Communications and Computing |

Volume | 22 |

Issue number | 4 |

DOIs | |

State | Published - Nov 2011 |

## Keywords

- Ate pairing
- Elliptic curves
- Pairing computation
- R-ate pairing
- Tate pairing