### Abstract

We present a scalar multiplication algorithm with recovery of the y-coordinate on a Montgomery form elliptic curve over any nonbinary field. The previous algorithms for scalar multiplication on a Montgomery form do not consider how to recover the y-coordinate. So although they can be applicable to certain restricted schemes (e.g. ECDH and ECDSA-S), some schemes (e.g. ECDSA-V and MQV) require scalar multiplication with recovery of the y-coordinate. We compare our proposed scalar multiplication algorithm with the traditional scalar multiplication algorithms (including Window-methods in Weierstrass form), and discuss the Montgomery form versus the Weierstrass form in the performance of implementations with several techniques of elliptic curve cryptosystems (including ECES, ECDSA, and ECMQV). Our results clarify the advantage of the cryptographic usage of Montgomery-form elliptic curves in constrained environments such as mobile devices and smart cards.

Original language | English |
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Title of host publication | Cryptographic Hardware and Embedded Systems - CHES 2001 - 3rd International Workshop, Proceedings |

Publisher | Springer Verlag |

Pages | 126-141 |

Number of pages | 16 |

Volume | 2162 |

ISBN (Print) | 3540425217 |

Publication status | Published - 2001 |

Event | 3rd International Workshop on Cryptographic Hardware and Embedded Systems, CHES 2001 - Paris, France Duration: May 14 2001 → May 16 2001 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 2162 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 3rd International Workshop on Cryptographic Hardware and Embedded Systems, CHES 2001 |
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Country | France |

City | Paris |

Period | 5/14/01 → 5/16/01 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Cryptographic Hardware and Embedded Systems - CHES 2001 - 3rd International Workshop, Proceedings*(Vol. 2162, pp. 126-141). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2162). Springer Verlag.