### Abstract

This paper proposes a fast elliptic curve multiplication algorithm applicable for any types of curves over finite fields Fp (p a prime), based on [Mon87], together with criteria which make our algorithm resistant against the side channel attacks (SCA). The algorithm improves both on an addition chain and an addition formula in the scalar multiplication. Our addition chain requires no table look-up (or a very small number of pre-computed points) and a prominent property is that it can be implemented in parallel. The computing time for n-bit scalar multiplication is one ECDBL + (n −1) ECADDs in the parallel case and (n −1) ECDBLs + (n −1) ECADDs in the single case. We also propose faster addition formulas which only use the x-coordinates of the points. By combination of our addition chain and addition formulas, we establish a faster scalar multiplication resistant against the SCA in both single and parallel computation. The improvement of our scalar multiplications over the previous method is about 37% for two processors and 5.7% for a single processor. Our scalar multiplication is suitable for the implementation on smart cards.

Original language | English |
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Title of host publication | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Editors | David Naccache, Pascal Paillier |

Publisher | Springer Verlag |

Pages | 280-296 |

Number of pages | 17 |

ISBN (Print) | 3540431683, 9783540431688 |

DOIs | |

Publication status | Published - Jan 1 2002 |

Event | 5th International Workshop on Practice and Theory in Public Key Cryptosystems, PKC 2002 - Paris, France Duration: Feb 12 2002 → Feb 14 2002 |

### 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 | 2274 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 5th International Workshop on Practice and Theory in Public Key Cryptosystems, PKC 2002 |
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Country | France |

City | Paris |

Period | 2/12/02 → 2/14/02 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)*(pp. 280-296). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2274). Springer Verlag. https://doi.org/10.1007/3-540-45664-3_20

**A fast parallel elliptic curve multiplication resistant against side channel attacks.** / Izu, Tetsuya; Takagi, Tsuyoshi.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics).*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 2274, Springer Verlag, pp. 280-296, 5th International Workshop on Practice and Theory in Public Key Cryptosystems, PKC 2002, Paris, France, 2/12/02. https://doi.org/10.1007/3-540-45664-3_20

}

TY - GEN

T1 - A fast parallel elliptic curve multiplication resistant against side channel attacks

AU - Izu, Tetsuya

AU - Takagi, Tsuyoshi

PY - 2002/1/1

Y1 - 2002/1/1

N2 - This paper proposes a fast elliptic curve multiplication algorithm applicable for any types of curves over finite fields Fp (p a prime), based on [Mon87], together with criteria which make our algorithm resistant against the side channel attacks (SCA). The algorithm improves both on an addition chain and an addition formula in the scalar multiplication. Our addition chain requires no table look-up (or a very small number of pre-computed points) and a prominent property is that it can be implemented in parallel. The computing time for n-bit scalar multiplication is one ECDBL + (n −1) ECADDs in the parallel case and (n −1) ECDBLs + (n −1) ECADDs in the single case. We also propose faster addition formulas which only use the x-coordinates of the points. By combination of our addition chain and addition formulas, we establish a faster scalar multiplication resistant against the SCA in both single and parallel computation. The improvement of our scalar multiplications over the previous method is about 37% for two processors and 5.7% for a single processor. Our scalar multiplication is suitable for the implementation on smart cards.

AB - This paper proposes a fast elliptic curve multiplication algorithm applicable for any types of curves over finite fields Fp (p a prime), based on [Mon87], together with criteria which make our algorithm resistant against the side channel attacks (SCA). The algorithm improves both on an addition chain and an addition formula in the scalar multiplication. Our addition chain requires no table look-up (or a very small number of pre-computed points) and a prominent property is that it can be implemented in parallel. The computing time for n-bit scalar multiplication is one ECDBL + (n −1) ECADDs in the parallel case and (n −1) ECDBLs + (n −1) ECADDs in the single case. We also propose faster addition formulas which only use the x-coordinates of the points. By combination of our addition chain and addition formulas, we establish a faster scalar multiplication resistant against the SCA in both single and parallel computation. The improvement of our scalar multiplications over the previous method is about 37% for two processors and 5.7% for a single processor. Our scalar multiplication is suitable for the implementation on smart cards.

UR - http://www.scopus.com/inward/record.url?scp=84958955271&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84958955271&partnerID=8YFLogxK

U2 - 10.1007/3-540-45664-3_20

DO - 10.1007/3-540-45664-3_20

M3 - Conference contribution

AN - SCOPUS:84958955271

SN - 3540431683

SN - 9783540431688

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 280

EP - 296

BT - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

A2 - Naccache, David

A2 - Paillier, Pascal

PB - Springer Verlag

ER -