### Abstract

Binary field multiplication is the most fundamental building block of binary field Elliptic Curve Cryptography (ECC) and Galois/Counter Mode (GCM). Both bit-wise scanning and Look-Up Table (LUT) based methods are commonly used for binary field multiplication. In terms of Side Channel Attack (SCA), bit-wise scanning exploits insecure branch operations which leaks information in a form of timing and power consumption. On the other hands, LUT based method is regarded as a relatively secure approach because LUT access can be conducted in a regular and atomic form. This ensures a constant time solution as well. In this paper, we conduct the SCA on the LUT based binary field multiplication. The attack exploits the horizontal Correlation Power Analysis (CPA) on weights of LUT. We identify the operand with only a power trace of binary field multiplication. In order to prevent SCA, we also suggest a mask based binary field multiplication which ensures a regular and constant time solution without LUT and branch statements.

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) |

Publisher | Springer Verlag |

Pages | 161-173 |

Number of pages | 13 |

Volume | 9503 |

ISBN (Print) | 9783319318745 |

DOIs | |

Publication status | Published - 2016 |

Event | 16th International Workshop on Information Security Applications, WISA 2015 - Jeju Island, Korea, Republic of Duration: Aug 20 2015 → Aug 22 2015 |

### Publication series

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

Volume | 9503 |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Other

Other | 16th International Workshop on Information Security Applications, WISA 2015 |
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Country | Korea, Republic of |

City | Jeju Island |

Period | 8/20/15 → 8/22/15 |

### Fingerprint

### Keywords

- Binary field multiplication
- Embedded processors
- Horizontal correlation power analysis
- Side channel attack

### ASJC Scopus subject areas

- Computer Science(all)
- Theoretical Computer Science

### Cite this

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)*(Vol. 9503, pp. 161-173). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9503). Springer Verlag. https://doi.org/10.1007/978-3-319-31875-2_14

**Secure binary field multiplication.** / Seo, Hwajeong; Chen, Chien Ning; Liu, Zhe; Nogami, Yasuyuki; Park, Taehwan; Choi, Jongseok; Kim, Howon.

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).*vol. 9503, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 9503, Springer Verlag, pp. 161-173, 16th International Workshop on Information Security Applications, WISA 2015, Jeju Island, Korea, Republic of, 8/20/15. https://doi.org/10.1007/978-3-319-31875-2_14

}

TY - GEN

T1 - Secure binary field multiplication

AU - Seo, Hwajeong

AU - Chen, Chien Ning

AU - Liu, Zhe

AU - Nogami, Yasuyuki

AU - Park, Taehwan

AU - Choi, Jongseok

AU - Kim, Howon

PY - 2016

Y1 - 2016

N2 - Binary field multiplication is the most fundamental building block of binary field Elliptic Curve Cryptography (ECC) and Galois/Counter Mode (GCM). Both bit-wise scanning and Look-Up Table (LUT) based methods are commonly used for binary field multiplication. In terms of Side Channel Attack (SCA), bit-wise scanning exploits insecure branch operations which leaks information in a form of timing and power consumption. On the other hands, LUT based method is regarded as a relatively secure approach because LUT access can be conducted in a regular and atomic form. This ensures a constant time solution as well. In this paper, we conduct the SCA on the LUT based binary field multiplication. The attack exploits the horizontal Correlation Power Analysis (CPA) on weights of LUT. We identify the operand with only a power trace of binary field multiplication. In order to prevent SCA, we also suggest a mask based binary field multiplication which ensures a regular and constant time solution without LUT and branch statements.

AB - Binary field multiplication is the most fundamental building block of binary field Elliptic Curve Cryptography (ECC) and Galois/Counter Mode (GCM). Both bit-wise scanning and Look-Up Table (LUT) based methods are commonly used for binary field multiplication. In terms of Side Channel Attack (SCA), bit-wise scanning exploits insecure branch operations which leaks information in a form of timing and power consumption. On the other hands, LUT based method is regarded as a relatively secure approach because LUT access can be conducted in a regular and atomic form. This ensures a constant time solution as well. In this paper, we conduct the SCA on the LUT based binary field multiplication. The attack exploits the horizontal Correlation Power Analysis (CPA) on weights of LUT. We identify the operand with only a power trace of binary field multiplication. In order to prevent SCA, we also suggest a mask based binary field multiplication which ensures a regular and constant time solution without LUT and branch statements.

KW - Binary field multiplication

KW - Embedded processors

KW - Horizontal correlation power analysis

KW - Side channel attack

UR - http://www.scopus.com/inward/record.url?scp=84962231350&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84962231350&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-31875-2_14

DO - 10.1007/978-3-319-31875-2_14

M3 - Conference contribution

AN - SCOPUS:84962231350

SN - 9783319318745

VL - 9503

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

SP - 161

EP - 173

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

PB - Springer Verlag

ER -