### Abstract

It has recently been reported that the performance of hyperelliptic curve cryptosystems (HECC) is competitive to that of elliptic curve cryptosystems (ECC). Concerning the security of HECC, the theta divisors play an important role. The scalar multiplication using a random base point is vulnerable to an exceptional procedure attack, which is a kind of side-channel attacks, using theta divisors. In the case of cryptographic protocols of the scalar multiplication using fixed base point, however, the exceptional procedure attack is not applicable. First, we present novel efficient scalar multiplication using theta divisors, which is the positive application of theta divisors on HECC. Second, we develop a window-based method using theta divisors that is secure against side-channel attacks. It is not obvious how to construct a base point D such that all pre-computed points are theta divisors. We present an explicit algorithm for generating such divisors.

Original language | English |
---|---|

Pages (from-to) | 151-160 |

Number of pages | 10 |

Journal | IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences |

Volume | E89-A |

Issue number | 1 |

DOIs | |

Publication status | Published - Jan 1 2006 |

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### All Science Journal Classification (ASJC) codes

- Signal Processing
- Computer Graphics and Computer-Aided Design
- Electrical and Electronic Engineering
- Applied Mathematics

### Cite this

*IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences*,

*E89-A*(1), 151-160. https://doi.org/10.1093/ietfec/e89-a.1.151

**Efficient hyperelliptic curve cryptosystems using theta divisors.** / Katagi, Masanobu; Akishita, Toru; Kitamura, Izuru; Takagi, Tsuyoshi.

Research output: Contribution to journal › Article

*IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences*, vol. E89-A, no. 1, pp. 151-160. https://doi.org/10.1093/ietfec/e89-a.1.151

}

TY - JOUR

T1 - Efficient hyperelliptic curve cryptosystems using theta divisors

AU - Katagi, Masanobu

AU - Akishita, Toru

AU - Kitamura, Izuru

AU - Takagi, Tsuyoshi

PY - 2006/1/1

Y1 - 2006/1/1

N2 - It has recently been reported that the performance of hyperelliptic curve cryptosystems (HECC) is competitive to that of elliptic curve cryptosystems (ECC). Concerning the security of HECC, the theta divisors play an important role. The scalar multiplication using a random base point is vulnerable to an exceptional procedure attack, which is a kind of side-channel attacks, using theta divisors. In the case of cryptographic protocols of the scalar multiplication using fixed base point, however, the exceptional procedure attack is not applicable. First, we present novel efficient scalar multiplication using theta divisors, which is the positive application of theta divisors on HECC. Second, we develop a window-based method using theta divisors that is secure against side-channel attacks. It is not obvious how to construct a base point D such that all pre-computed points are theta divisors. We present an explicit algorithm for generating such divisors.

AB - It has recently been reported that the performance of hyperelliptic curve cryptosystems (HECC) is competitive to that of elliptic curve cryptosystems (ECC). Concerning the security of HECC, the theta divisors play an important role. The scalar multiplication using a random base point is vulnerable to an exceptional procedure attack, which is a kind of side-channel attacks, using theta divisors. In the case of cryptographic protocols of the scalar multiplication using fixed base point, however, the exceptional procedure attack is not applicable. First, we present novel efficient scalar multiplication using theta divisors, which is the positive application of theta divisors on HECC. Second, we develop a window-based method using theta divisors that is secure against side-channel attacks. It is not obvious how to construct a base point D such that all pre-computed points are theta divisors. We present an explicit algorithm for generating such divisors.

UR - http://www.scopus.com/inward/record.url?scp=32244431590&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=32244431590&partnerID=8YFLogxK

U2 - 10.1093/ietfec/e89-a.1.151

DO - 10.1093/ietfec/e89-a.1.151

M3 - Article

AN - SCOPUS:32244431590

VL - E89-A

SP - 151

EP - 160

JO - IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

JF - IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

SN - 0916-8508

IS - 1

ER -