### Abstract

XTR is one of the most efficient public-key cryptosy stems that allow us to compress the communication bandwidth of their ciphertext. The compact representation can be achieved by deploying a subgroup Fq2 of extension field F 6, so that the compression ratio of XTR cryptosystem is 1/3. On the other hand, Dijk et al. proposed an efficient public-key cryptosystem using a torus over Fq30 whose compression ratio is 4/15. It is an open problem to construct an efficient public-key cryptosystem whose compression ratio is smaller than 4/15. In this paper we propose a new variant of XTR cryptosystem over finite fields with characteristic three whose compression ratio is 1/6. The key observation is that there exists a trace map from Fq6 to Fq in the case of characteristic three. Moreover, the cost of compression and decompression algorithm requires only about 1% overhead compared with the original XTR cryptosystem. Therefore, the proposed variant of XTR cryptosystem is one of the fastest public-key cryptosystems with the smallest compression ratio.

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

Pages (from-to) | 2843-2850 |

Number of pages | 8 |

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

Volume | E91-A |

Issue number | 10 |

DOIs | |

Publication status | Published - Oct 2008 |

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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*,

*E91-A*(10), 2843-2850. https://doi.org/10.1093/ietfec/e91-a.10.2843

**A more compact representation of XTR cryptosystem.** / Shirase, Masaaki; Han, Dong Guk; Hibino, Yasushi; Kim, Howon; Takagi, Tsuyoshi.

Research output: Contribution to journal › Article

*IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences*, vol. E91-A, no. 10, pp. 2843-2850. https://doi.org/10.1093/ietfec/e91-a.10.2843

}

TY - JOUR

T1 - A more compact representation of XTR cryptosystem

AU - Shirase, Masaaki

AU - Han, Dong Guk

AU - Hibino, Yasushi

AU - Kim, Howon

AU - Takagi, Tsuyoshi

PY - 2008/10

Y1 - 2008/10

N2 - XTR is one of the most efficient public-key cryptosy stems that allow us to compress the communication bandwidth of their ciphertext. The compact representation can be achieved by deploying a subgroup Fq2 of extension field F 6, so that the compression ratio of XTR cryptosystem is 1/3. On the other hand, Dijk et al. proposed an efficient public-key cryptosystem using a torus over Fq30 whose compression ratio is 4/15. It is an open problem to construct an efficient public-key cryptosystem whose compression ratio is smaller than 4/15. In this paper we propose a new variant of XTR cryptosystem over finite fields with characteristic three whose compression ratio is 1/6. The key observation is that there exists a trace map from Fq6 to Fq in the case of characteristic three. Moreover, the cost of compression and decompression algorithm requires only about 1% overhead compared with the original XTR cryptosystem. Therefore, the proposed variant of XTR cryptosystem is one of the fastest public-key cryptosystems with the smallest compression ratio.

AB - XTR is one of the most efficient public-key cryptosy stems that allow us to compress the communication bandwidth of their ciphertext. The compact representation can be achieved by deploying a subgroup Fq2 of extension field F 6, so that the compression ratio of XTR cryptosystem is 1/3. On the other hand, Dijk et al. proposed an efficient public-key cryptosystem using a torus over Fq30 whose compression ratio is 4/15. It is an open problem to construct an efficient public-key cryptosystem whose compression ratio is smaller than 4/15. In this paper we propose a new variant of XTR cryptosystem over finite fields with characteristic three whose compression ratio is 1/6. The key observation is that there exists a trace map from Fq6 to Fq in the case of characteristic three. Moreover, the cost of compression and decompression algorithm requires only about 1% overhead compared with the original XTR cryptosystem. Therefore, the proposed variant of XTR cryptosystem is one of the fastest public-key cryptosystems with the smallest compression ratio.

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UR - http://www.scopus.com/inward/citedby.url?scp=72449138469&partnerID=8YFLogxK

U2 - 10.1093/ietfec/e91-a.10.2843

DO - 10.1093/ietfec/e91-a.10.2843

M3 - Article

AN - SCOPUS:72449138469

VL - E91-A

SP - 2843

EP - 2850

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 - 10

ER -