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XTR is one of the most efficient public-key cryptosystems that allow us to compress the communication bandwidth of their ciphertext. The compact representation can be achieved by deploying a subgroup *F*_{q2} of extension field *F*_{q6}, 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 *F*_{q30} 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 *F*_{q6} to *F*_{q} 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.

- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E91-A No.10 pp.2843-2850

- Publication Date
- 2008/10/01

- Publicized

- Online ISSN
- 1745-1337

- DOI
- 10.1093/ietfec/e91-a.10.2843

- Type of Manuscript
- Special Section PAPER (Special Section on Information Theory and Its Applications)

- Category
- Cryptography and Information Security

The copyright of the original papers published on this site belongs to IEICE. Unauthorized use of the original or translated papers is prohibited. See IEICE Provisions on Copyright for details.

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Masaaki SHIRASE, Dong-Guk HAN, Yasushi HIBINO, Howon KIM, Tsuyoshi TAKAGI, "A More Compact Representation of XTR Cryptosystem" in IEICE TRANSACTIONS on Fundamentals,
vol. E91-A, no. 10, pp. 2843-2850, October 2008, doi: 10.1093/ietfec/e91-a.10.2843.

Abstract: XTR is one of the most efficient public-key cryptosystems that allow us to compress the communication bandwidth of their ciphertext. The compact representation can be achieved by deploying a subgroup *F*_{q2} of extension field *F*_{q6}, 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 *F*_{q30} 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 *F*_{q6} to *F*_{q} 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.

URL: https://global.ieice.org/en_transactions/fundamentals/10.1093/ietfec/e91-a.10.2843/_p

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@ARTICLE{e91-a_10_2843,

author={Masaaki SHIRASE, Dong-Guk HAN, Yasushi HIBINO, Howon KIM, Tsuyoshi TAKAGI, },

journal={IEICE TRANSACTIONS on Fundamentals},

title={A More Compact Representation of XTR Cryptosystem},

year={2008},

volume={E91-A},

number={10},

pages={2843-2850},

abstract={XTR is one of the most efficient public-key cryptosystems that allow us to compress the communication bandwidth of their ciphertext. The compact representation can be achieved by deploying a subgroup *F*_{q2} of extension field *F*_{q6}, 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 *F*_{q30} 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 *F*_{q6} to *F*_{q} 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.},

keywords={},

doi={10.1093/ietfec/e91-a.10.2843},

ISSN={1745-1337},

month={October},}

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TY - JOUR

TI - A More Compact Representation of XTR Cryptosystem

T2 - IEICE TRANSACTIONS on Fundamentals

SP - 2843

EP - 2850

AU - Masaaki SHIRASE

AU - Dong-Guk HAN

AU - Yasushi HIBINO

AU - Howon KIM

AU - Tsuyoshi TAKAGI

PY - 2008

DO - 10.1093/ietfec/e91-a.10.2843

JO - IEICE TRANSACTIONS on Fundamentals

SN - 1745-1337

VL - E91-A

IS - 10

JA - IEICE TRANSACTIONS on Fundamentals

Y1 - October 2008

AB - XTR is one of the most efficient public-key cryptosystems that allow us to compress the communication bandwidth of their ciphertext. The compact representation can be achieved by deploying a subgroup *F*_{q2} of extension field *F*_{q6}, 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 *F*_{q30} 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 *F*_{q6} to *F*_{q} 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.

ER -