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A More Compact Representation of XTR Cryptosystem
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- Authors
- Masaaki Shirase, Dong-Guk Han, Yasushi Hibino, Ho Won Kim, Tsuyoshi Takagi
- Issue Date
- 2008-10
- Citation
- IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, v.E91-A, no.10, pp.2843-2850
- ISSN
- 1745-1337
- Publisher
- 일본, 전자정보통신학회 (IEICE)
- Language
- English
- Type
- Journal Article
- 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. Copyright © 2008 The Institute of Electronics, Information and Communication Engineers.
- KSP Keywords
- Compact Representation, Decompression algorithm, Extension field, Finite field, Information and communication, Open Problem, Public-key Cryptosystems, compression ratio