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 q 2 of extension field F q 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 F q 30 whose compression ratio is 4/15. It is an open problem to construct an efficient public-key cryptosystem

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... hose 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 q 6 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.