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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 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 cryptosystemdoi:10.1093/ietfec/e91-a.10.2843 fatcat:o57gxgybprcphbfr26hekydt44