%A JIANG Zheng-tao, SUN Xi, WANG Yu-min, TIAN Lei %T Further research on public-key cryptosystems based on third-order recurrence sequence %0 Journal Article %D 2006 %J Front. Electr. Electron. Eng. %J Frontiers of Electrical and Electronic Engineering %@ 2095-2732 %R 10.1007/s11460-006-0039-7 %P 287-290 %V 1 %N 3 %U {https://journal.hep.com.cn/fee/EN/10.1007/s11460-006-0039-7 %8 2006-09-05 %X Properties of third-order recurrence sequences were investigated and a new variant of the GH public-key cryptosystem, which was further improved to be a probabilistic public-key cryptosystem, was proposed. Then security analysis of the proposed scheme was provided and it was proved that the one-wayness of the proposed scheme is equivalent to partial discrete logarithm and its semantic security is equivalent to decisional Diffie-Hellman problem in ring extension. Finally, efficiency analysis of the proposed scheme was provided, and that these two encryption schemes need to transfer 2log N and 4log N bits data respectively.