Further research on public-key cryptosystems based on third-order recurrence sequence - JIANG Zheng-tao 1; SUN Xi 1; TIAN Lei 2; WANG Yu-min 1 (Tongxin xuebao)
Properties of third-order recurrence sequences were investtgated and a new variant of GH public-key cryptosystem was proposed. It is further improved to be a probabilistic public-key cryptosystem. Then security analysis of the proposed schemes were provided. The one-wayness of the proposed scheme was equivalent to partial discrete logarithm in ring extension and its semantic security was equivalent to decisional Diffie-Hellman problem in ring extension. At last efficiency analysis of the proposed schemes were provided, and these two encryption schemes need to transfer 2logN and 4logN- bit respectively.