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单项式多变量公钥密码算法的等价密钥问题

DOI: 10.3969/j.issn.1006-7043.201405045

Keywords: 公钥密码学, 多变量, 单项式, 等价密钥, 保形变换, 有限域

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Abstract:

对基于单项式的多变量公钥密码算法中的等价密钥问题进行了研究,利用保形变换和有限域方面的知识计算出了其等价密钥的数量。这是一个更一般的结论,是已有结论的推广形式。进一步地,C*, C*-和Square等算法中等价密钥的数量可以看作是该结论的特殊情形。研究结果表明:选私钥仿射结构具有稀疏特性的矩阵作为等价类的代表元,可以有效地节省存储空间、缩短操作时间。同时,多变量公钥密码算法要想达到预想的安全强度,就必须提高算法参数的大小。

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