利用有限域上循环矩阵的性质,使用2种不同方法去解决有限域上可逆循环矩阵的个数问题. 最后给出有限域上可逆循环矩阵个数的计算公式,并对多变量密码学中的循环矩阵的应用进行简要分析, 这对矩阵理论研究和相关密码学的分析有促进作用.
Study on the number of nonsingular circulant matrices over finite fields is significant in both maticx theory and practice. We characterize the properties of circulant matrices over finite fields and find two different ways to solve the problem. Finally, we give the formula to figure out the number of the nonsingular circulant matrices over finite fields in all circumstances and analyze some applications of circulant matrices in MPKC.
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