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考虑定义在模数N的剩余类环上的矩阵所构成的矩阵环上的求根问题的困难性,本文设计了一个数字签名算法,证明了攻击者能够成功伪造一个签名当且仅当攻击者能够求解矩阵环上的求根问题.对矩阵环上的求根问题的困难性进行了分析,在一种特殊情况下,证明了矩阵环上的求根问题与整数分解问题是等价的.分析表明,该数字签名算法是一个高效安全的签名算法.
Considering the difficulty of solving the rooting problem on the matrix ring formed by the matrices on the remaining classes of modules N, a digital signature algorithm is designed to prove that the attacker can successfully forge a signature if and only if the attacker Can solve the root problem of the matrix ring.The difficulty of solving the root problem on the matrix ring is analyzed.In a special case, it is proved that the root-seeking problem on the matrix ring is equivalent to the integer decomposition problem. Analysis shows that the digital signature algorithm is an efficient and secure signature algorithm.