非确定的公钥密码及其实现

首先引入非确定的公钥密码和解密成功率的概念, 并基于有限域上多变元问题的困难性, 给出其实现方案N-HFMS; 然后对F_q［M］中非奇异矩阵的数量进行分析, 利用Euler-φ_q函数推导出F_q［M］中非奇异矩阵的精确计数公式. 结果表明, 该方法不仅可对任意特定N-HFMS实例的解密成功率进行精确估算, 还可推导出N-HFMS方案的解密成功率下限, 从而在理论上证明N-HFMS的可行性. 利用N-HFMS方案, 可约定会话密钥, 进而实现保密通讯.

Nondeterministic Public Key Cryptography and Its Implementation

First, we introduced the concept of the nondeterministic public key cryptography (PKC) and decryption success rate (DSR),  and gave its implementation scheme N HFMS based on the difficulty of the multivariate problem over finite field . Then， we analyzed the number of nonsingular matrices in F_q［M］ and deduced the accurate counting formula of nonsingular matrices in F_q［M］ by using Euler-φ_q function. The results show that the method can not only accurately estimate the DSR of any specific instance of N HFSM, but also deduce the the lower limit of DSR of N HFSM scheme, which theoretically proves the feasibility of N HFMS. By using N HFSM scheme, the session key can be agreed, thus secure communication can be realized.