一种四元整数公钥密码体制

A Public-key Cryptography Using Integral Quaternions

RSA型公钥密码体制广泛应用在网络安全技术中 .它在数学方面的中心原理就是找到一个具有特殊性质的有限群 ,根据群内元素之间的运算规则得出密码中的加密算法和解密算法 .在目前的网络安全技术中 ,通常使用的是模n既约有理整数同余类群 ,在此 ,通过对四元数体、四元整数环、模n既约四元整数同余类群等数学概念及性质的研究 ,得出这样一个结论

The RSA public key oryptography is widely applied to internet security technology.Its core principal in mathmatics is to find a finite group with specific properties and conclude the methods of encryption and decryption according to the arithmetic rules between elements.At present,it is usually the congruences classes group of rational integer that is used in the internet security technology.In this paper,based on the analysis of quaternions,ring of integral quaternions and congruences classes group of integral quaternions,we draw the following conclusion:the congruences classes group of integral quaternions just has the speeific properties qualified for the RSA public key cryptography.