一种基于圆锥曲线的RSA密码体制改进方案

An RSA cryptosystem improvement plan based on conic curve

利用D⁃H密钥交换体制的特点,文中提出一种基于圆锥曲线的RSA密码体制改进方案。该体制在已有研究的基础上进一步改进,主要有两方面创新之处:一方面是对于通信双发的会话密钥处理,采取的措施是通过D⁃H密钥交换体制来直接交换通信双方的会话密钥,这样不仅可以达到通信双方共享会话密钥的要求,同时也可以减少计算量来提高算法的效率;另一方面是在求解私钥的问题上,不是直接利用圆锥曲线上基点的阶作为模数,而是利用圆锥曲线上基点的阶和共享会话密钥的乘积来作为其模数,进而对明文进行加密,这样不仅可以将通信双方的会话密钥和圆锥曲线上基点的阶紧密结合起来,也能增加破译者破解密文的难度。基于文中的改进方案,即使破译者知道会话密钥也无法一步到位地得到求解私钥的模数。最后通过实例证明了改进方案的可行性,并通过算法分析了改进方案的性能。

Based on the characteristics of D⁃H(diffie⁃hellman)key exchange system,an RSA(rivest⁃shamir⁃adleman)cryptosystem improvement plan based on conic curve is proposed.The system is further improved on the basis of existing research,and there are two main innovations.The one is the session key processing of communication double transmission,the D⁃H key exchange system is adopted to directly exchange the session keys between two communication parties,which can not only meet the requirements of sharing session key between two communication parties,but also reduce the amount of calculation to improve the efficiency of the algorithm.The other is the problem of solving the private key,the product of the order of the base point on the conical curve and the shared session key are used as the modulus instead of directly using the order of the base point on the conical curve as the modulus,and then the plaintext is encrypted,which can not only closely combine the session key of both communication parties with the order of the base point on the conical curve,but also make it more difficult for the decipherer to crack the ciphertext.Based on the improved scheme in this paper,even if interpreter knows the session key,he cannot get the modulus of solving the private key in one step.The feasibility of the improved scheme is proved by an example,and the performance of the improved scheme is analyzed by means of the algorithm.