Research On Digital Signature Technology Based On RSA Public Key Algorithm

With the continuous development of the Internet and information society,the application fields and depth of network communication technology are expanding.This brings benefits to people and also brings challenges to information safety.In order to solve the safety problems in practical applications,many targeted technologies and solutions have emerged.As one of the important technologies,RSA public key algorithm can not only be applied in data encryption,but also used as a digital signature scheme.Digital signature based on RSA is a vital approach to defend against security issues such as denial,falsification,and counterfeiting in Internet transactions.How to improve the efficiency of RSA algorithm and ensure its safety,so that it can be better applied in digital signature,has always been a hot topic to be researched.This paper had taken the RSA algorithm as the research object,the mathematical theory foundations,safety and signature efficiency of the algorithm were studied in depth.In terms of safety,the attacks of RSA algorithm,such as factorization attack,chosen-message attack,and the means to defend against them were expounded.An improved scheme which uses parameter x to replace modulus n based on the traditional RSA algorithm was proposed.In addition,a scheme which uses multiple key e exponents in the algorithm was also suggested.The correctness of the improved schemes was proved,their advantages in enhancing the safety of RSA algorithm were analyzed.Considering the its efficiency,This paper had discussed relevant factors that restrict the efficiency and optimization means were introduced through further research on the existing SMM algorithm and Miller-Rabin algorithm.Digital signature based on RSA algorithm were also realized.Based on the analysis of proposed approaches,the scheme which uses four-prime and replaced parameter was combined with improved SMM algorithm and sliding window exponentiation algorithm to design a new safe and fast RSA algorithm.Finally,this paper had completed the implementation of combined RSA cryptosystem.The traditional RSA algorithm,improved SMM algorithm,multiple keys algorithm and combined algorithm were used for encryption anddecryption experiments and the consumed time of each algorithm were compared.The results show that the signature efficiency of the combined RSA algorithm is improved by 54.3% compared with the traditional RSA algorithm,which shows a better effect.Digital signature not only requires authentication,authenticity,but also the safety of information and efficiency of signature.The proposed algorithms in this paper can be applied to solving the shortcomings in digital signature based on RSA public key algorithm.