Improved Analysis And Research Of Multi-prime RSA Algorithm

Nowadays,human society has entered an era of rapid development.The development of computer technology and the expansion of network scale have made our lives more and more convenient.The intertwined network of large user groups will produce an exponential amount of information.At the same time,ensuring the security of information has become a primary issue.Research on the generation,transmission,and reception of information is very important to prevent hacker attacks.Therefore,cryptography is specially established to ensure the security of information during transmission.The RSA algorithm is widely used as a representative of the asymmetric cryptographic algorithm.Not only does the asymmetric performance of the algorithm key ensure the security of information,but also it can be jointly guaranteed by digital signature and identity verification.Although the RSA algorithm provides better security,there are still certain flaws.First,the modulus n will be subjected to a factorized brute force attack,thereby deciphering the key and disrupting security.In addition,the algorithm decryption calculation speed is very slow,which seriously delays work efficiency.Therefore,in response to these two issues,this paper proposes an improvement strategy for the RSA algorithm,that is,a dual enhanced RSA algorithm,which separately guarantees security and improves the speed of calculation.The work and innovation of this paper are as follows:First of all,based on the current research status of the multi-prime RSA algorithm,a dual enhanced RSA algorithm is proposed,which is gradually improved in three stages.Finally,the correctness of the algorithm is mathematically proved,and the algorithm is decrypted for three simulation comparison experiments.(1)In the algorithm key generation stage,the characteristics of this stage are analyzed,that is,the generated private key is kept secret,and the public key is made public,resulting in a violent attack on the modulus n.Therefore,a hidden key solution is proposed to avoid direct attacks.In addition,a secret key is generated for encryption stage improvement.(2)In the algorithm encryption stage,the public key is used to encrypt the plaintextinformation.Since the modulus n is easy to be attacked,in order to improve security,a secret key and a public key are jointly encrypted.Even if the modulus n is cracked,there are still secrets The key can guarantee security.(3)In the algorithm decryption stage,because the decryption process involves a large integer exponentiation operation,the amount of calculation is very huge.On the basis of multiple prime numbers,three methods of calculation of the solution are proposed,which are the phases of Euler's theorem and modular repeated square algorithm In combination,Euler's theorem is combined with Chinese residual theorem,and Chinese residual theorem is combined with Fermat's theorem.The final result shows that the double enhanced RSA algorithm can accurately restore the ciphertext message to plaintext,and the hidden key and secret key increase the difficulty of cracking and improve the security.In addition,from three simulation comparison experiments,we can see that after using the resolution method The average decryption time of the optimized four prime RSA algorithm is somewhat shorter than that of the ordinary four prime RSA algorithm.