Study On RSA Modular Prime Number Theorem And Random Packed Probability Digital Signature

The RSA is a kind of public key algorithm, its encrypting key and algorithm all can decrypt an decipher to then return customer publicly private own.From is born from that day, RSA because the safe strength is high and uses convenience etc. the outstanding function is subjected to concern, and get extensively applied.Currently, in many password systems all the inlay the RSA password the calculate way.But, the plain RSA algorithm safety differs, contrary, as long as the larg hard-core conjecture for RSA establishes, the so random packed RSA algorithm will acquire a very high safety under the current technique condition.This text aims at the safety of RSA modular, making use of the prime number theorem of arithmetic progression to carry on a classification to the big prime number, analyze the influence of the prime number upon the RSA modular safety and function of categorizing the empress, and safety of the RSA modular used for turning to fill random probability digital signature, experiment result the certificate turns to fill random of RSA probability digital signature is safe.This thesis finished main work is as follows:The RSA algorithm's relevant foundation is theoretical of the study and the research.This text studies and studies the relevant property of RSA modular and Blum number, and analyzed these influence of the property upon the RSA algorithm safety;Put forward a kind of certificate method of the prime number theorem of arithmetic progression, and introduce a kind of combine I am false to count born calculate way to produce big prime number random of calculate way. Give RSA of the random packed probability digital signature and formal certificate.The RSA function is one-way function, promising RSA public-key cryptosystem the safety thus.This text gives RSA all the formal certificate of the probability digital signature.Designed a kind of RSA random packed probability digital signature of concrete carry out a method.It verified the RSA algorithm parameter selection in the textual experiment process, include how to produce big prime number and structure RSA algorithm parameter;Carry out concrete of the digital signature produced, include to touch of power operation, and the verification process of digital signature, the RSA which includes to turn to fill random all probability digital signature algorithm and it concretely carries out.