b=b×1=b(ra+sp)=r(ab)+psb=r(pc)+psb=p(rc+sb).
This is the required factorization ofb that features the prime p as a factor.In conclusion, the number theory underlying RSA enciphering makes the system sound, although various protocols that have not been explained here must be respected in order to safeguard the integrity of the system. There are issues ofauthentification(what if Eve contacts Alice pretending to be Bob?), non-repudiation(what if Bob pretends that it was Eve who sent his message to Alice?), and identityfraud(what ifAlice abuses confidential identification sent to her by Bob and tries to impersonate him online?). Moreover, other weaknesses in the system can be exposed when predictable or repeated messages proliferate.However, these difficulties may potentially arise in any public key cryptosystem. They can be overcome and in the main are unrelated to the underlying mathematical techniques that ensure high quality and robust encyryption.