Alice and Bob are two friends and want to talk to each other privately. Oscar is a bad guy who wants to hear

what they say. Keeping their communication private is the job of cryptography systems. One of the oldest

but widely used systems is RSA invented by Rivest, Shamir, and Adleman in $1977.$ The RSA system is based

on the assumption that it is easy to multiply two large prime numbers but difficult to factor out the resulting

large composite number. The RSA system is still being widely used by modern computers to encrypt and

decrypt messages, for example, in electronic commerce protocols. The RSA system is believed to be secure

if sufficiently large prime numbers are used. This system has three main steps: