RSA encryption Mathematics & Economics Math Problem

RSA Encryption: An In-depth Review
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Introduction
RSA is an encryption algorithm that facilitates communication in situations where an opportunity for distributing keys safely has not been available. It is an asymmetric cryptography algorithm that works on two keys; Public Key and Private Key. The algorithm was invented in 1977 and is named after the inventors: Ron Rivest, Adi Shamir, and Len Adleman. Clifford Cocks discovered the basic technique in 1973, but this remained a secret until 1997. The age of the internet saw RSA gain widespread adoption as an essential security tool. Today, the RSA cryptosystem is the most popular public-key cryptography algorithm available.
RSA encryption may be implemented in different systems such as wolfCrypt, OpenSSL, cryptlib among other cryptographic libraries. It was the original algorithm used in PGP encryption and TLS. Today, the system is seen in a broad range of VPNs, web browsers, chat, email, and other communication channels. It can be used for both digital signatures and public-key encryption.
Body
RSA encryption systems are often combined with other encryption schemes or for digital signatures. The security of this system is formed based on the difficulty in factoring large integers. A message is encrypted with a code known as a public key, which may be shared openly. The unique mathematical properties of this encryption system allow messages encrypted with the public key to only be encrypted with the private key. The private key must not be shared and only an entity with access to the RSA private key can decrypt the symmetric key (Mahajan, P., & Sachdeva, A. 2013). The scheme helps in keeping files and messages secure without the need for many computation resources.
How the system works
In the RSA encryption scheme, trapdoor functions work under the premise that the algorithm can be easily computed in one direction, but is nearly impossible in reverse. For instance, if 701,111 is said to be a product of two prime numbers, figuring out what these numbers are, may not be an easy thing to do. However, the problem would be easy to solve when one of the prime numbers and the resulting product are provided:
For example 773 X ? = 701,111
The example above proves that certain equations can be solved easily in one way but are almost impossible in the other way. It is worth noting that in real RSA applications, large numbers with varying sizes are used. These keys can either be 2048 or 1024 bits long.
The first step in RSA encryption is generating keys. This requires prime numbers such as p and q. These numbers need to be large and relatively far apart, making them hard to crack. Discovering the modulus (n) is the second stage.
Here is the formula used:
n = p x q
Where p is 673 and q is 919
n = 673 x 919
n = 618,487
Generating public keys
Under this system, public keys include a prime number e and n. The number denoted as e may be anything between 1 and the value of n (Goshwe, N. Y. 2013). Since the public key is shared openly, it does not need to be selected randomly. It is generally set as 65,537. We can take e to be 13.
e = 13
Ciphertext denoted as (c) is the final encrypted data i...