Submit a single C++ source code file that generates an RSA public key and a private key pair given two positive prime numbers on the command line. The program consists of three files described below. Download each of these files from the Assignment #3 page in Canvas:

• program3-driver.cpp - This file contains a completed main() function and other functions that test the key generation and the encryption and decryption keys. Make no changes to this file.
• RSA_Keys.h - This file contains the function prototype for the generateKeys() function. Make no changes to this file.
• student3.cpp - This is the file where you will put your source code additions.
• Make sure that the three downloaded source code files will compile, link, and run with no errors by entering the following at the command shell prompt:
  • % g++ program3-driver.cpp Name3.cpp % a.exe
  A program usage message should appear on the screen, and the program should exit.
• Finish the implementation of the generateKeys() function, whose prototype is shown below and whose stubbed-out function definition is in the Name3.cpp file. This function is called from the main() function in the program3-driver.cpp file.
  • void generateKeys(int primeA, int primeB, int &encryptionExponent, int &decryptionExponent)

  In doing the implementation of the generateKeys() function, you may also want to implement these three private (i.e., static) helper functions:

  • int relativelyPrime(int number) Purpose: Computes a value Y that is relatively prime to X Called by: generateKeys() function

    int gcd(int numberV, int numberW) Purpose: Computes the greatest common divisor of V and W Called by: relativelyPrime() function

    int inverse(int numberX, int modulusN) Purpose: Computes the multiplicative inverse of x mod N Called by: generateKeys() function

  Note that your implementation of these functions should not prompt the user for any information nor should they directly produce any screen output. In addition, your implementation should not use the value 1 as a relatively prime number. In other words, it should start with the value 2 as the first possible value to check.

• When you run the program, be sure to check the test case results displayed on the screen to help you in testing your key generation code. The sample-run.txt file shows sample command line input and program output.

• Large Numbers and a Finite Implementation

• To generate an RSA public and private key pair, we need to choose two "large" prime numbers for p and q. Because the RSA algorithm produces very large numbers from a very small input, we only have a limited set of values for p and q that we can use for testing. The numbers 3 and 11 fit into that window; therefore, you can safely use them as a test case for your software.

  This limited set of input values can be somewhat overcome. This is done by implementing a repeated squaring algorithm for calculating the powers of numbers modulo N. However, we are not implementing that algorithm in this assignment.

  As a side note, in a language such as Haskell, the range of values for positive integers is not limited by what the computer can store; consequently, a person can use large values for p and q.

• Implementation Constraints

• Follow the same coding standards given in previous assignments
• Make sure that the three downloaded source code files will compile, link, and run with no errors by entering the following at the command shell prompt:
  • % g++ program3-driver.cpp Name3.cpp % a.exe
  A program usage message should appear on the screen, and the program should exit.
• Finish the implementation of the generateKeys() function, whose prototype is shown below and whose stubbed-out function definition is in the Name3.cpp file. This function is called from the main() function in the program3-driver.cpp file.
  • void generateKeys(int primeA, int primeB, int &encryptionExponent, int &decryptionExponent)

  In doing the implementation of the generateKeys() function, you may also want to implement these three private (i.e., static) helper functions:

  • int relativelyPrime(int number) Purpose: Computes a value Y that is relatively prime to X Called by: generateKeys() function

    int gcd(int numberV, int numberW) Purpose: Computes the greatest common divisor of V and W Called by: relativelyPrime() function

    int inverse(int numberX, int modulusN) Purpose: Computes the multiplicative inverse of x mod N Called by: generateKeys() function

  Note that your implementation of these functions should not prompt the user for any information nor should they directly produce any screen output. In addition, your implementation should not use the value 1 as a relatively prime number. In other words, it should start with the value 2 as the first possible value to check.

• When you run the program, be sure to check the test case results displayed on the screen to help you in testing your key generation code. The sample-run.txt file shows sample command line input and program output.

• Large Numbers and a Finite Implementation

• To generate an RSA public and private key pair, we need to choose two "large" prime numbers for p and q. Because the RSA algorithm produces very large numbers from a very small input, we only have a limited set of values for p and q that we can use for testing. The numbers 3 and 11 fit into that window; therefore, you can safely use them as a test case for your software.

  This limited set of input values can be somewhat overcome. This is done by implementing a repeated squaring algorithm for calculating the powers of numbers modulo N. However, we are not implementing that algorithm in this assignment.

  As a side note, in a language such as Haskell, the range of values for positive integers is not limited by what the computer can store; consequently, a person can use large values for p and q.

• Implementation Constraints

1. h the implementation of the generateKeys() function, whose prototype is shown below and whose stubbed-out function definition is in the Name3.cpp file. This function is called from the main() function in the program3-driver.cpp file.
   • void generateKeys(int primeA, int primeB, int &encryptionExponent, int &decryptionExponent)

   In doing the implementation of the generateKeys() function, you may also want to implement these three private (i.e., static) helper functions:

   • int relativelyPrime(int number) Purpose: Computes a value Y that is relatively prime to X Called by: generateKeys() function

     int gcd(int numberV, int numberW) Purpose: Computes the greatest common divisor of V and W Called by: relativelyPrime() function

     int inverse(int numberX, int modulusN) Purpose: Computes the multiplicative inverse of x mod N Called by: generateKeys() function

   Note that your implementation of these functions should not prompt the user for any information nor should they directly produce any screen output. In addition, your implementation should not use the value 1 as a relatively prime number. In other words, it should start with the value 2 as the first possible value to check.

2. When you run the program, be sure to check the test case results displayed on the screen to help you in testing your key generation code. The sample-run.txt file shows sample command line input and program output.

Large Numbers and a Finite Implementation

• To generate an RSA public and private key pair, we need to choose two "large" prime numbers for p and q. Because the RSA algorithm produces very large numbers from a very small input, we only have a limited set of values for p and q that we can use for testing. The numbers 3 and 11 fit into that window; therefore, you can safely use them as a test case for your software.

  This limited set of input values can be somewhat overcome. This is done by implementing a repeated squaring algorithm for calculating the powers of numbers modulo N. However, we are not implementing that algorithm in this assignment.

  As a side note, in a language such as Haskell, the range of values for positive integers is not limited by what the computer can store; consequently, a person can use large values for p and q.

#include #include "RSA_Keys.h"

using namespace std;

// ################################################################## void generateKeys(int primeA, int primeB, int &encryptionExponent, int &decryptionExponent) {

encryptionExponent = 1; decryptionExponent = 1;

} // End generateKeys

Student3.cpp

include #include "RSA_Keys.h"

using namespace std;

// ################################################################## void generateKeys(int primeA, int primeB, int &encryptionExponent, int &decryptionExponent) {

encryptionExponent = 1; decryptionExponent = 1;

} // End generateKeys