CS 7081 Fall 2017 Advanced Algorithms Assignment 1 due September 8th 2017.
Assignment intstructions follow:
Algorithm topics covered: Applying efficient algorithm for computing powers (slightly revised to perform modular exponentiation), changing bases, Euclid GCD and Extended Euclid GCD, prime testing using Miller-Rabin probabilistic algorithm. Write a C++ program that involves implementing the RSA cryptosystem. In practice for the encryption to be secure and to handle larger messages you would need to utilize a class for large integers. However, for this assignment you can use built-in types to store integers, e.g., unsigned long int. Also, rather than using the ASCII table for this assignment use BEARCATII, which restricts the characters to the blank character and the upper case letters of the alphabet as follows: blank character is assigned the value 0. A, …, Z are assigned the values 1, …, 26, respectively. The message M will be represented by replacing each character in the message with its assigned integer base 27. For example, the message M = “TEST” will be represented as
N = 20 5 19 20 Translating this to decimal we obtain: D = 20 + 1927 + 5272 + 20*273 = 397838 Note that to convert back to base 27, we simply apply the algorithm we discussed in class, i.e., the least significant digit (rightmost) is obtained by performing the operations D mod 27 and performing a recursive call with D/27. For the example above we obtain, 397838 / 27 397838 mod 27 = 14734 20 → 14734 / 27 14734 mod 27 20 = 545 19 20 → 545/27 545 mod 20 19 20 = 20 5 19 20 Find primes p and q by choosing positive integers at random and testing for primality using Miller-Rabin probabilistic algorithm. Your program should prompt the user to input a positive integer representing the public key e. If the user enters a number that is not relatively prime to n = pq, then have the user reenter and keep doing this until e and n are coprime, i.e., gcd(e,φ(n)) = 1. Also prompt the user to enter the message M (as a character string). For handing purposes in run your program with M = “TEST”. Output p, q, n, M, C, P where C is the encrypted message, i.e., cyber text, and P is the decrypted message, i.e., plaintext. If your program is working correctly then M should be equal to P.