Welcome to ProgrammingHomeworkHelp.com, your trusted resource for mastering cryptography. In today's digital landscape, cryptography serves as the cornerstone of secure communication and data protection. Whether you're a student navigating through cryptographic algorithms or a professional aiming to strengthen your expertise, our platform offers unparalleled assistance. From fundamental concepts to advanced encryption techniques, our experts are dedicated to guiding you every step of the way. In this post, we'll delve into a master-level cryptography question implemented through code, exemplifying the depth of support available through our online cryptography assignment help service.

Question:

Implement the RSA encryption and decryption algorithm in Python. Your program should generate public and private keys, encrypt a given message, and decrypt the ciphertext to retrieve the original message. Ensure your implementation adheres to the RSA algorithm's principles and handles prime number generation securely.

Solution:

import random
from sympy import isprime

def gcd(a, b):
    while b != 0:
        a, b = b, a % b
    return a

def extended_gcd(a, b):
    if a == 0:
        return b, 0, 1
    else:
        g, y, x = extended_gcd(b % a, a)
        return g, x - (b // a) * y, y

def mod_inv(a, m):
    g, x, y = extended_gcd(a, m)
    if g != 1:
        raise Exception('Modular inverse does not exist')
    else:
        return x % m

def generate_prime(bits):
    while True:
        p = random.getrandbits(bits)
        if isprime(p):
            return p

def generate_keys():
    # Generate two distinct prime numbers
    p = generate_prime(128)
    q = generate_prime(128)
    n = p * q
    phi = (p - 1) * (q - 1)

    # Choose a public exponent e
    e = 65537

    # Ensure e and phi(n) are coprime
    while gcd(e, phi) != 1:
        e += 2

    # Compute the private exponent d
    d = mod_inv(e, phi)

    # Return public and private keys
    return (n, e), (n, d)

def encrypt(message, public_key):
    n, e = public_key
    return pow(message, e, n)

def decrypt(ciphertext, private_key):
    n, d = private_key
    return pow(ciphertext, d, n)

# Example usage
message = 123456789
public_key, private_key = generate_keys()
print("Public Key:", public_key)
print("Private Key:", private_key)

encrypted_message = encrypt(message, public_key)
print("Encrypted Message:", encrypted_message)

decrypted_message = decrypt(encrypted_message, private_key)
print("Decrypted Message:", decrypted_message)

Conclusion

In this post, we've provided a Python implementation of the RSA encryption and decryption algorithm. By generating secure prime numbers, computing public and private keys, and performing encryption and decryption operations, our solution demonstrates the practical application of cryptography principles. Whether you're exploring RSA for academic purposes or practical encryption needs, understanding its implementation is essential. If you require further assistance with cryptography assignments or wish to deepen your knowledge, our platform offers expert guidance and support. With our online cryptography assignment help, mastering cryptography becomes an achievable goal. Stay tuned for more coding examples and insights to enhance your cryptographic skills.