Mastering Cryptography: Sample Assignments and Expert Solutions

Are you struggling with your cryptography assignments? Worry not, for we are here to provide you with expert assistance at programminghomeworkhelp.com. Cryptography, the art of secure communication, often poses intricate challenges for students. If you find yourself grappling with concepts like encryption, decryption, and cryptographic protocols, you've come to the right place. Our team of seasoned cryptography experts is dedicated to helping you unravel the complexities of this fascinating field. In this post, we present a couple of master-level cryptography questions along with their comprehensive solutions, meticulously crafted by our experts. So, if you're thinking, "who can do my cryptography assignment," let's delve into these intriguing challenges.

Question 1: Consider the RSA encryption scheme with public key (n, e) = (3233, 17) and private key (n, d) = (3233, 413). You intercept a ciphertext c = 855. Decrypt the message using RSA.

Solution 1: RSA encryption relies on the difficulty of factoring large integers. To decrypt the ciphertext c using RSA, we utilize the private key (n, d) = (3233, 413) as follows:

We first compute the plaintext message m using the formula: $�={�}^{�}\mathrm{m}\mathrm{o}\mathrm{d}�$

Substituting the given values: $�=855^{413}\mathrm{m}\mathrm{o}\mathrm{d}3233$

Using modular exponentiation techniques: $�\equiv 855^{413}\mathrm{m}\mathrm{o}\mathrm{d}3233$ $�\equiv 1234\mathrm{m}\mathrm{o}\mathrm{d}3233$

Thus, the decrypted message is 1234.

Question 2: You're tasked with implementing the Diffie-Hellman key exchange protocol. Given the prime number $�=23$ and the primitive root $�=5$, Alice chooses her secret key $�=6$ while Bob chooses his secret key $�=15$. Calculate the shared secret key.

Solution 2: The Diffie-Hellman key exchange protocol allows two parties to establish a shared secret key over an insecure channel. To compute the shared secret key, we follow these steps:

1. Alice computes $�={�}^{�}\mathrm{m}\mathrm{o}\mathrm{d}�$ $�=5^6\mathrm{m}\mathrm{o}\mathrm{d}23$ $�\equiv 8\mathrm{m}\mathrm{o}\mathrm{d}23$

2. Bob computes $�={�}^{�}\mathrm{m}\mathrm{o}\mathrm{d}�$ $�=5^{15}\mathrm{m}\mathrm{o}\mathrm{d}23$ $�\equiv 19\mathrm{m}\mathrm{o}\mathrm{d}23$

3. Alice and Bob exchange their computed values $�$ and $�$.

4. Alice computes the shared secret key $�$ using ${�}^{�}\mathrm{m}\mathrm{o}\mathrm{d}�$ $�={�}^{�}\mathrm{m}\mathrm{o}\mathrm{d}�$ $�=19^6\mathrm{m}\mathrm{o}\mathrm{d}23$ $�\equiv 2\mathrm{m}\mathrm{o}\mathrm{d}23$

5. Similarly, Bob computes the shared secret key $�$ using ${�}^{�}\mathrm{m}\mathrm{o}\mathrm{d}�$ $�={�}^{�}\mathrm{m}\mathrm{o}\mathrm{d}�$ $�=8^{15}\mathrm{m}\mathrm{o}\mathrm{d}23$ $�\equiv 2\mathrm{m}\mathrm{o}\mathrm{d}23$

Hence, both Alice and Bob compute the same shared secret key $�=2$.

Conclusion

Mastering cryptography requires a deep understanding of mathematical concepts and cryptographic protocols. Through our expert guidance and sample assignments, we aim to enhance your proficiency in this field. Whether you're grappling with RSA encryption, Diffie-Hellman key exchange, or any other cryptographic algorithm, our team is here to assist you every step of the way. So, the next time you find yourself pondering, "do my cryptography assignment," remember programminghomeworkhelp.com is your trusted partner in conquering cryptographic challenges.