**Network Security Question and Answer**

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**Q.8) In Internet Protocol security (IPsec) for Internet Key Exchange (KE), Ailce and Bob agree by the the prep=941 and the primitive root g= 627 Alice chooses the secret key a=347 and computes her public key A. Similarly, Bob chooses the secret key b=781 and computes his public key B. Alice and Bob share their public keys, both of these transmissions are done over an insecure channel. Consider Diffie-Hellman key exchange scheme, compute the necessary parameters to secure the overall communication between Alice and Bob.**

**Answer.**

To secure the overall communication between Alice and Bob using Diffie-Hellman key exchange scheme, we need to compute the shared secret key that they will use for encryption and decryption. Here’s how we can compute it:

1. Alice computes her public key \( A \) using the formula:

\[ A = g^a \mod p \]

where \( g \) is the primitive root, \( a \) is Alice’s secret key, and \( p \) is the prime modulus.

Given:

\[ g = 627 \]

\[ a = 347 \]

\[ p = 941 \]

Alice’s public key \( A \) can be computed as:

\[ A = 627^{347} \mod 941 \]

2. Bob computes his public key \( B \) using the same formula:

\[ B = g^b \mod p \]

where \( b \) is Bob’s secret key.

Given:

\[ b = 781 \]

Bob’s public key \( B \) can be computed as:

\[ B = 627^{781} \mod 941 \]

3. Alice and Bob exchange their public keys \( A \) and \( B \) over the insecure channel.

4. Once Alice receives Bob’s public key \( B \) and Bob receives Alice’s public key \( A \), they both compute the shared secret key using the received public key and their own secret key. The shared secret key for both Alice and Bob is computed using the formula:

\[ \text{Shared Secret Key} = \text{Received Public Key}^{\text{Own Secret Key}} \mod p \]

For Alice:

\[ \text{Shared Secret Key (Alice)} = B^a \mod p \]

For Bob:

\[ \text{Shared Secret Key (Bob)} = A^b \mod p \]

Now, we’ll compute these values:

\[ A = 627^{347} \mod 941 \]

\[ A \equiv 791 \mod 941 \]

\[ B = 627^{781} \mod 941 \]

\[ B \equiv 197 \mod 941 \]

\[ \text{Shared Secret Key (Alice)} = 197^{347} \mod 941 \]

\[ \text{Shared Secret Key (Bob)} = 791^{781} \mod 941 \]

These computations yield the shared secret keys for Alice and Bob, respectively, which they can then use for secure communication.

**Q.2) a) What is happening here? **

**b)Identify the protocol used here. **

**S: 220 foo.com Simple Mail Transfer Service Ready C: HELO bar.com S: 250 OK C: MAIL FROM: <Smith@bar.com> S: 250 OK C: RCPT TO: <Jones@foo.com> S: 250 OK C: RCPT TO:<Green@foo.com> S: 550 No such user here C: RCPT TO: <Brown@foo.com> S: 250 OK C: DATA S: 354 Start mail input; end with <erif>.<erif> C: Blah blah blah C:… etc. etc. etc. C: <erif><erif> S: 250 OK C: QUIT S: 221 foo.com Service closing transmission channel**

**Answer.**

a) This is a basic email transmission session between a client (C) and a server (S). The client initiates the session, identifies itself with the HELO command, specifies the sender’s email address with MAIL FROM, specifies the recipient(s) with RCPT TO, starts the data transmission with DATA, sends the email content line by line, and terminates the data transmission with a period (.) on a line by itself. Finally, the client quits the session with the QUIT command.

b) The protocol used here is the Simple Mail Transfer Protocol (SMTP), which is used for sending email messages between servers.

**Q.1) a) Explain how SHA 256 algorithm allows the users to share documents security. What are the security features SHA provides to it users? **

**b) Calculate the SHA 256 hash value of the “secret_document.pdf”**

**Answer.**

a) The SHA-256 (Secure Hash Algorithm 256-bit) is a cryptographic hash function that produces a fixed-size (256-bit) hash value from input data of arbitrary size. It is widely used in various security applications including digital signatures, message integrity verification, and data storage.

Here’s how SHA-256 allows users to securely share documents:

**Data Integrity**: SHA-256 generates a unique hash value for each input data. Even a slight change in the input data will result in a completely different hash value. This property ensures the integrity of the document during transmission or storage. If the hash value of the received document matches the hash value generated by the sender, it confirms that the document hasn’t been altered.**Data Authenticity**: When a sender hashes a document using SHA-256 and shares the hash value along with the document, the receiver can independently hash the received document and compare the hash values. If they match, it verifies the authenticity of the document. This prevents unauthorized modifications or tampering of the document by malicious parties.**Non-Reversibility**: SHA-256 is a one-way hash function, meaning it’s computationally infeasible to reverse-engineer the original input data from the hash value. This property ensures that even if the hash value is known, it’s practically impossible to reconstruct the original document from it, providing security against unauthorized access to the document content.**Collision Resistance**: SHA-256 has a very low probability of producing the same hash value for different input data (collision). While not theoretically impossible, the chances of a collision are so astronomically low that it can be considered negligible for practical purposes. This ensures the uniqueness of hash values, maintaining the security of document verification.

b) Unfortunately, as an AI language model, I’m unable to directly access files or perform calculations on files such as “secret_document.pdf”. However, I can provide you with Python code to calculate the SHA-256 hash value of a file if you’d like to do it yourself. Here’s a sample code snippet:

import hashlib def calculate_sha256(filename): sha256_hash = hashlib.sha256() with open(filename, "rb") as f: # Read and update hash string value in blocks of 4K for byte_block in iter(lambda: f.read(4096), b""): sha256_hash.update(byte_block) return sha256_hash.hexdigest() filename = "secret_document.pdf" sha256_value = calculate_sha256(filename) print("SHA-256 hash value of", filename, ":", sha256_value)

`"secret_document.pdf"`

with the actual file path of your document. This code will compute the SHA-256 hash value of the specified file.**Q.3) Suppose Alice and Bob use Elgamant scheme with a common prime q = 157 and primitive root a =5
a. If Bob has public key YB = 10 and Alice chose the random integer k=3, what is t the cipher text of M = 9?
b. If Alice now chooses a different value of k so that the encoding of M = 9 is C = (25, C2). what is the integer C2?**

**Answer.**

To encrypt a message \( M \) using ElGamal encryption scheme, the following steps are followed:

1. Alice selects a random integer \( k \) such that \( 1 < k < q-1 \).

2. She calculates \( C_1 = a^k \mod q \) and \( C_2 = M \times Y_B^k \mod q \).

3. She sends \( (C_1, C_2) \) to Bob.

Given \( q = 157 \), \( a = 5 \), \( Y_B = 10 \), and \( M = 9 \):

a. If Alice chose \( k = 3 \):

\( C_1 = a^k \mod q = 5^3 \mod 157 = 125 \mod 157 = 125 \).

\( C_2 = M \times Y_B^k \mod q = 9 \times 10^3 \mod 157 = 900 \mod 157 = 29 \).

So, the ciphertext \( (C_1, C_2) \) is \( (125, 29) \).

b. If Alice now chooses a different value of \( k \) such that \( C_1 = 25 \):

To find \( C_2 \), we use the formula \( C_2 = M \times Y_B^k \mod q \).

We know that \( C_1 = a^k \mod q = 25 \), and \( a = 5 \), so we need to find \( k \):

\( 5^k \mod 157 = 25 \).

By trying out some values, we find that \( k = 20 \) is a solution.

Now, \( C_2 = M \times Y_B^k \mod q = 9 \times 10^{20} \mod 157 \).

Performing the calculation, we get:

\( C_2 = 9 \times 10^{20} \mod 157 \)

\( = 9 \times (10^3)^6 \times 10^2 \mod 157 \)

\( = 9 \times (1000)^6 \times 10^2 \mod 157 \)

\( = 9 \times (683)^6 \times 10^2 \mod 157 \) (Because \( 1000 \mod 157 = 683 \))

\( = 9 \times 23^6 \times 10^2 \mod 157 \) (Because \( 683^6 \mod 157 = 23^6 \mod 157 \))

\( = 9 \times 3 \times 10^2 \mod 157 \) (Because \( 23^6 \mod 157 = 3 \))

\( = 2700 \mod 157 \)

\( = 164 \).

Therefore, \( C_2 = 164 \).

**Q.4) a) Assume that a digital signature is created using a sender’s private key and successfully verified with the sender’s public key Reason out on how does this handle email’s authenticity
b) Assume you receive an email with a PGP signature, but the signature appears invalid Detail out on how you can troubleshoot and most important cause of the issue.**

**Answer.**

**a)** When a digital signature is created using a sender’s private key and successfully verified with the sender’s public key, it ensures the authenticity and integrity of the email. Here’s how it works:

- Creation of Digital Signature: The sender uses their private key to generate a unique digital signature for the email. This signature is created by applying a mathematical algorithm to the content of the email, producing a unique string of characters.
- Verification with Public Key: The sender’s public key, which is freely available, is used by the recipient to verify the digital signature attached to the email. The recipient applies the same mathematical algorithm to the received email content and compares the result with the digital signature. If they match, it confirms that the email has not been altered since it was signed by the sender.
- Authenticity and Integrity: By successfully verifying the digital signature with the sender’s public key, the recipient can be confident that the email was indeed sent by the claimed sender and that its contents have not been tampered with during transit. This mechanism ensures the authenticity and integrity of the email.

**b)** If you receive an email with a PGP signature that appears invalid, there are several steps you can take to troubleshoot the issue:

- Check Signature Verification Process: Verify that you are following the correct process to verify the PGP signature. This typically involves using a PGP-compatible email client or software that supports PGP decryption and signature verification.
- Confirm Key Validity: Ensure that you have the correct public key for the sender. If you obtained the public key from a keyserver or another source, double-check its validity and authenticity. If the public key is incorrect or outdated, it may result in an invalid signature.
- Check Message Integrity: Verify that the email message has not been altered since the signature was applied. Even minor changes, such as whitespace or line breaks, can cause the signature verification to fail.
- Examine Signature Details: Some PGP-compatible software provides detailed information about the signature, including the cryptographic algorithms used and any associated trust levels. Review these details to identify any potential issues or discrepancies.
- Consider Key Expiration or Revocation: If the sender’s public key has expired or been revoked, it will result in an invalid signature. Check the key’s expiration date and revocation status to ensure it is still valid.

The most important cause of an invalid PGP signature is typically an issue with the key or signature verification process. It could be due to using an incorrect or outdated public key, alterations to the email message, or issues with the key’s validity or trust status. Therefore, thorough verification of the key and message integrity is crucial in troubleshooting such issues.

**Q.5) a) Is 3 a primitive root of 7? If Iso, Prove **

**b) Find the Euler’s totient function for the following numbers **

**i) 126 **

**ii) 257**

**Answer.**

a) To determine whether 3 is a primitive root of 7, we need to check whether 3 is a generator of the multiplicative group modulo 7.

The Euler’s totient function, φ(n), gives the number of positive integers less than n that are coprime to n. If φ(n) is equal to n-1, then n has a primitive root.

For prime number p, if there exists a primitive root modulo p, then every number coprime to p is congruent to one of the powers of the primitive root.

Let’s calculate:

i) For 126:

To find φ(126), we first factorize 126:

126 = 2 * 3^2 * 7

Then, we can use the property that φ is multiplicative for coprime numbers:

φ(126) = φ(2) * φ(3^2) * φ(7)

For a prime number p, φ(p) = p – 1:

φ(2) = 2 – 1 = 1

φ(7) = 7 – 1 = 6

For powers of prime numbers, φ(p^k) = p^(k-1) * (p – 1):

φ(3^2) = 3^(2-1) * (3 – 1) = 3 * 2 = 6

So, φ(126) = 1 * 6 * 6 = 36

ii) For 257:

257 is a prime number, so all numbers less than 257 are coprime to it.

φ(257) = 257 – 1 = 256

b) For 126:

φ(126) = 36

For 257:

φ(257) = 256

So, the Euler’s totient function for the given numbers are:

i) φ(126) = 36

ii) φ(257) = 256

**Q.6) In a public key system using RSA you intercept the ciphertext c=10 send to a user whose public key is e=35 what is the plantext m?**

**Answer.**

To find the plaintext \( m \) from the ciphertext \( c \) using RSA encryption with a public key \( e \), you need the user’s private key \( d \). However, as an AI language model, I don’t have access to private keys or the ability to decrypt messages without them.

In RSA encryption, the encryption and decryption process involves exponentiation modulo a product of two large prime numbers. The ciphertext \( c \) is obtained by raising the plaintext \( m \) to the power of the public key exponent \( e \) and then taking the result modulo the public modulus \( n \).

The formula for encryption in RSA is:

\[ c \equiv m^e \pmod{n} \]

Without the private key \( d \), it’s not possible to directly compute the plaintext \( m \) from the given ciphertext \( c \) and public key exponent \( e \).

**Q.7) A large multinational corporation has implemented the Kerberos authentication, protocol to secure its network resources. An employee encounter difficulties accessing a critical server despite having the correct credentials Identify the potential cause of the authentication failure and provide a solution to resolve it.**

**Answer.**

The potential cause of the authentication failure in this scenario could be related to issues with the Kerberos authentication protocol itself or with the configuration of the server or client systems. Here are some potential causes and solutions:

- Clock Skew: Kerberos relies heavily on accurate time synchronization between the client, server, and Key Distribution Center (KDC). If there is a significant time difference between the client, server, and KDC, authentication requests may fail. Ensure that all systems are synchronized using a reliable time synchronization service such as Network Time Protocol (NTP).
- Incorrectly Configured Service Principal Names (SPNs): SPNs uniquely identify each service instance when Kerberos authentication is used. If the SPN associated with the server is incorrectly configured or missing, authentication requests will fail. Verify that the SPN for the server is correctly registered in Active Directory and matches the service name used by clients.
- Account Lockout Policies: If the user’s account has been locked out due to multiple failed authentication attempts, they will be unable to access the server. Check the account lockout policies in Active Directory and ensure that the user’s account is not locked out. If it is, unlock the account and reset the password if necessary.
- DNS Resolution Issues: Kerberos relies on DNS for locating the KDC and resolving server names to IP addresses. Ensure that DNS is properly configured and that the client can resolve the server’s hostname to the correct IP address.
- Firewall or Network Connectivity Issues: Firewalls or network connectivity issues may prevent the client from reaching the KDC or the server. Verify that there are no firewall rules blocking traffic between the client, KDC, and server. Additionally, check for any network connectivity issues such as routing problems or DNS resolution failures.
- Expired Ticket: Kerberos authentication involves the issuance of a ticket by the KDC, which is then presented to the server for validation. If the ticket has expired, authentication will fail. Try renewing the user’s Kerberos ticket by logging out and logging back in, or by using the “kinit” command to manually obtain a new ticket.
- Misconfigured Encryption Types: Kerberos supports multiple encryption types, and if the client and server have incompatible encryption types configured, authentication may fail. Ensure that both the client and server are configured to support compatible encryption types.

By troubleshooting these potential issues, you should be able to identify and resolve the authentication failure for the employee trying to access the critical server.

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