Asymmetric Cryptography and Key Management Quiz Answers

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Asymmetric Cryptography and Key Management Week 01 Quiz Answers

Quiz 1: Asymmetric Cryptography Overview

Q1. Given any plaintext p, a cipher supporting asymmetric cryptography with an encryption function (Enc) and the corresponding decryption function (Dec), and the public-private key pair (Ki,ki) for any user i, which of the following are true for a cipher that can be used for both message confidentiality and source integrity/signature, e.g., RSA cipher? Select all that apply.

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1.Dec(K2,Enc(k2,p))=p
2.Dec(k1,Enc(K1,p))=p
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Q2. Which of the following are true about asymmetric cryptography? Check all that apply.

[expand title=View Answer]
1.Key distribution and management should be addressed when using asymmetric cryptography.
2.Asymmetric cryptography supersedes and generalizes symmetric cryptography.
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Q3. Which of the following are false for asymmetric cipher requirements? Select all that apply.

[expand title=View Answer]
1.Both the public key and the private key should remain secret against an attacker.
2.Both the sender and the receiver can use the same private key for encryption and decryption.
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Q4. Suppose f is a trapdoor one-way function designed to be used with the key, k. Which of the following are computationally easy?

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Solving f(x) if the input and k are known

Solving the inverse of f if the input to the f-inverse and k are known

Solving the inverse of f if the input to the f-inverse is known

Finding k if the input and the corresponding output of f are known
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Q5. Which of the following does the RSA algorithm support? Select all that apply.

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Key exchange

Digital signature

Encryption/decryption
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Q6. Which of the following does Diffie-Hellman Key Exchange support: encryption/decryption, digital signatures, key exchange? Select all that apply.

[expand title=View Answer]
Key exchange

Encryption/decryption
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Asymmetric Cryptography and Key Management Week 02 Quiz Answers

Quiz 1: RSA Operations Quiz Answers

Q1. What is the Euler Totient Function of 12, phi(12)?

[expand title=View Answer] 4 [/expand]

Q2. Using the same notations as in the lecture, e.g., p and q are the two primes and e and d are the public key and the private key, respectively, p=5, q=11, e=3. What is the value of phi(n) where phi(n) is the Euler Totient function of n and n is the modulus for RSA cipher?

[expand title=View Answer]40 [/expand]

Q3. (This question builds on the previous question.) Using the same notations as in the lecture, e.g., p and q are the two primes and e and d are the public key and the private key, respectively, p=5, q=11, e=3. Using the phi(n) that you found in the previous question and the Extended Euclidean algorithm yields d=27. What is the ciphertext C when encrypting M=9?

[expand title=View Answer] 14[/expand]

Q4. Using the same notations as in the lecture, e.g., p and q are the two primes and e and d are the public key and the private key, respectively, p=7, q=11, e=17. What is the value of phi(n) where phi(n) is the Euler Totient function of n and n is the modulus for RSA cipher?

[expand title=View Answer] 60 [/expand]

Q5. (This question builds on the previous question.) Using the same notations as in the lecture, e.g., p and q are the two primes and e and d are the public key and the private key, respectively, p=7, q=11, e=17. Using the phi(n) that you found in the previous question and the Extended Euclidean algorithm yields d=53. What is the ciphertext C when encrypting M=8?

[expand title=View Answer] 57 [/expand]

Quiz 2: RSA Algorithm Quiz Answers

Q1. Using the same notations as in the lecture, p and q are the two prime factors of n, and e and d are the public key and the private key, respectively. Which of the followings are to be secret against the attacker, assuming that the Prime Factorization problem remains difficult to solve?

[expand title=View Answer]
1.The Euler totient function of n, phi(n)
2.p
3.d
4.q
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Q2. Using the same notations as in the lecture, p and q are the two prime factors of n, and e and d are the public key and the private key, respectively.

Which of the following statements about the RSA cipher are true? Select all that applies.

[expand title=View Answer]
1.After choosing e, the Extended Euclidean algorithm can be used to derive d.
2.e and d are independent from p and q.
3.For the public-private keys of RSA, e and d, given any plaintext m, m raised to the power of e.d (m^{e.d}) is equal to m.
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Q3. Using the same notations as in the lecture, e.g., p and q are the two primes and e and d are the public key and the private key, respectively, p=5, q=11. Alice chooses a private key d and derives the public key e. Which of the followings can work for the values of d?

[expand title=View Answer]
1.17
2.21
3.9
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Q4. Using the same notations as in the lecture, e.g., p and q are the two primes and e and d are the public key and the private key, respectively, p=3, q=11, and e=7.

The attacker performs a chosen-ciphertext attack (CCA). It has a known ciphertext 14 and wants to retrieve the corresponding plaintext. It computes c’ = c * r^e mod n and chooses the ciphertext 14 * 2187 mod 33 = 27 and retrieves the corresponding plaintext, 15. What is the plaintext corresponding to the ciphertext 14?

[expand title=View Answer] 5 [/expand]

Asymmetric Cryptography and Key Management Week 03 Quiz Answers

Quiz 1: Discrete Logarithm and Primitive Root

Q1. What is the value of the discrete logarithm of 3 base 2 mod 5?

[expand title=View Answer] 3 [/expand]

Q2. What is the value of the discrete logarithm of 4 base 5 mod 7?

[expand title=View Answer] 2 [/expand]

Q3. Identify the primitive roots of the prime number 3. Select all that applies.

[expand title=View Answer] 2 [/expand]

Q4. Identify the primitive roots of the prime number 7. Select all that applies.

[expand title=View Answer]
1.3
2.5
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Q5. Which of the following statements are true?

[expand title=View Answer]
1.Using the primitive roots of a prime modulus p yields the maximum p-1 possible outcome values for the discrete logarithm, which is desired for cryptography.
2.Given a large modulus n, the discrete logarithm problem is computationally difficult.
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Quiz 2: Diffie-Hellman Key Exchange and El Gamal Encryption

Q1. Alice and Bob exchange a key using the Diffie-Hellman Key Exchange protocol. Which of the following do Alice know by the end of the protocol? Select all that apply.

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Bob’s public key (Y_B)

The prime modulus (p)

The primitive root of the prime modulus (a)

The shared key by the protocol (K)
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Q2. Alice and Bob exchange a key using the Diffie-Hellman Key Exchange protocol. Which of the following are to be secret against a passive attacker (who wishes to learn the shared key)? Select all that apply.

[expand title=View Answer]
1.The shared key by the protocol (K)
2.Bob’s private key (Y_B)
[/expand]

Q3. Alice and Bob use Diffie-Hellman Key Exchange to share a key with a common prime p=11 and a primitive root a=2. If Alice has a public key Y_A=9, what is her private key X_A?

[expand title=View Answer] 6 [/expand]

Q4. (This question builds on the previous question.) Alice and Bob use Diffie-Hellman Key Exchange to share a key with a common prime p=11 and a primitive root a=2. If Bob has a public key Y_B=3, what is the secret key K shared with Alice?

[expand title=View Answer] 3 [/expand]

Q5. Which of the following are true for the Diffie-Hellman Key Exchange and Man-in-the-middle (MITM) attack? Select all that apply.

[expand title=View Answer] Diffie-Hellman Key Exchange protocol is vulnerable to MITM attack because of the lack of authentication. [/expand]

Q6. Which of the following is true about El Gamal Encryption?

[expand title=View Answer]
1.El Gamal Encryption includes the message and the key that is used to protect the message, and the key itself is protected against eavesdropping.
2.El Gamal Encryption uses a prime modulus and a primitive root of the modulus.
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Asymmetric Cryptography and Key Management Week 04 Quiz Answers

Quiz 1: Key Distribution and Management

Q1. Alice and Bob want to communicate with each other. They first use the Diffie-Hellman Key Exchange protocol to establish a session key and then use the session key to encrypt the messages from Alice to Bob. An attacker eavesdrops on the resulting ciphertext and conducts a brute-force attack on the encryption. Suppose the attacker succeeds in her brute-force search. Which of the following remain secure (secret against the attacker)? Select all that apply.

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1.Bob’s private key
2.Bob’s public key
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Q2. Which of the following is the most temporary by design?

[expand title=View Answer] Nonce [/expand]

Q3. What are the purposes of a nonce in key distribution? Select all that apply.

[expand title=View Answer]To connect the response to the corresponding communication[/expand]

Q4. There are 5 computers (hardware. Each computer hosts 4 virtual machines (VM) with different addresses, and each VM hosts 10 applications. How many key exchange sessions (in one session, two logical parties share a key) are needed if the decentralized key distribution is used so that all VMs share a pair-wise key?

[expand title=View Answer] 190 [/expand]

Q5. (This problem has the same setup as the previous question but asks a different question.) There are 5 computers (hardware. Each computer hosts 4 virtual machines (VM) with different addresses, and each VM hosts 10 applications. How many key exchange sessions (in one session, two logical parties share a key) are needed if the decentralized key distribution is used so that all applications share a pair-wise key?

[expand title=View Answer] 19900 [/expand]

Q6. Which of the following are needed for a CA to generate a digital certificate?

[expand title=View Answer]
1.The public key of the user (the certificate subject)
2.The request for the user’s certificate
3.The private key of CA
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Q7. Which of the following are required to verify the signature of the digital certificate signed by a CA?

[expand title=View Answer]
1.The certificate itself
2.The public key of CA
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Q8. Which of the following statements are true? Select all that apply.

[expand title=View Answer]
1.Once the digital certificates signed by a Certificate Authority (CA), a user can share it with anybody whom it wants to communicate.
2.Digital certificates can be requested before using it to share the public key.
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Q9. Which of the following are the PKI’s responsibilities? Select all that apply.

[expand title=View Answer]
Manage certificates

Store certificates

Create certificates

Revoke certificates

Distribute certificates
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