# Asymmetric Cryptography and Key Management Quiz Answers

## Get All Week Asymmetric Cryptography and Key Management Quiz Answers

### 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

Q2. Which of the following are true about asymmetric cryptography? Check all that apply.

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1.Key distribution and management should be addressed when using asymmetric cryptography.
2.Asymmetric cryptography supersedes and generalizes symmetric cryptography.

Q3. Which of the following are false for asymmetric cipher requirements? Select all that apply.

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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.

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

Q5. Which of the following does the RSA algorithm support? Select all that apply.

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Key exchange

Digital signature

Encryption/decryption

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

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Key exchange

Encryption/decryption

### 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)?

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4

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?

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40

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?

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14

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?

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60

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?

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57

#### 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?

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1.The Euler totient function of n, phi(n)
2.p
3.d
4.q

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.

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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.

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?

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1.17
2.21
3.9

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?

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5

### 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?

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3

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

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2

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

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2

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

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1.3
2.5

Q5. Which of the following statements are true?

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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.

#### 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)

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.

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1.The shared key by the protocol (K)
2.Bob’s private key (Y_B)

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?

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6

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?

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3

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

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Diffie-Hellman Key Exchange protocol is vulnerable to MITM attack because of the lack of authentication.

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

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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.

### 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

Q2. Which of the following is the most temporary by design?

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Nonce

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

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To connect the response to the corresponding communication

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?

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190

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?

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19900

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

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1.The public key of the user (the certificate subject)
2.The request for the user’s certificate
3.The private key of CA

Q7. Which of the following are required to verify the signature of the digital certificate signed by a CA?

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1.The certificate itself
2.The public key of CA

Q8. Which of the following statements are true? Select all that apply.

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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.

Q9. Which of the following are the PKI’s responsibilities? Select all that apply.

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Manage certificates

Store certificates

Create certificates

Revoke certificates

Distribute certificates

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