# Foundations of Cryptography | NPTEL | Week 1 Assignment Solutions

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### Foundations of Cryptography NPTEL Week 1 Assignment Solutions

Q1. Which of the following condition(s) is/are sufficient to get a perfectly-secure encryption scheme?

a) Ensure that key-generation algorithm outputs a uniformly random key from the key space
b) Ensure that the encryption algorithm is randomized
c) Ensure that the key is as large as the plaintext
d) None of these

Q2. Identify the incorrect statement(s) from the following

a) A scheme is COA-secure if and only if it is KPA-secure
b) A scheme is KPA-secure if and only if it is CPA-secure
c) A scheme is CPA-secure if and only if it is CCA-secure
d) None of these

Q3. Consider an instance of shift cipher with the probability distribution over the message space as follows: P[M=a] = 0.4, P[M=b] = 0.3, P[M=c] = 0.3. What is the probability that the ciphertext is ‘D’?

a) 1/26
b) 1/13
c) 3/26
d) None of these

Q4. Consider an instance of shift cipher with the probability distribution over the message space as follows: P[M=a] = 0.3, P[M=b] = 0.6, P[M=c] = 0.1. Then identify the correct statement(s) from the following.

a) Probability that the ciphertext is “D” is the same as the probability that the ciphertext is “E”
b) Probability that the ciphertext is “D” is less than the probability that the ciphertext is “E”
c) Probability that the ciphertext is “D” is more than the probability that the ciphertext is “E”
d) Nothing can be said regarding the probability that the ciphertext is “D” and the probability that the ciphertext is “E”

Answer: a) Probability that the ciphertext is “D” is the same as the probability that the ciphertext is “E”

Q5. Which of the following is/are valid condition(s) for a perfectly-secure encryption scheme?

a) Pr[M=m | C=c]= Pr[M=m]
b) P[C=c]= Pr[M=m]
c) Pr[C=c | M=m]= Pr[K=k]
d) None of these

Answer: a) Pr[M=m | C=c]= Pr[M=m]

Foundations of Cryptography NPTEL Week 1 Assignment Solutions

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