Cryptography

1.     Assume you are given a 500-character encrypted message, encrypted in Vigenère cryptosystem, in which you know the plaintext word CRYPTOGRAPHY occurs exactly two times, and we know that the ciphertext sequence PTFDLSTTHDZC is the encryption of CRYPTOGRAPHY. The first occurrence starts at character position 24 and second at character position 198 (we start counting from 1). What is the length of the key used for encryption?

• 5

• 6

• 8

• 9

Which of the following statement(s) is/are correct?

1. 1.Any encryption scheme with key length less than message length can not be a perfectly-secure scheme. 

2. 2.A scheme is COA secure if and only if it is KPA secure

3. 3.The one-time pad scheme is perfectly-secure if on any subsequent invocation of the key generation algorithm, an earlier key gets re-generated. 

4. 4.A scheme is CPA secure if and only if it is CCA secure

• 1 and 3

• 1,2,and 3

• 2 and 4

• Neither of 1, 2, 3 or 4

Consider an instance of shift cipher with the probability distribution over the message space as follows: P[M=a] = 0.25, P[M=b] = 0.5, P[M=c] = 0.25. Then identify the correct statement(s) from the following?

• Probability that the ciphertext is “D” is the same as the probability that the ciphertext is “E”

• Probability that the ciphertext is “D” is half the probability that the ciphertext is “E”

• Probability that the ciphertext is “A” is 1/4th the probability that the ciphertext is “D”

• Probability that the ciphertext is “D” is 1/26

Which of the following is/are true for the Vernam cipher?

• The scheme is CPA-secure

• The scheme is not single-message COA-secure, if the sender obtains a key k=0n

   from the key-generation algorithm

• The scheme is not single-message COA-secure, as the encryption algorithm is deterministic

• The scheme is not CPA-secure

Which of the following is/are not perfectly secure encryption scheme(s):

• Playfair Cipher

• Vernam Cipher

• Affine Cipher

• Vigenère Cipher

Let G:{0,1}m→{0,1}n be a secure PRG. Then consider the function G′:{0,1}m+1→{0,1}n+1 , where G′(s1||s2)=defG(s1)||s2. Then which of the following is/are false for G′?

• The construction G′ is not a secure PRG, as it always leaks the last bit of the seed.

• The construction G′ is a secure PRG, provided its seeds are chosen uniformly random.

• The construction G′ is not a secure PRG, even if its seeds are chosen randomly.

• The construction G′ is a secure PRG, no matter how its seeds are chosen.

Let G:{0,1}m→{0,1}n be a secure PRG. Then which of the following is/are not a secure PRG?

• G′:{0,1}m→{0,1}n, where G′(s)=defG(s)⊕1n

• G′:{0,1}m→{0,1}n, where G′(s)=defG(s)⊕0n

• G′:{0,1}m→{0,1}2n, where G′(s)=defG(s)||G(s)

• None of the above

Suppose we want to execute OTP encryption scheme over message space M={0,1}ℓ+1

 but with key-space K={0,1}ℓ. For this, to encrypt an (ℓ+1)-bit message using an ℓ-bit random key k, the encryption algorithm picks an additional random bit x and outputs the ciphertext c=m⊕(k∥x).

• The adversary will not learn any information about the underlying message

• The adversary can learn something about the underlying message

• The scheme satisfies correctness property without any error

• The scheme satisfies the correctness property except with probability ½

Let G:{0,1}m→{0,1}n be a secure PRG. Then which of the following is/are true?

• G′:{0,1}2m→{0,1}n, where G′(s1||s2)=defG(s1)⊕G(s2) is a secure PRG.

• G′:{0,1}2m→{0,1}n, where G′(s1||s2)=defG(s1)⊕G(s2) is not a secure PRG.

• G′:{0,1}2m→{0,1}2n, where G′(s1||s2)=defG(s1)||G(s2) is a secure PRG.

• G′:{0,1}2m→{0,1}m+n, where G′(s1||s2)=defs1||G(s2) is not a secure PRG.

Difference between perfect security and semantic security involves one or more of the following:

• Bounds on how long the adversary can run the experiment

• In the respective indistinguishability experiment, adversary has the exact same probability of success

• Bounds on computational capabilities of the adversary

• None of the above