# Foundations of Cryptography | NPTEL | Week 6 Assignment Solutions

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### Foundations of Cryptography NPTEL Week 6 Assignment Solutions

Q1. Choose the incorrect option(s) from the following:

a) (R,× ) is a group
b) (R-{0},+) is a group
c) (Z – {0}, +) is an abelian group
d) (R -{0} ,× ) is a group

Q2. Select the incorrect option(s) for the Merkle-Damgård transformation:

a) It employs a multi-stage approach and used in many popular hash algorithms like MD5, SHA256
b) This construction will always add a padding to the message which depends upon the length of the message
c) The initial vector (IV) used in this construction can be randomized
d) The transformation is a deterministic function of the input

Q3. Given H is a collision-resistant hash function. Then which of the following is/are false?

a) The function H_1 (x)≝H(x)||H(x) is not collision-resistant
b) The function H_1 (x)≝H(x)||H(x) is collision-resistant
c) The function H_2 (x)≝1||H(x) is collision-resistant
d) The function H_2 (x)≝1||H(x) is not collision-resistant

Q4.

Neither the construction in part (a), nor the construction in part(b) is secure

The construction in part (a), as well as the construction in part(b) are secure

Q5. Let F:{0, 1}n X {0, 1}n be a keyed function and let H: M => {0, 1}n be a function, where M = {0, 1}l, where l is some polynomial function of the security parameter. Then consider the keyed function F’: {0, 1}n X M => {0, 1}n, where F’k(m) = Fk(H(m)). Which of the following is/are true?

a) If F is a secure PRF, then F’ is a secure PRF
b) If H is collision-resistant, then F’ is a secure PRF
c) If F is a secure PRF and H is collision-resistant, then F’ is a secure PRF
d) Even if F is a secure PRF and H is collision-resistant, the function F’ need not be a secure PRF

Foundations of Cryptography NPTEL Week 6 Assignment Solutions

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### 6 thoughts on “Foundations of Cryptography | NPTEL | Week 6 Assignment Solutions”

1. Bro plz upload week-7, today is last date.

2. Chacha hamare Vidhayak

3. 1. 4. 1. 