## NPTEL Foundations of Cryptography Week 3 Assignment Answers 2024

1. Which of the following is/are true for One-Way Functions (OWF)?

- They are deterministic functions
- OWF can be a many-to-one function
- A One-Way Permutation (OWP) is an OWF which is also a bijection
- The time complexity to compute the inverse of OWFs is a polynomial function of the security parameter

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2.

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3. Select the incorrect option(s):

- Trivium is a hardware-oriented stream cipher
- In the CPA security model, the adversary is allowed to interact with the encryption oracle a polynomial number of times
- RC4 cipher is a practical instatiation of a secure PRG
- Encryption algorithm in any stream cipher is randomized

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4. Let II =(Gen,Enc,Dec) be a symmetric-key cipher. Then consider a variant II ′=(Gen,Enc′,Dec′) of II , where Enc′k(m)=Enck(reverse(m)). The steps of Dec′ are performed accordingly. Here reverse(m)denotes the bit string obtained by reversing the order of the bits of m.

- If II is multi-message COA-secure, then II ′II ′ is also multi-message COA-secure
- If II is single-message COA-secure, then II ′II ′ may not be single-message COA-secure
- If II is CPA-secure, then II ′II ′ is also CPA-secure
- If II II is CCA-secure, then II ′II ′ may not be CCA-secure

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

- If a PRG exists, then so does one-way functions and vice-versa
- Determining the sign of x , for x∈R , given x2 , is an example of a hard-core predicate
- A single-message CPA-secure encryption scheme is also a multi-message CPA-secure scheme
- Secure PRGs can be constructed using secure PRFs and vice-versa

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