Define the generator G by G(x) = x | x. (G maps inputs of length n to outputs of length 2n). Which of the following algorithms A distinguishes the output of G from uniform?

Which of the following BEST describes the security offered by the Diffie-Hellman key-exchange protocol (assuming the DDH problem is hard)?

Which of the following is a drawback of the private-key setting that is NOT addressed by the public-key setting?

What is the size of key space |K| for a shift cipher, considering the message space as English alphabets, and encryption algorithm as Enc​(m)=(m+shift)mod 26?

If the message “cryptoisfun” is encrypted with the shift cipher and key 25. What is the resulting ciphertext?

Say G is in the subgroup Z*11, generated by g = 4. Let’s say, the group has order 5.  The public key contains h = 3. What is encryption of the message m = 5, using the secret exponent y = 3?

What is 7th root of 2 modulo 33? (Note that ϕ(33) = 20, and 3 . 7 = 1 mod 20)

Which of the following is the most appropriate primitive for achieving message integrity between two users sharing a key?

3-1 mod 7 = ? Alternatively, what is the inverse of 3 mod 7 on multiplication?

Question 8 (2 points) Assume that I saw all the mobility data in class and I watched the presentation of Chetty et al’s work on social capital that we also saw in class, and that I summarized it as saying that kids that grow up in single-parent households have less upward-mobility than do kids that grow up in two-parent households. Based on the material from class, what is not right about that statement? What might have some truth to it? Teach it to me, making reference to material from class.