1. (9 points) Let's work on an example for the garbled circuit discussed in Lecture 17 between Alice and Bob who want to compute f- NAND(a, b) a) (1 points) Suppose 0 and 1 on each wire is encrypted into a 5-bit number (0 to 31). Alice chooses Ao7, A-17, Bo 19, B 3, and O 18, 01-6. What are SA and Sp? how Alice garbles the circuit her input? b) (2 points) For the encryption function ek,)i+k2+x) mod 32, show c) (1 points) Suppose Alice chooses a -1. What Alice should send to Bob as d) (2 points) Suppose Bob chooses b 0. Show how Bob encrypts his input with Alice's help using OT. Assume Alice's RSA public key to be (n-35, e = 5) e) (1 points) Show how Bob computes with the garbled circuit and the en- crypted inputs, and then communicates with Alice to determine f. f) (2 points) Show that Bob cannot decide Alice's choice of a (assuming OT only reveals Bo but no additional information). As a hint, is it possible for Alice to choose A0 = 17, A,-7 while sending Bob exactly the same garbled circuit and inputs? 1. (9 points) Let's work on an example for the garbled circuit discussed in Lecture 17 between Alice and Bob who want to compute f- NAND(a, b) a) (1 points) Suppose 0 and 1 on each wire is encrypted into a 5-bit number (0 to 31). Alice chooses Ao7, A-17, Bo 19, B 3, and O 18, 01-6. What are SA and Sp? how Alice garbles the circuit her input? b) (2 points) For the encryption function ek,)i+k2+x) mod 32, show c) (1 points) Suppose Alice chooses a -1. What Alice should send to Bob as d) (2 points) Suppose Bob chooses b 0. Show how Bob encrypts his input with Alice's help using OT. Assume Alice's RSA public key to be (n-35, e = 5) e) (1 points) Show how Bob computes with the garbled circuit and the en- crypted inputs, and then communicates with Alice to determine f. f) (2 points) Show that Bob cannot decide Alice's choice of a (assuming OT only reveals Bo but no additional information). As a hint, is it possible for Alice to choose A0 = 17, A,-7 while sending Bob exactly the same garbled circuit and inputs