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) Suppose 0 and 1 on each wire is encrypted into a 5-bit number (Oto31). AlicechoosesA0 -7,A1 17,B0 19,B1 -3,ando0-18, 01 6 What are SA and SB? b) For the encryption function ek1| k2 (x) (k1 +k2 +x) mod 32, show how Alice garbles the circuit c) Suppose Alice chooses a 1. What Alice should send to Bob as her input? d) 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) Show how Bob computes with the garbled circuit and the en- crypted inputs, and then communicates with Alice to determine f. f) Show that Bob cannot decide Alice's choice of a (assuming OT only reveals B0 but no additional information). As a hint, is it possible for Alice to choose A0 17, A1 7 while sending Bob exactly the same garbled circuit and inputs? 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) Suppose 0 and 1 on each wire is encrypted into a 5-bit number (Oto31). AlicechoosesA0 -7,A1 17,B0 19,B1 -3,ando0-18, 01 6 What are SA and SB? b) For the encryption function ek1| k2 (x) (k1 +k2 +x) mod 32, show how Alice garbles the circuit c) Suppose Alice chooses a 1. What Alice should send to Bob as her input? d) 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) Show how Bob computes with the garbled circuit and the en- crypted inputs, and then communicates with Alice to determine f. f) Show that Bob cannot decide Alice's choice of a (assuming OT only reveals B0 but no additional information). As a hint, is it possible for Alice to choose A0 17, A1 7 while sending Bob exactly the same garbled circuit and inputs