Practice Problems Cryptography and Network Security

(a) Alice and Bob wish to resolve a dispute over telephone. We can encode the possibilities of the dispute by a binary value. For this they engage a protocol: i. Alice → Bob: Alice picks up randomly an x, which is a 200 bit number and computes the function f(x). Alice sends f(x) to Bob. ii. Bob → Alice: Bob tells Alice whether x was even or odd. iii. Alice → Bob: Alice then sends x to Bob, so that Bob can verify whether his guess was correct. If Bob’s guess was right, Bob wins. Otherwise Alice has the dispute solved in her own way. They decide upon the following function, f : X → Y , where X is a random variable denoting a 200 bit sequence and Y is a random variable denoting a 100 bit sequence. The function f is defined as follows: