1 Asymmetric trusted party protocol for non?repudiation (35 points) Part of material considered in class is a symmetric exchange protocol between Alice and Bob involving a trusted party (Carol) and achieving non-repudiation. We considered only a symmetric key protocol. Formulate such a protocol for the case of asymmetric keys where the parties use their public and private keys. Your solution should include. • Description of a protocol in terms of sequence of operations performed by the parties (Alice does this, Bob does that, Carol does that, etc.) • Justification as to why you believe such a protocol makes it hard for Alice to disown her message. Remark. There can be more than one possible solution. I will accept any provided that it is well justified. 2 Symmetric exchange keys between banks and PCOs The purpose of this exercise is to demonstrate the impraticality of any two banks sharing their secret keys. Suppose that there are 10000 = 104 banks and 10 payment card organizations (PCOs). 1. (15 points) How many secret keys will be needed if each PCO shares a unique secret key with each bank? 2. (15 points) How many extra secret keys will be needed if every two banks share a unique secret key? 3 Zero knowledge proofs (35 points) Suppose Alice has in her computer a file with her address. Alice does not show Bob the content of the file because she does not want him to know her exact address. However, she wants to convince Bob that she lives in London. How can she do that? Remark. Please explain in detail the corresponding protocol and why you believe it works the intended way.