Tasks: Write the following protocols

- Protocol 1:
A and B do not share any secret. Write a key exchange protocol for A and B to share a symmetric key. Analyse potential attacks and give a method of prevention.

- Protocol 2:

A and B share a long term secret key. Write a key exchange protocol for A and B to share a session key. Must consider mutual authentication, freshness, integrity and forward security in the protocol. Analyse its security.

- Protocol 3:

A and B both have their own un-certified public key, respectively. Write a key transport protocol for them to establish a session key. Analyse potential attacks and give a method of prevention.

- Protocol 4:

A and B both have their own certi_ed public key, respectively. Give a protocol for them to establish a session key. Must consider mutual authentication, reshness and integrity in the protocol. Analyse its security.

- Protocol 5:

A and B want to have a private \handshake". Upon a handshake, both know that they are communicating with an authorised party but the identity of its partner is not revealed. Let assume that both A and B come from an organisation and hold a signed public key by the organisation. Let us say: A's public key is y_A = g^a mod p and B's pubic key is y_B = g mod p, where p is a safe prime, g is a generator of Z_p,a ∈ Z_P is the identity of A and b  ∈ Z_P is the identity of B. Further, we assume that SA is the signature on yA signed by the organisation and SB is the signature on yB signed by the organisation. Write a concrete private handshake by using a zero-knowledge proof technique.

- Protocol 6:

Similar to Protocol 5, but now you add (authenticated) key exchange into it so that they can establish a shared session key, upon a handshake. Analyse its security.

- Protocol 7:

There are three mobile service domains; each has an authentication server. We denote by AS1, AS2, and AS3 the corresponding authentication servers. For simplicity, let AS1 AS2, and AS3 represent those three domains. This mobile system can provide mobile communication services to a large number of users.

For simplicity, we assume that two mobile users (A and B) are currently in the system only, where A has registered with AS1 and B has registered with AS2.

They, therefore, call their registering domain home (therefore, share a long term secret key with their home). Both A and B are mobile, in the sense that they can move to any existing domains and they want to communicate securely and anonymously wherever they are located. In this task, you consider the case where A has travelled to AS2 and B has travelled to AS3. Write an authenticated key establishment protocol for A and B to establish a session key.

Security Requirements:

- Authenticity: All parties involved in the communication must be authenticated by related communication partners.
- Confidentiality: All information must be protected against eavesdropping.
- Anonymity: User ID must be protected against outsiders.
- Freshness: All messages must be fresh and secure against reply attacks.
- Integrity: Integrity protection should be applied to all communication flows.