Diffie-Hellman Key Exchange Protocol Analysis

Diffie- Hellman key exchange (DHKE) is the earliest public key exchange protocol, it allows prior shared secret key irrespective of past and future keys used in many security protocols. Diffie Hellman Key exchange protocol may be used for initial authentication in Kerberos V5(DHAUTH). The axioms presented in this paper are used in protocol composition logic (PCL). Three innovative ideas presented are essential for formal proofs for DHAUTH.(i) Bugs in DH axiom are fixed (ii) The secrecy conditions for DHKE are proved using general inductive method (iii) Cipher text integrity assumptions based axiom reasoning are established. Computational PCL reasons directly about properties of probabilistic polynomial time execution of protocols. As formulated
The security definition of the protocol specifies that , an adversary who interferes with the key exchange protocol should not be able to extract information because it may compromise the application protocol. Security of a key exchange protocol is given as , ∑ with respect to an application protocol π in a set S via a two-phase adversary experiment given as A = (Ae,Ac). The first phase, key exchange phase includes the honest parties to run multiple sessions of the protocol as per the standard execution model. The standard execution model has each principal executing multiple sessions of the protocol with other principals with controlled communication between parties by the adversary Ae. At the final stage of the key exchange phase, sid, a challenge session id is chosen by the adversary among the sessions executed by the honest parties, and outputs some state information St representing the information Ae along with a key, k. The challenge phase comes up with the goal to demonstrate the attack of adversary using the key k. with input St , to Ae it starts interacting with π the adversary in the application protocol, S. Since the secure sessions are to be concentrated, IND-CPA is formalized .Ac has access to a left-right encryption oracle under k, along with the state information
In logical proofs involving key exchange protocols and their use, we use a derived predicate SharedKey, which asserts that a key is good against any agent not among those sharing the key. Formulas involving SharedKey are also used in reasoning protocols involving key generated by a key exchange protocol, which is used to encrypt and authenticate subsequent communication ,referred to as a secure session or secure channel. A session provides authentication if a receiver accepts a message from A only if A indeed sent it, with overwhelming probability. We express these additional probabilistic properties using other predicates of Computational