Diffie hellman key algorithm

Diffie hellman key algorithm

1. GANDHINAGAR INSTITUTE OF TECHNOLGY Department of Information Technology Diffie-Hellman Key Algorithm Group ID: IT_B1_00 Student Name(Enroll No): Shaishav Shah(170120116094) Name of Faculty: Prof. Alpa Oza INS(2170709)

2. Introduction The Diffie-Hellman key agreement protocol was developed by Diffie and Hellman in 1976. This protocol allows two users to exchange a secret key over an insecure medium without any prior secrets. The protocol has two system parameters p and g. They are both public and may be used by all users in a system. Parameter p is a prime number and parameter g is an integer less than p, with the following property: For every number n between 1 and p – 1 inclusive. There is a power k of g such that .  

3. Introduction The protocol depends on the discrete algorithm problem for its security. It assumes that it is computationally infeasible to calculate the shared secret key given the two public values and when the prime p is sufficiently large. The Diffie – Hellman key exchange is vulnerable to a man-in-the-middle attack. This vulnerability is present because Diffie-Hellman key exchange does not authenticate the participants. Possible solutions include the use of digital signatures and other protocol variants.  

4. Algorithm Select two numbers: Prime number . an integer that is a primitive root of . Suppose the users A and B wish to exchange a key. User A select a random integer and computes . User A select a random integer and computes . Both side keeps the X value private and makes the Y value available publicly to the other sides. User A computes the key as . User B computes the key as .  

5. Algorithm Both side gets same results:  

6. Example User A and User B use the Diffie-Hellman key exchange technique with a common prime and a primitive root If user A has private key , what is A’s public key ? If user B has private key , what is B’s public key ? What is the shared secret key?   Solution: A’s public key = = 16807 mod 71 = 51 B’s public key = = 13841287201 mod 71 = 4 A’s public key  

7. Advantages Any user can choose a random x and publish in a public database such as a phone book. Phone book must be maintained by a TTP. Other users can look up the database and get the public key for the individual and use it to encrypt the message. Ideal for use with emails.  

8. Disadvantages Does not protect against man in middle attacks. Even can intercept all traffic between Alice and Bob and generate separate keys for communication with them. If Alice sends an encrypted message for Bob with his public key, Even simply forwards it. For large prime is an even number and so will have an subgroup of order 2.  

9. Thank You