# Diffie-Hellman Algorithm in Java

Diffie-Hellman algorithm is one of the most important algorithms used for establishing a shared secret. At the time of exchanging data over a public network, we can use the shared secret for secret communication. We use an elliptic curve for generating points and getting a secret key using the parameters.

1. We will take four variables, i.e., P (prime), G (the primitive root of P), and a and b (private values).
2. The variables P and G both are publicly available. The sender selects a private value, either a or b, for generating a key to exchange publicly. The receiver receives the key, and that generates a secret key, after which the sender and receiver both have the same secret key to encrypt.

Let's understand the process step by step for user1 (sender) and user2 (receiver):

Steps User1 User2
1. P, G => available public keys. P, G => available public keys.
2. a is selected as a private key. b is selected as a private key.
3. Eq. to generate key:
x=Ga modP
Eq. to generate key:
y=Gb modP
4. After exchanging keys, user1 receives key y. After exchanging keys, user2 receives key x.
5. User1 generates a secret key by using the received key y:
ka=ya modP
User2 generates a secret key by using the received key x:
kb=xb modP

Algebraically, 5th step can be shown as follows:

```ka=kb
```

It means that both the users have the symmetric secret key to encrypt.

Example:

1. User1 and User2 get public keys P = 33 and G = 8.
2. User1 selects a as a private key, i.e., 3, and User2 selects b as a private key, i.e., 2.
3. User1 calculate the public value:
x=(83 mod 33)=512mod33=17
4. User2 calculate the public value:
y=(82 mod33)=64mod33= 31
5. User1 and User2 exchange public keys, i.e., 17 and 31.
6. User1 receives public key y = 31 and User2 receives public key x = 17.
7. User1 and User2 calculate symmetric keys:
User1: ka=ya modP=313 mod33=29791mod33=25
User2:kb=xb modP=172 mod33=289mod33=25
8. 25 is the shared secret.

Now, let's implement the Java code for the Diffie-Hellman algorithm:

DiffieHellmanAlgorithmExample.java

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