`1` ```exercism fetch csharp diffie-hellman ```

# Diffie Hellman

Diffie-Hellman key exchange.

Alice and Bob use Diffie-Hellman key exchange to share secrets. They start with prime numbers, pick private keys, generate and share public keys, and then generate a shared secret key.

## Step 0

The test program supplies prime numbers p and g.

## Step 1

Alice picks a private key, a, greater than 1 and less than p. Bob does the same to pick a private key b.

## Step 2

Alice calculates a public key A.

 `1` ```A = g**a mod p ```

Using the same p and g, Bob similarly calculates a public key B from his private key b.

## Step 3

Alice and Bob exchange public keys. Alice calculates secret key s.

 `1` ```s = B**a mod p ```

Bob calculates

 `1` ```s = A**b mod p ```

The calculations produce the same result! Alice and Bob now share secret s.

## Hints

This exercise requires you to perform calculations on large numbers. To correctly represent large numbers, the BigInteger struct is used.

### Submitting Exercises

Note that, when trying to submit an exercise, make sure the exercise file that you're submitting is in the `exercism/csharp/<exerciseName>` directory.

For example, if you're submitting `bob.cs` for the Bob exercise, the submit command would be something like `exercism submit <path_to_exercism_dir>/csharp/bob/bob.cs`.

## Source

Wikipedia, 1024 bit key from www.cryptopp.com/wiki. http://en.wikipedia.org/wiki/Diffie%E2%80%93Hellman_key_exchange

## Submitting Incomplete Solutions

It's possible to submit an incomplete solution so you can see how others have completed the exercise.