# Diffie Hellman in F#

#### Diffie-Hellman key exchange.

1 | ```
exercism fetch fsharp 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

For this exercise the following F# feature comes in handy:

## 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.