# Diffie Hellman in Elixir

#### Diffie-Hellman key exchange.

1 | ```
exercism fetch elixir 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.

For generating random numbers, Erlang's `:rand.uniform`

or `Enum.random`

are
good places to start.

`:math.pow |> round`

can be used to find the power of a number, and `rem`

for
the modulus.

Neither of those works particularly well (or quickly) for very large integers. Cryptography generally makes use of numbers larger than 1024 bits. Erlang's :crypto module has a useful function for finding the modulus of a power, particularly for enormous integers, but you might need :binary to decode it.

## Running tests

Execute the tests with:

1 |
```
$ elixir diffie_hellman_test.exs
``` |

### Pending tests

In the test suites, all but the first test have been skipped.

Once you get a test passing, you can unskip the next one by
commenting out the relevant `@tag :pending`

with a `#`

symbol.

For example:

Or, you can enable all the tests by commenting out the
`ExUnit.configure`

line in the test suite.

1 |
```
# ExUnit.configure exclude: :pending, trace: true
``` |

For more detailed information about the Elixir track, please see the help page.

## 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.