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# jgo's solution

## to Diffie Hellman in the Python Track

Published at Jan 16 2021 · 0 comments
Instructions
Test suite
Solution

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.

``````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.

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

Bob calculates

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

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

## Should I use random or secrets?

Python, as of version 3.6, includes two different random modules.

The module called `random` is pseudo-random, meaning it does not generate true randomness, but follows an algorithm that simulates randomness. Since random numbers are generated through a known algorithm, they are not truly random.

The `random` module is not correctly suited for cryptography and should not be used, precisely because it is pseudo-random.

For this reason, in version 3.6, Python introduced the `secrets` module, which generates cryptographically strong random numbers that provide the greater security required for cryptography.

Since this is only an exercise, `random` is fine to use, but note that it would be very insecure if actually used for cryptography.

## Exception messages

Sometimes it is necessary to raise an exception. When you do this, you should include a meaningful error message to indicate what the source of the error is. This makes your code more readable and helps significantly with debugging. Not every exercise will require you to raise an exception, but for those that do, the tests will only pass if you include a message.

To raise a message with an exception, just write it as an argument to the exception type. For example, instead of `raise Exception`, you should write:

``````raise Exception("Meaningful message indicating the source of the error")
``````

## Running the tests

To run the tests, run `pytest diffie_hellman_test.py`

Alternatively, you can tell Python to run the pytest module: `python -m pytest diffie_hellman_test.py`

### Common `pytest` options

• `-v` : enable verbose output
• `-x` : stop running tests on first failure
• `--ff` : run failures from previous test before running other test cases

For other options, see `python -m pytest -h`

## Submitting Exercises

Note that, when trying to submit an exercise, make sure the solution is in the `\$EXERCISM_WORKSPACE/python/diffie-hellman` directory.

You can find your Exercism workspace by running `exercism debug` and looking for the line that starts with `Workspace`.

For more detailed information about running tests, code style and linting, please see Running the Tests.

## 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.

### diffie_hellman_test.py

``````import unittest

from diffie_hellman import private_key, public_key, secret

# Tests adapted from `problem-specifications//canonical-data.json`

class DiffieHellmanTest(unittest.TestCase):
def test_private_key_is_greater_than_1_and_less_than_p(self):
primes = [5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47]
for p in primes:
self.assertTrue(1 < private_key(p) < p)

def test_private_key_is_random(self):
"""
Can fail due to randomness, but most likely will not,
due to pseudo-randomness and the large number chosen
"""
p = 2147483647
private_keys = [private_key(p) for _ in range(5)]
self.assertEqual(len(set(private_keys)), len(private_keys))

def test_can_calculate_public_key_using_private_key(self):
p = 23
g = 5
private_key = 6
self.assertEqual(8, public_key(p, g, private_key))

def test_can_calculate_secret_using_other_party_s_public_key(self):
p = 23
their_public_key = 19
my_private_key = 6
self.assertEqual(2, secret(p, their_public_key, my_private_key))

def test_key_exchange(self):
p = 23
g = 5
alice_private_key = private_key(p)
bob_private_key = private_key(p)
alice_public_key = public_key(p, g, alice_private_key)
bob_public_key = public_key(p, g, bob_private_key)
secret_a = secret(p, bob_public_key, alice_private_key)
secret_b = secret(p, alice_public_key, bob_private_key)
self.assertTrue(secret_a == secret_b)

if __name__ == "__main__":
unittest.main()``````
``````from random import randrange

def private_key(p):
return randrange(2, p)

def public_key(p, g, private):
return g**private % p

def secret(p, public, private):
return public**private % p``````