Diffie-Hellman

Instructions

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 = gᵃ 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 = Bᵃ mod p

Bob calculates

s = Aᵇ mod p

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

Should I use random or secrets here?

As of Python 3.6, there are two different modules for producing "random" numbers:

The module called random is pseudo-random, meaning it does not generate true randomness, but follows an algorithm that simulates randomness. Since these "random numbers" are generated through a known algorithm, they are not truly random. As a result, th random module is not correctly suited for cryptography and should not be used, precisely because it is pseudo-random.

The module called secrets generates cryptographically strong "random" numbers that provide the greater security required for cryptography. They are still pseudo-random in the strictest sense — but they have guarantees that the numbers they produce are absolutely unpredictable.

Since this is only a practice exercise, using the random module is fine, but note that it would be very insecure if actually used for cryptography.

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Source

Wikipedia, 1024 bit key from www.cryptopp.com/wiki.