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.

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.

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Source

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