PGP Fundamentals: Diffie-Hellman Key Exchange

After watching @ecmendenhall’s talk about GPG tools I was inspired to learn more about encryption. The video demonstrated the Diffie-Hellman Key Exchange, in which Alice and Bob communicate while an omnipresent observer stands by, unable to determine the true meaning of their communication despite watching every bit of information passing between them.

Because I couldn’t pause the video during the presentation, and because, well, math, I wasn’t able to fully grok how it worked. So when I got home today I decided to write some code to help explain it to myself.

class DiffieHellmanKeyExchange
  def initialize(prime_modulus, generator)
    @prime_modulus = prime_modulus
    @generator     = generator
  end

  def create_public_message(secret_key)
    @generator ** secret_key % @prime_modulus
  end

  def decrypt_common_secret(message, secret_key)
    message ** secret_key % @prime_modulus
  end
end

Naturally, there are some tests.

require "diffie_hellman_key_exchange"

describe DiffieHellmanKeyExchange do
  before(:each) do
    @exchange = described_class.new(23, 5)
    @alices_key = 6
    @bobs_key = 15
  end

  it "creates a public message from a secret" do
    @exchange.create_public_message(@alices_key).should == 8
    @exchange.create_public_message(@bobs_key).should == 19
  end

  it "decrypts the common secret" do
    bobs_message = 19
    alices_message = 8

    @exchange.decrypt_common_secret(bobs_message, @alices_key).should == 2
    @exchange.decrypt_common_secret(alices_message, @bobs_key).should == 2
  end
end

For further consideration, now that there’s a way to agree upon a cipher, how could this key exchange be used as part of a set of encryption tools?