system
Given the following post, respond as if you're commenting on Reddit:
human
Are modern encryption techniques (like 256-bit SSL encryption) more complicated than ciphers used in WWII (e.g. Enigma)? By how much?

I understand the *basics* behind encryption of messages, and thanks to a recent analogy posted (I think) on reddit, also understand the basics behind how one-way hashes are created (but cannot easily be reversed).

How do modern encryption techniques compare to those used by the English/German militaries in WWII? Are new encryption techniques simply iterations on existing methods (linear improvement), or completely disruptive changes that alter the fundamentals of encryption?
gpt
SSL relies on a mathematical technique that was unknown to militaries until the seventies.

That specific technique was public key encryption, and the first (known, declassified) instance of a military using PKI was in the 70s in the UK, at the GCHQ in 1972. Diffie and Hellman also discovered the same technique as the GCHQ in 1976, but their work was out in the public domain, so it was used in a non military context immediately after. 

What's interesting is that the idea of "easy to compute, hard to invert" had been thought of in the context of cryptography and number factoring sometime in the late 1800s, but it was never theorized that the two could be logically combined. 

SSL relies on the RSA algorithm, which was invented in 1977 and again, in private by a mathematician in the employ of the GCHQ in 1973. 

At the very minimum the public key infrastructure of SSL would've been something unknown to militaries in the 40s, whose keying systems were essentially just moving the keying information down from location to location. With Diffie Hellman key exchange, you can generate a shared secret over an insecure channel, and with RSA, you can encrypt messages with public keys that are distributed beforehand (in practice, you just encrypt the session key with RSA, and then use a standard block cipher). Being able to not have to physically move your key around is a sea change from the 40s: captured key books were a common source of Enigma cracks. 

Block ciphers would've probably been more familiar to mathematicians of the 40s, but the first known (unclassified) example of a modern block cipher was with IBM's Lucifer in 1971. As you can see, almost all modern cryptography is now based on math that was developed in the 70s. That's not very surprising given that all modern crypto now relies on computers instead of electromechanical devices and scramblers which were de rigeur during the 40s, 50s and 60s.