Could a civilization without access to computers have cryptography?
- There's a person who has enough working knowledge of our current real-world methods of cryptography (e.g. knows how a few modern algorithms work and could implement one or two from scratch).
- That person becomes a member of an alien civilization where people are generally intelligent and educated (in fields like math), but they haven't invented electricity or computers.
- That person is willing to teach this civilization how to use cryptography and the military of that civilization is willing to learn about cryptography and apply it in order to have an advantage over a potential enemy.
- A potential enemy could have anything between no computers at all, to computers computationally comparable to our current everyday desktops.
Could the civilization realistically implement some form of secure (probably manual) encryption of simple textual messages (or more), without access to computers? Or is it out of their league computationally to make their method cryptographically secure?
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1 answer
In two words: absolutely yes.
Cryptography, at its core, is not about computers at all. Sure; automated, programmable, electronic computers operating at about a gazillion instructions per millifortnight allow us to perform some pretty neat tricks that would be difficult to pull off otherwise, but there is nothing inherent about cryptography that requires electronic computers. There was serious cryptographic work being done in the 1700s and 1800s, and while those ciphers are trivially breakable with modern methods, they held up pretty well to the adversaries of the day. The Vigenère cipher is an excellent example of this.
That said, given what we know today, and within the limits of your question, your protagonist's best bet is probably (and I'll likely get shot down for this) be the German Enigma.
Yes, it was broken. But we now know quite well what allowed it to be broken, and to a large extent, what allowed breaking the Enigma was poor operating procedures. Things like reencrypting the same plaintext under multiple systems with different security properties, standard message preambles, test transmissions using real key material (the infamous LLLLL... transmission provided an invaluable crib to codebreakers in the UK), ... Really, these are things that any motivated security-inclined professional should be able to keep up with without any major difficulties. Even something as simple as starting each and every single message with a random number of letters (symbols) selected at random followed by one particular letter to mark the end of the part to be ignored, would probably be a huge improvement.
The Enigma is relatively easy to implement electromechanically (we did it with 1930s technology), and I don't think it is too much of a stretch to build one that operates purely mechanically. (Though relaxing your requirement that these aliens have not discovered electricity might make for a more believable story. You could, if you want to, make electricity very limited, and restricted to military applications, but still present in the world.)
Especially against an adversary that doesn't have computers or even electricity, the Enigma's theoretical key space is gigantic. With reasonable assumptions, Wikipedia claims that the Enigma's key space was approximately $10^{23} \approx 2^{76}$; with ideal assumptions, it had a theoretical key space of around $10^{114} \approx 2^{380}$. Make use of all of it.
By giving the aliens some Enigmas, as well as explaining to them that those have been broken, how they were broken, and how to avoid the mistakes that allowed them to be broken, your protagonist will be giving that side of a conflict a major upper hand (tentacle, or whatever) in a conflict, because for all intents and purposes, they will have the ability to keep messages secret even if messengers are intercepted or their communications are being monitored by the adversary.
Compare also How cryptographically secure was the original WW2 Enigma machine, from a modern viewpoint? on the Cryptography Stack Exchange.
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