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This question was originally posted here on Crypto StackExchange. As suggested by an answer I am posting it here to help get a better perspective on the math side.

Public-key cryptography was not invented until the 1970's. Apart from the idea not existing earlier (as talked about here), is there any reason it could not have been used earlier? For example, are there forms that are easy enough to perform by hand but complicated enough to not be solved (easily) by hand?

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  • $\begingroup$ We had machines doing (and undoing) cryptography in the 40s (not just enigma). So no reason it had to be by hand, even in the 70s. $\endgroup$ – Arthur Aug 14 '19 at 14:28
  • $\begingroup$ @Arthur that's a good point! When I say "by hand" I really mean without electronics. $\endgroup$ – Captain Man Aug 14 '19 at 14:32
  • $\begingroup$ @Moo Yes, I am aware, but the idea of asymmetric/public key crypto is very new (considering the entirety of history). $\endgroup$ – Captain Man Aug 14 '19 at 14:33
  • $\begingroup$ @Moo In summary, two distinct parties came upon the idea at roughly the same time in the 1970's. en.wikipedia.org/wiki/Public-key_cryptography#History Whether or not it existed (long) before and was in use is out of scope of this question and sounds more like a conspiracy theory. (But given the nature of wanting to keep secrets secret, it wouldn't be the craziest thing to suggest! ;) ) $\endgroup$ – Captain Man Aug 14 '19 at 14:41
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I think that a system like RSA would have been impractical in pre-computer days. How to generate large enough primes? There were tables for the smaller primes, but your opponent has the same tables, so then trial division would be a threat...

Also, modular exponentiation is no party to do by hand either. And encoding a message to a number is awkard too. I posit that it's impractical to do by hand for parameters that would have been considered safe.

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My hypothesis is a bit different. From Euclid's ''Elements'' enough number theory (gcd, lcm) has been available to introduce (with some research) the theory of the RSA algorithm. The necessity to use cryptography can be seen from the Caesar cipher. Some handcrafting could have led to some larger primes and encrypting/decrypting via modular arithmetic would have not been a big deal due to successive multiplication and reduction.

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