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We all know about public-key cryptosystems, and we know some of these are computationally secure (for the time being, of course).

Are there any algorithms out there which allow safe communication between peers in a non “public/private” key fashion? If so, I would like to know some of these. If not, does any kind of formal demonstration of the infeasibility of such algorithms exist?

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  • $\begingroup$ Would you accept quantum crypto? $\endgroup$
    – SEJPM
    Commented Jun 19, 2015 at 20:56
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    $\begingroup$ Or simply symmetric crypto? I don't see anything in the question that rules that out. $\endgroup$
    – Stephen Touset
    Commented Jun 19, 2015 at 20:57
  • $\begingroup$ Would you accept TLS-PSK with TLS_PSK_WITH_AES_128_GCM_SHA256? RFC 5487 $\endgroup$
    – SEJPM
    Commented Jun 19, 2015 at 20:59
  • $\begingroup$ Something like TLS-PSK, but without pre-shared keys. I'm interested in the demonstration of infeasibility of secure communications with these constraints. $\endgroup$
    – Alberto Fernández
    Commented Jun 19, 2015 at 21:04
  • $\begingroup$ The whole point of public keys and signature is to verify identity of the parties and to agree on keys without trusted third parties. PKI allows the CA to sign keys offline and thus associate keys with entities. If you're willing to assume an online trusted third party, which shares a symmetric key with every participant, you indeed wouldn't need all this public key stuff. $\endgroup$
    – SEJPM
    Commented Jun 19, 2015 at 21:18

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The obvious answer is symmetric keys. You'll find that this is actually what asymmetric keys end up used for, exchanging symmetric keys. If you trust someone who gives you a key, and you can trust that no one else has it, that's about as secure as it gets. The difficult of satisfying those requirements is why we have asymmetric keys.

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