Is it possible to device lightweight (i.e. without asymmetric crypto and PKI; and without third party Trent) provably secure (in the exact security sense) scheme? Were there any attempts? Is it possible to make entity authentication using only one pre-shared secret key without MitM attacks?

Some remarks. By exact security I mean concrete security approach (by Bellare and Rogaway).

By entity authentication I mean to prove that it is me who interacts with device. MAC is not an option because everyone who can intercept my message can pretend that he is me actually.

  • $\begingroup$ The question is not clear to me. Would you please clarify what do you mean without public key infrastructure and secure against MitM attack? I suspect you wanna use the symmetric key schemes to authenticate a message and the most relevant approach is the MAC (Message Authentication Code). $\endgroup$
    – Mahdi
    Nov 1 '19 at 10:24
  • $\begingroup$ Is "device" intended to be "devise"? Do you use "lightweight " in the sense it has in the tag (Small and/or fast ciphers and other cryptographic primitives designed for use in constrained environments, such as embedded MCUs and smart cards)? Bellare and Rogaway's concrete security assumes a crypto primitive modeled as PRP or PRF; are you willing to assume that? If so, is there anything wrong with the classical entity authentication using challenge/PRF/response//check? $\endgroup$
    – fgrieu
    Nov 1 '19 at 10:47
  • $\begingroup$ Yes, by lightweight I mean these TAG things. What do you mean by "classical" challenge-response? Imagine the situation: TAG wants to prove me that it posesses some secret key K. I generate random number R as challenge and send it to TAG. I want to get back something of the form E_K(R), right? But it is possible that there is some adversary, who can intercept messages. Then he can "catch" the message E_K(R) from TAG and pretend that it was him who generate this message, and there is no method for me to check who really generate the response. $\endgroup$ Nov 1 '19 at 16:36