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How can we modify classical cryptography system to provide non-repudiation?

I want to ensure non-repudiation in symmetric key cryptography so that we can find out who is sender of a particular message.As sender and receiver share the same key, we can't find out who the sender was.

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    $\begingroup$ Have both sides use hash based signatures to sign their messages? $\endgroup$ – poncho Apr 12 '16 at 17:38
  • $\begingroup$ Either yes or no both will work. You can answer from any perspective. $\endgroup$ – Shridhar R Kulkarni Apr 12 '16 at 17:56
  • $\begingroup$ I'm not sure whether you fully understand what poncho is meaning. I think he is referring to hash based signatures, which turn hashes into proper asymmetric digital signatures. $\endgroup$ – SEJPM Apr 12 '16 at 20:24
  • $\begingroup$ Okay. No, both the sides have not used hash based signatures to sign their messages. $\endgroup$ – Shridhar R Kulkarni Apr 12 '16 at 22:52

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