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To my understanding, there are two "approaches" to t out of n threshold encryption. In both of them, n shares are given to different shareholders, and at least t of them must agree to "proceed". "Proceed" can take two different meanings: either the shares are the input to derive a secret that can be used to perform a traditional decryption (e.g. Shamir) or the shareholders produce a partial encryption that can be put together to generate the decryption (e.g. Damgård-Jurik).

I have found the first scenario to be known as secret sharing, but I am looking for a term to describe the second approach unambiguously. Does such term exist?

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I believe there is strong enough precedence for using the term threshold decryption for the second.

The abstract of this paper states:

A threshold decryption scheme is a multi-party public key cryptosystem that allows any sufficiently large subset of participants to decrypt a ciphertext, but disallows the decryption otherwise.

Sounds to me like what you are talking about. A search for "threshold decryption" turns up plenty of hits too.

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  • $\begingroup$ Perhaps it's more common to call it "Threshold encryption"? See for instance this paper by Boneh et al.. Anyway, I admit that "threshold decryption" is more precise, technically speaking. $\endgroup$
    – cygnusv
    Feb 19, 2016 at 15:57
  • $\begingroup$ @cygnusv Yeah, I've seen Threshold Encryption before too. Probably either works just as well. $\endgroup$
    – mikeazo
    Feb 19, 2016 at 16:20
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    $\begingroup$ A scheme supporting this is a "threshold encryption scheme" -- i.e., an encryption scheme of the threshold variety -- or just "threshold encryption" for short. But since the threshold part only comes into play during decryption, it's fine to refer to that process as "threshold decryption" $\endgroup$
    – Mikero
    Feb 19, 2016 at 16:29

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