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Given that I have a secret which I want to split into 2 parts (n=2) and require 2 parts to restore it (k=2), does it still make sense to use Shamir's Scheme or would a trivial scheme with XOR (generate a random string, same long as the secret, XOR those, random string and the XOR result become shares) be just as secure? Are there any benefits in using Shamir's Scheme in such case?

In general, what would be the recommended sharing scheme for this use case?

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Except for the extensibility (being able to latter add a third user), the trivial scheme with XOR works just as well as Shamir; the trivial scheme retains the following properties:

  • The length of each share is still as long as the original secret (in fact, you don't need to bother assigning share identifiers, which you have to with Shamir's scheme)

  • It is information theoretically secure.

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  • $\begingroup$ Thanks, @poncho that's exactly what I wanted to know! May I ask one more question - given the secret being shared is an RSA private key, and I have one share and the public key, is it possible to recover the full private key? $\endgroup$ – Tristan Tzara Jul 2 at 9:47
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    $\begingroup$ @TristanTzara: the secret sharing is informationally secure; that is, a single share gives no information (other than possibly length) about the secret. Hence, they can recover the private key from the share and the public key only if they can recover it from the public key only... $\endgroup$ – poncho Jul 2 at 13:45
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I would recommend Shamirs Secret sharing still because:

  • The length of each share will not exceed the length of the original secret data

  • If you decide to add more participants, but still require 2 shares to unlock then I believe this is possible.

  • It is information theoretically secure.

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