0
$\begingroup$

Can Shamir's secret sharing work on any size of key?

$\endgroup$

1 Answer 1

2
$\begingroup$

Can Shamir's secret sharing work on any size of key?

Yes; you have three options (of course, you might count the last one as cheating):

  • Shamir's secret sharing works with arbitrarily large fields. For example, if the secret is a 4k RSA private key, you can pick a prime larger than 4096 bits, and do secret sharing using that prime. The only drawback is that doing arithmetic in a field that large is annoying; it is quite doable

  • You can divide your secret into chunks and secret share each chunk individually. For example, if you need to distribute no more than 255 shares, you can divide your 512 byte secret into 512 individual bytes, and perform a secret sharing on each byte. Secret sharing individual bytes is convenient; you can do everything using $GF(2^8)$ arithmetic, which is not that difficult [1]. It is perfectly safe to use the same $x$ coordinate to all the secrets you give to a party; however the secret coefficients for each byte needs to be generated independently.

  • You can pick your favorite symmetric crypto (e.g. AES), and secret share the AES key; then, use AES to encrypt your huge secret, and you're good to do - to recover the huge secret, they would need to reconstruct the AES key using their shares, and then decrypt the public ciphertext.

[1]: Even though, for some odd reason, it is rarely taught in grade school...

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.