what are the encryption algorithm used for secint function

[gro41]

what are the encryption algorithm used for secint function

[lschoe]

The short answer is: Shamir secret sharing.

[spyder73]

And what is the degree of the polynomial chosen?
If, N = amount of parties - is the degree of the polynomial then t = N-1, so that all parties are necessary for the reconstruction of the secret?
or is it t = N/2, since

The MPC protocols are based on Shamir’s threshold secret sharing scheme and withstand passive adversaries controlling less than half of the parties.

Best regards
Spyder

[lschoe]

Hi @spyder73. So, for $m$ parties tolerating at most $t$ corrupt parties, $t<m/2$ is required, which can be phrased as "an adversary controlling less than half of the parties." This enables the use of Shamir secret sharing for secure multiplication of two secret-shared values, which involves a product polynomial of double degree $2t$ shared between $m$ parties. Such a product polynomial of degree $2t$ can only be reconstructed from $2t+1$ shares, which is another way to understand why $m\geq2t+1$, which is equivalent to $t<m/2$, is required.

To tolerate $t=1$ corrupt party we thus need $m\geq3$ parties, which means that we have an honest majority.

[spyder73]

thank you very much! this means the protocol "only" functions with an honest majority, because if we have less we can not reconstruct the secret?

[lschoe]

Right, one wouldn't be able to reconstruct any output after at least one secure multiplication has been performed. If we only do secure additions then $t$ can be anything between 0 and $m-1$ , but that's not very interesting. Also note that we assume passively corrupt parties (a.k.a. semi-honest or honest-but-curious parties); to withstand $t$ actively corrupt parties one generally requires $t<m/3$.