How is prime p and the order of the finite field determined for thresha.random_split

[RetoKrummenacher]

Hi Berry,

Sorry for disturbing you again, but I was wondering how MPyC sets field.modulus and field.order used to create the Shamir Polynomials in thresha.random_split()

I saw that they are set to be the same in finfields.pGF and that the prime $p$ is determined with find_prime_root(l) with bit length l=bit_length+sec_param, defaulting to $62=32+30$ as defined in the get_arg_parser().

But not sure if that is really the case?

Thanks for a clarification.

[lschoe]

So, field.modulus and field.order are in general not the same. This is only true for prime order fields, which you are probably considering. For extension fields, we have that field.modulus is actually a polynomial (irreducible), and field.order is then a prime power (and there is also field.characteristic, which is always a prime number).

Functions like mpc.SecFld() and mpc.SecInt() create finite fields of the appropriate type, and the code for this is in the module mpyc.sectypes.

[RetoKrummenacher]

Thank you for the fast reply.

If I understand it correctly, if the parties are computing the sum of secure integers via mpc.input(secint(integer)), MPyC is using mpc.SecInt() as fields?

Those are prime order fields created with sectypes.SecInt calling sectypes._pfield, which finds a large prime number of given bit length via sectypes.find_prime_root() and creating the Galois field with finfields.pGF() where the order and the modulus are the same.
Those two are then used in thresha.random_split()?

[lschoe]

Right! So, if you set secint = mpc.SecInt(), then you can extract the corresponding field using field = secint.field. This will be a prime field, of which you can inspect field.modulus and field.order, which are both equal to the prime number used for secret sharing.

[RetoKrummenacher]

Thank you very much