shamir.shamir_secret_sharing_integers module

Utility for Shamir secret sharing over the integers.

class shamir.shamir_secret_sharing_integers.IntegerShares(shamir_sss, shares, degree, scaling)[source]

Bases: object

Class that keeps track of the shares for a certain value that is secret shared over the integers.

Add the shares belonging to the two given IntegerShares values together.

Parameters:: other (IntegerShares) – Shares to be added to these shares.
Raises:: ValueError – In case a different secret sharing scheme was used.
Return type:: IntegerShares
Returns:: New IntegerShares object where the shares have been added together.

Multiply the shares belonging to the two given IntegerShares values together. Only possible when both schemes are the same.

Parameters:: other (IntegerShares) – Shares to be multiplied with these shares.
Return type:: IntegerShares
Returns:: New IntegerShares object where the shares have been multiplied together.

__rmul__(other)[source]

Multiply the shares belonging to this value with a given scalar integer or ShamirShares object.

Parameters:: other (Any) – ShamirShares or scalar to be multiplied with these shares.
Return type:: Any
Returns:: New IntegerShares object where the shares have been multiplied together.

reconstruct_secret(modulus=0)[source]

Function that uses the shares from other parties to reconstruct the secret

Parameters:: modulus (int) – the modulus to use
Raises:: ValueError – In case not enough shares are present to reconstruct the secret.
Return type:: int
Returns:: original secret

serialize()[source]

Serialization function

Return type:: Dict[str, Union[int, Dict[int, int], Dict[str, int], Dict[str, Dict[str, int]]]]
Returns:: json object containing the necessary information to deserialize

class shamir.shamir_secret_sharing_integers.ShamirSecretSharingIntegers(kappa=40, max_int=5, number_of_parties=10, polynomial_degree=4)[source]

Bases: object

Class with Shamir Secret sharing functionality over the integers

__eq__(other)[source]

Compare equality between this ShamirSecretSharingIntegers and the other object.

Parameters:: other (object) – Object to compare with.
Return type:: bool
Returns:: Boolean stating (in)equality

__init__(kappa=40, max_int=5, number_of_parties=10, polynomial_degree=4)[source]

Initialize a secret sharing over the integers

Parameters:

kappa (int) – statistical security parameter
max_int (int) – Value that together with kappa and number_of_parties determines the interval from which polynomial coefficients are randomly sampled. In general, the Paillier modulus is used for max.
number_of_parties (int) – number of shares that need to be created for each sharing
polynomial_degree (int) – degree of polynomials used to share secrets

serialize()[source]

Serialization function

Return type:: Dict[str, int]
Returns:: json object containing the necessary information to deserialize

share_secret(secret)[source]

Function that creates shares of a value for each party

Parameters:: secret (int) – secret to be shared
Return type:: IntegerShares
Returns:: sharing of the secret

property van_der_monde: List[List[int]]

Vandermonde matrix for evaluation of polynomials at points [1,..,n]. This essentialy creates a matrix that precomputes i**j for all possible i**j that are needed for the evaluation of sharing polynomials. We now have that i**j = Vm[i][j]. To evaluate a polynomial p(x) = a0 + a1 * x + … + ad * x**d we can simply compute a0 * Vm[x][0] + a1 * Vm[x][1] + … + ad * Vm[x][d].

Returns:: A VanDerMonde matrix of dimpensions self.polynomial_degree + 1 x self.number_of_parties