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: SupportsSerialization

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

class SerializedIntegerShares[source]¶

Bases: TypedDict

Class which contains the information of the integer shares from which deserialization is possible.

degree: int¶

scaling: int¶

scheme: SerializedShamirSecretSharingIntegers¶

shares: dict[int, int]¶

__add__(other)[source]¶

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.

__eq__(other)[source]¶

Compare equality between this IntegerShares and the other object.

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

__mul__(other)[source]¶

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.

static deserialize(obj, **_kwargs)[source]¶

Deserialization function for the integer shares and corresponding scheme, which will be passed to the communication module

Parameters:

obj (SerializedIntegerShares) – serialization of the integer shares.
**_kwargs (Any) – optional extra keyword arguments

Return type:

IntegerShares

Returns:

Deserialized IntegerShares object.

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(**_kwargs)[source]¶

Serialization function for the integer shares and corresponding scheme, which will be passed to the communication module

Parameters:: **_kwargs (Any) – optional extra keyword arguments
Return type:: SerializedIntegerShares
Returns:: Dictionary containing the serialization of this IntegerShare object.

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

Bases: SupportsSerialization

Class with Shamir Secret sharing functionality over the integers

class SerializedShamirSecretSharingIntegers[source]¶

Bases: TypedDict

Class which contains the information of the shamir secret share from which deserialization is possible.

kappa: int¶

max_int: int¶

number_of_parties: int¶

polynomial_degree: int¶

__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

static deserialize(obj, **_kwargs)[source]¶

Deserialization function for the shamir secret sharing integers scheme, which will be passed to the communication module

Parameters:

obj (SerializedShamirSecretSharingIntegers) – serialization of a shamir secret sharing integers scheme.
**_kwargs (Any) – optional extra keyword arguments

Return type:

ShamirSecretSharingIntegers

Returns:

Deserialized ShamirSecretSharingInteger scheme.

serialize(**_kwargs)[source]¶

Serialization function for the shamir secret sharing integers scheme, which will be passed to the communication module

Parameters:: **_kwargs (Any) – optional extra keyword arguments
Return type:: SerializedShamirSecretSharingIntegers
Returns:: Dictionary containing the serialization of this ShamirSecretSharingIntegers scheme.

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