shamir.shamir module¶

Utility for Shamir secret sharing.

class shamir.shamir.ShamirSecretSharingScheme(modulus, number_of_parties, polynomial_degree)[source]¶

Bases: object

Class with Shamir Secret sharing functionality.

__eq__(other)[source]¶

Compare equality between this ShamirSecretSharingScheme and the other object.

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

__init__(modulus, number_of_parties, polynomial_degree)[source]¶

Initialize a $t$-out-of-$n$ secret sharing scheme where

$t$ = text{polynomial_degree} + 1$
$n$ = text{number_of_parties}$

Note that polynomial_degree is the same as the corruption threshold.

Parameters:

modulus (int) – prime modulus of the coefficients in the polynomials used to create shares
number_of_parties (int) – number of shares that need to be created for each sharing
polynomial_degree (int) – degree of the polynomials used to create shares

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:: ShamirShares
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

class shamir.shamir.ShamirShares(shamir_sss, shares)[source]¶

Bases: object

Class that keeps track of the shares for a certain value

__add__(other)[source]¶

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

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

__mul__(other)[source]¶

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

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

__rmul__(other)[source]¶

Multiply the shares belonging to this value with a given scalar integer or IntegerShares object. Note: This operation returns a Shamir sharing which inherits the statistical security of the integer sharing and should therefore only be used with caution.

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

__str__()[source]¶

String formatted version of this ShamirShares object.

Return type:: str
Returns:: Pretty string.

__sub__(other)[source]¶

Subtract other ShamirShares (subtrahend) from these ShamirShares(minuend).

Parameters:: other (ShamirShares) – Shares to be subtracted from these shares.
Raises:: ValueError – In case a different secret sharing scheme was used.
Return type:: ShamirShares
Returns:: New ShamirShares object representing the difference between these shares and other.

reconstruct_secret()[source]¶

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

Raises:: ValueError – In case not enough shares are known to reconstruct the secret.
Return type:: int
Returns:: original secret

serialize()[source]¶

Serialization function

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