matrix_inverse.matrix_inverse module

The code below is based on the demo ridgeregression.py from the MPyC library on Feb 26th, 2020, as implemented by Frank Blom. https://github.com/lschoe/mpyc/blob/2de1dd76db632bdc2a48acfbbaab841fa73cf8bd/demos/ridgeregression.py. The underlying theory is published in the paper ‘Efficient Secure Ridge Regression from Randomized Gaussian Elimination’ by Frank Blom, Niek J. Bouman, Berry Schoenmakers, and Niels de Vreede, presented at TPMPC 2019 by Frank Blom. See https://eprint.iacr.org/2019/773 (or https://ia.cr/2019/773).

matrix_inverse.matrix_inverse.bareiss_gaussian_elimination(prime_field, matrix)

Bareiss-like integer-preserving Gaussian elimination adapted for Zp. Using exactly one modular inverse in Zp per row of the provided matrix. Apart from variable names, this is an unmodified copy of the code in the demo.

Parameters:

• prime_field (Type[PrimeFieldElement]) – Zp

• matrix (List[List[TypeVar(SecureNumberType, bound= SecureNumber)]]) – input matrix containing secure values

Return type:

Tuple[List[List[TypeVar(SecureNumberType, bound= SecureNumber)]], TypeVar(SecureNumberType, bound= SecureNumber)]

Returns:

inverse matrix of the input matrix

matrix_inverse.matrix_inverse.convert_matrix_to_large_sec_fxp(input_matrix)

Convert a matrix with secure elements to a matrix with secure fixed points with twice as large bit lengths.

Parameters:

input_matrix (List[SecureNumber]) – input matrix

Return type:

List[SecureFixedPoint]

Returns:

the input matrix with each element converted to a fixed point number with large bit length

matrix_inverse.matrix_inverse.determine_order_secfld(bit_length, dimension)

Function to determine the minimal order of a field, based on the bit length and dimension. Based on main() and paper

Parameters:

• bit_length (int) – bit length of each element in the field

• dimension (int) – dimension of the original matrix

Return type:

int

Returns:

minimal order

matrix_inverse.matrix_inverse.matrix_inverse(input_matrix)

Function that securely computes the inverse of a matrix with secure fixed point elements.

Parameters:

input_matrix (List[List[SecureFixedPoint]]) – input matrix

Return type:

List[List[SecureFixedPoint]]

Returns:

inverse of the input matrix

matrix_inverse.matrix_inverse.random_matrix_determinant(secure_object_type, dimension)

Generate a random d x d matrix from the set of LU decomposable matrices over a given field. Apart from variable names, this is an unmodified copy of the code in the demo.

Parameters:

• secure_object_type (Type[TypeVar(SecureNumberType, bound= SecureNumber)]) – Secure type

• dimension (int) – The dimension d

Return type:

Tuple[List[List[TypeVar(SecureNumberType, bound= SecureNumber)]], TypeVar(SecureNumberType, bound= SecureNumber)]

Returns:

A random invertible matrix and the determinant of its inverse

matrix_inverse.matrix_inverse.reciprocal_sec_num(sec_num)

compute the reciprocal of a secure number.

Parameters:

sec_num (TypeVar(SecureNumberType, bound= SecureNumber)) – secure number

Return type:

TypeVar(SecureNumberType, bound= SecureNumber)

Returns:

the reciprocal of the input

matrix_inverse.matrix_inverse.scale_and_convert_matrix_to_sec_fld(input_matrix)

Function that scales and converts each element of a matrix with secure fixed point elements to a secure integer.

Parameters:

input_matrix (List[List[SecureFixedPoint]]) – matrix containing secure fixed point numbers

Return type:

List[List[SecureFixedPoint]]

Returns:

matrix containing secure integers

matrix_inverse.matrix_inverse.scale_and_convert_to_secint(to_convert)

Function that scales and converts secure fixed points to secure integers with the same modulus. Effectively removes the point in the fixed point notation.

Parameters:

to_convert (Union[List[SecureNumber], SecureNumber]) – secure fixed point or list of secure fixed points

Return type:

Union[List[SecureInteger], SecureInteger]

Returns:

secure integer or list of secure integers (depending on the input)