API

Linear System of Equations

Local

This module contains pure numpy implementation of the secure LSE algorithm.

secure_mask(A[, Q, P, Z, l, p, q])	Perform secure masking Q @ (A + Z) @ P.
slse_transformation(A, b, l)	Performs SLSE Transformation to the input problem.
ppcgm(Ap, bp, l[, tol])	Performs Privacy Preserving Conjugate Gradient Method (PPCGM).
solve(A, b[, tol])	Solve any linear system of equations using the proposed algorithm.

secout.LSE.local.secure_mask(A, Q=None, P=None, Z=None, l=16, p=8, q=4)

Perform secure masking Q @ (A + Z) @ P.

Parameters

A(M, N) array_like

The array to be masked

Q(M, M) array_like, optional

Row permutation matrix. If Q is not supplied, a random permutation matrix of corresponding shape is generated.

P(N, N) array_like, optional

Column permutation matrix. If P is not supplied, a random permutation matrix of corresponding shape is generated.

Z(M, N) array_like, optional

Additive noise matrix. If Z is not supplied, a random additive noise of A.shape is generated

lint, optional

Parameter for additive noise, assuming that the value of A is within (-2^l, 2^l) (the default is 16)

pint, optional

parameter for additive noise (the default is 8).

qint, optional

parameter for additive noise (the default is 4).

Returns

(M, N) array_like

The result of the secure mask Q @ (A + Z) @ P

Z(M, N) array_like

Additive noise

Q(M, M) array_like

Row permutation matrix

P(N, N) array_like

Column permutation matrix

secout.LSE.local.slse_transformation(A, b, l)

Performs SLSE Transformation to the input problem.

Computes \(A.T A\) and \(A.T b\) using the proposed secure LSE transformation using local computational resources.

Parameters

A(M, N) matrix_like

Coefficient matrix to the linear system of equations

b(M,) matrix_like

Constant matrix to the linear system of equations

lint

Constraint for A: The values in A must be within \((-2^l, 2^l)\)

Returns

Ap(N, N) ndarray

The transformed coefficient matrix. \(A.T A\)

bp(N,) ndarray

The transformed constant matrix. \(A.T b\)

secout.LSE.local.ppcgm(Ap, bp, l, tol=1e-05)

Performs Privacy Preserving Conjugate Gradient Method (PPCGM).

Computes the result of the input linear system using the proposed PPCGM with local computational resources. The input linear system must be nonsingular, symmetric and positive definite.

Parameters

Ap(N, N) array_like

Coefficient matrix that is nonsingular, symmetric and positive definite.

bp(N,) array_like

Constant matrix

lint

Constraint for A: The values in A must be within \((-2^l, 2^l)\)

tolfloat, optional

The stopping threshold for PPCGM (default is 1e-5)

Returns

x(N,) array_like

The solution to the linear system computed by PPCGM

secout.LSE.local.solve(A, b, tol=1e-05)

Solve any linear system of equations using the proposed algorithm.

Transform the input A and b using SLSE_transformation and compute the result using PPCGM.

Parameters

A(M, N) matrix_like

Coefficient matrix to the linear system of equations

b(M,) matrix_like

Constant matrix to the linear system of equations

tolfloat, optional

The stopping threshold for PPCGM (default is 1e-5)

Returns

x(N,) array_like

The solution to the linear system computed by PPCGM

Dask

class secout.LSE.DaskLSE(A, b, l=16, p=6, q=3, remote=None, local=None)

Secure solver for linear system of equation.

Solves the specified linear system of equation by exploiting local and remote computational resources using the proposed algorithms.

Parameters

A: (M, N) array_like

The coefficient matrix of the linear system to be solved

b: (M,) matrix_like

The constant matrix of the linear system to be solved

l: int, optional

Parameter for additive noise, assuming that the value of A is within (-2^l, 2^l) (the default is 16)

p: int, optional

parameter for additive noise (the default is 8).

q: int, optional

parameter for additive noise (the default is 4).

remote: dask.distributed.Client

The client instance represents remote resources

local: dask.distributed.Client

The client instance represents local resources

See also

dask.distributed.Client

Attributes

Ap(N, N) array_like

Transformed coefficient matrix

bp(N, ) array_like

Transformed constant matrix

x(N,) array_like

Solution for the input problem

Methods

denormalize_problem()	Recover coefficient A and constant b to de-normalized form
normalize_problem()	Normalize the coefficient matrix A and constant matrix b
ppcgm([tol])	Performs Privacy Preserving Conjugate Gradient Method (PPCGM).
secure_mask(A[, Q, P, Z])	Perform secure masking Q @ (A + Z) @ P.
slse_transformation()	Performs SLSE transformations to the given problem.
solve([tol])	Solve any linear system of equations using the proposed algorithm.

denormalize_problem()

Recover coefficient A and constant b to de-normalized form

Returns

None

normalize_problem()

Normalize the coefficient matrix A and constant matrix b

The normalization is based on the upper and lower bound of A.

Returns

None

ppcgm(tol=1e-05)

Performs Privacy Preserving Conjugate Gradient Method (PPCGM).

The result is saved as a instance attribute x.

Parameters

tol: float, optional

The stopping threshold for PPCGM (default is 1e-5)

Returns

None

secure_mask(A, Q=None, P=None, Z=None)

Perform secure masking Q @ (A + Z) @ P.

Parameters

A: (M, N) array_like

The array to be masked

Q: (M, M) array_like, optional

Row permutation matrix. If Q is not supplied, a random permutation matrix of corresponding shape is generated.

P: (N, N) array_like, optional

Column permutation matrix. If P is not supplied, a random permutation matrix of corresponding shape is generated.

Z: (M, N) array_like, optional

Additive noise matrix. If Z is not supplied, a random additive noise of A.shape is generated

Returns

(M, N) array_like

The result of the secure mask Q @ (A + Z) @ P

Z: (M, N) array_like

Additive noise

Q: (M, M) array_like

Row permutation matrix

P: (N, N) array_like

Column permutation matrix

slse_transformation()

Performs SLSE transformations to the given problem.

Computes \(A.T A\) and \(A.T b\) using the proposed secure LSE transformation. The results are saved as instance attributes Ap and bp.

Returns

None

solve(tol=1e-05)

Solve any linear system of equations using the proposed algorithm.

Transform the input A and b using SLSE_transformation and compute the result using PPCGM.

Parameters

tol: float, optional

The stopping threshold for PPCGM (default is 1e-5)

Returns

None

Quadratic Programming

Dask

This module contains

class secout.QP.DaskQP(Q, b, A, c, remote=None, local=None)

Secure Quadratic Programming solver

See also

dask.distributed.Client

Methods

dual_formulation
secure_mask

dual_formulation()

secure_mask(H, V=None, T=None)