mr_algorithm

class cryptographic_estimators.MREstimator.mr_algorithm.MRAlgorithm(problem: MRProblem, **kwargs)

Bases: BaseAlgorithm

Base class for MR algorithms complexity estimator.

Parameters:

  • problem (MRProblem) – MRProblem object including all necessary parameters

  • **kwargs –

    Additional keyword arguments

    w (int, optional) - linear algebra constant. Defaults to 3.

Examples

>>> from cryptographic_estimators.MREstimator.mr_algorithm import MRAlgorithm
>>> from cryptographic_estimators.MREstimator.mr_problem import MRProblem
>>> E = MRAlgorithm(MRProblem(q=7, m=9, n=10, k=15, r=4))
>>> E
BaseMRAlgorithm estimator for the MinRank problem with (q, m, n, k, r) = (7, 9, 10, 15, 4)
property attack_type

Returns the attack type of the algorithm.

property complexity_type

Returns the attribute _complexity_type.

cost_reduction(a, lv)

Return the cost of computing the reduced instance.

The reduced instance is obtained after one guess of a kernel vectors.

Parameters:

a – Number of vectors to guess in the kernel of the low-rank matrix

get_optimal_parameters_dict()

Returns the optimal parameters dictionary.

get_problem_parameters_reduced(a, lv)

Return the problem parameters of the reduced instance.

Returns the problem parameters after guessing a kernel vectors and lv entries in the solution vector.

Args: - a – no. of vectors to guess in the kernel of the low-rank matrix - lv – no. of entries to guess in the solution vector

has_optimal_parameter()

Return True if the algorithm has optimal parameter.

Tests:
>>> from cryptographic_estimators import BaseAlgorithm, BaseProblem
>>> BaseAlgorithm(BaseProblem()).has_optimal_parameter()
False
hybridization_factor(a, lv)

Return the logarithm of the number of reduced instances to be solved.

Parameters:

  • a – No. of vectors to guess in the kernel of the low-rank matrix.

  • lv – No. of entries to guess in the solution vector.

linear_algebra_constant()

Return the linear algebra constant.

Tests:
>>> from cryptographic_estimators.MREstimator.mr_algorithm import MRAlgorithm
>>> from cryptographic_estimators.MREstimator.mr_problem import MRProblem
>>> MRAlgorithm(MRProblem(q=7, m=9, n=10, k=15, r=4), w=2).linear_algebra_constant()
2
property memory_access

Returns the attribute _memory_access.

memory_access_cost(mem: float)

Returns the memory access cost (in logarithmic scale) of the algorithm per basic operation.

Parameters:

mem (float) – Memory consumption of an algorithm.

Returns:

Memory access cost in logarithmic scale.

Return type:

float

Note

memory_access: Specifies the memory access cost model (default: 0, choices: 0 - constant, 1 - logarithmic, 2 - square-root, 3 - cube-root or deploy custom function which takes as input the logarithm of the total memory usage)

memory_complexity(**kwargs)

Return the memory complexity of the algorithm.

Parameters:

**kwargs –

Arbitrary keyword arguments.

optimal_parameters - If for each optimal parameter of the algorithm a value is provided, the computation is done based on those parameters.

optimal_parameters()

Return a dictionary of optimal parameters.

Tests:
>>> from cryptographic_estimators import BaseAlgorithm, BaseProblem
>>> BaseAlgorithm(BaseProblem()).optimal_parameters()
{}
parameter_names()

Return the list with the names of the algorithm’s parameters.

Tests:
>>> from cryptographic_estimators import BaseAlgorithm, BaseProblem
>>> BaseAlgorithm(BaseProblem()).parameter_names()
[]
property parameter_ranges

Returns the set ranges for optimal parameter search.

Returns the set ranges in which optimal parameters are searched by the optimization algorithm (used only for complexity type estimate).

reset()

Resets internal state of the algorithm.

set_parameter_ranges(parameter: str, min_value: float, max_value: float)

Set range of specific parameter.

If optimal parameter is already set, it must fall in that range.

Parameters:

  • parameter (str) – Name of parameter to set

  • min_value (float) – Lowerbound for parameter (inclusive)

  • max_value (float) – Upperbound for parameter (inclusive)

set_parameters(parameters: dict)

Set optimal parameters to predifined values.

Parameters:

parameters (dict) – Dictionary including parameters to set (for a subset of optimal_parameters functions)

time_complexity(**kwargs)

Return the time complexity of the algorithm.

Parameters:

**kwargs –

Arbitrary keyword arguments.

optimal_parameters - If for each optimal parameter of the algorithm a value is provided, the computation is done based on those parameters.