f5

class cryptographic_estimators.MQEstimator.MQAlgorithms.f5.F5(problem: MQProblem, **kwargs)

Bases: MQAlgorithm

Construct an instance of the F5 complexity estimator.

Note

The complexity formula is taken from Proposition 1 in [BFP09].

Parameters:

• problem (MQProblem) – The MQProblem object including all necessary parameters.

• h (int, optional) – The external hybridization parameter. Defaults to 0.

• w (float, optional) – The linear algebra constant. Defaults to 2.81.

• degrees (list, tuple, optional) – A list or tuple of the degrees of the polynomials. Defaults to [2] * m.

Examples

>>> from cryptographic_estimators.MQEstimator.MQAlgorithms.f5 import F5
>>> from cryptographic_estimators.MQEstimator.mq_problem import MQProblem
>>> E = F5(MQProblem(n=10, m=5, q=3))
>>> E
F5 estimator for the MQ problem with 10 variables and 5 polynomials

property attack_type

Returns the attack type of the algorithm.

property complexity_type

Returns the attribute _complexity_type.

degree_of_polynomials()

Return a list of degree of the polynomials.

Examples

>>> from cryptographic_estimators.MQEstimator.MQAlgorithms.f5 import F5
>>> from cryptographic_estimators.MQEstimator.mq_problem import MQProblem
>>> E = F5(MQProblem(n=10, m=5, q=3))
>>> E.degree_of_polynomials()
[2, 2, 2, 2]

get_optimal_parameters_dict()

Returns the optimal parameters dictionary.

get_reduced_parameters()

has_optimal_parameter()

Return True if the algorithm has optimal parameter.

Tests:

>>> from cryptographic_estimators import BaseAlgorithm, BaseProblem
>>> BaseAlgorithm(BaseProblem()).has_optimal_parameter()
False

linear_algebra_constant()

Returns the linear algebra constant.

Tests:

>>> from cryptographic_estimators.MQEstimator.mq_algorithm import MQAlgorithm
>>> from cryptographic_estimators.MQEstimator.mq_problem import MQProblem
>>> MQAlgorithm(MQProblem(n=10, m=5, q=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.

npolynomials_reduced()

Return the number of polynomials after applying the Thomae and Wolf strategy.

Returns:

The number of polynomials after applying the Thomae and Wolf strategy.

Return type:

int

Tests:

>>> from cryptographic_estimators.MQEstimator.mq_algorithm import MQAlgorithm
>>> from cryptographic_estimators.MQEstimator.mq_problem import MQProblem
>>> MQAlgorithm(MQProblem(n=5, m=10, q=2)).npolynomials_reduced()
10
>>> MQAlgorithm(MQProblem(n=60, m=20, q=2)).npolynomials_reduced()
18

nvariables_reduced()

Return the number of variables after fixing some values.

Tests:

>>> from cryptographic_estimators.MQEstimator.mq_algorithm import MQAlgorithm
>>> from cryptographic_estimators.MQEstimator.mq_problem import MQProblem
>>> MQAlgorithm(MQProblem(n=5, m=10, q=2)).nvariables_reduced()
5
>>> MQAlgorithm(MQProblem(n=25, m=20, q=2)).nvariables_reduced()
20

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.