hybrid_f5¶

class cryptographic_estimators.MQEstimator.MQAlgorithms.hybrid_f5.HybridF5(problem: MQProblem, **kwargs)¶

Bases: MQAlgorithm

Construct an instance of HybridF5.

HybridF5 is an algorithm to solve systems of polynomials over a finite field proposed in [BFP09], [BFP12]. The algorithm is a tradeoff between exhaustive search and Groebner bases computation. The idea is to fix the value of, say, $k$ variables and compute the Groebner bases of $q^{k}$ subsystems, where $q$ is the order of the finite field. The Grobner bases computation is done using F5 algorithm.

Notes

See also: mpkc.algorithms.f5.F5, class to compute the complexity of F5 algorithm.

Parameters:

problem (MQProblem) – The MQProblem object including all necessary parameters.
h (int, optional) – The external hybridization parameter (default: 0).
w (float, optional) – The linear algebra constant (2 <= w <= 3) (default: 2.81).
degrees (list, optional) – A list/tuple of degree of the polynomials (default: [2]*m, i.e. quadratic system).

Examples

>>> from cryptographic_estimators.MQEstimator.MQAlgorithms.hybrid_f5 import HybridF5
>>> from cryptographic_estimators.MQEstimator.mq_problem import MQProblem
>>> H = HybridF5(MQProblem(q=256, n=5, m=10))
>>> H
HybridF5 estimator for the MQ problem with 5 variables and 10 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.hybrid_f5 import HybridF5
>>> from cryptographic_estimators.MQEstimator.mq_problem import MQProblem
>>> H = HybridF5(MQProblem(q=31, n=5, m=5), degrees=[3]*5)
>>> H.degree_of_polynomials()
[3, 3, 3, 3, 3]

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

k()¶

Return the optimal k.

Examples

>>> from cryptographic_estimators.MQEstimator.MQAlgorithms.hybrid_f5 import HybridF5
>>> from cryptographic_estimators.MQEstimator.mq_problem import MQProblem
>>> H = HybridF5(MQProblem(q=31, n=23, m=23))
>>> H.k()
5

Tests:

>>> H = HybridF5(MQProblem(q=256, n=10, m=10))
>>> H.k()
1
>>> H = HybridF5(MQProblem(q=256, n=20, m=10))
>>> H.k()
1

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).

quantum_time_complexity()¶: Return quantum gate complexity

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.