leon

class cryptographic_estimators.PEEstimator.PEAlgorithms.leon.Leon(problem: PEProblem, **kwargs)

Bases: PEAlgorithm

Complexity estimate of Leon’s algorithm [Leo82].

Estimates are adapted versions of the scripts derived in [Beu20] with the code accessible at https://github.com/WardBeullens/LESS_Attack

Parameters:

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

  • codewords_needed_for_success – Number of low word codewords needed for success (default = 100)

  • sd_parameters – Dictionary of parameters for SDFqEstimator used as a subroutine (default: {})

Examples

>>> from cryptographic_estimators.PEEstimator.PEAlgorithms import Leon
>>> from cryptographic_estimators.PEEstimator import PEProblem
>>> Leon(PEProblem(n=100,k=50,q=3))
Leon estimator for permutation equivalence problem with (n,k,q) = (100,50,3)
property attack_type

Returns the attack type of the algorithm.

property complexity_type

Returns the attribute _complexity_type.

get_optimal_parameters_dict()

Returns the optimal parameters dictionary.

has_optimal_parameter()

Return True if the algorithm has optimal parameter.

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

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.

w()

Return the optimal parameter w used in the algorithm optimization.

Examples

>>> from cryptographic_estimators.PEEstimator.PEAlgorithms import Leon
>>> from cryptographic_estimators.PEEstimator import PEProblem
>>> A = Leon(PEProblem(n=100,k=50,q=3))
>>> A.w()
20