direct_attack

class cryptographic_estimators.UOVEstimator.UOVAlgorithms.direct_attack.DirectAttack(problem: UOVProblem, **kwargs)

Bases: UOVAlgorithm

Construct an instance of DirectAttack estimator.

The most straightforward attack against UOV, (and even against most of the MPKC cryptosystems) is the direct attack, where the attacker aims to solve an instance of the MQ problem associated with the public key [TW12].

Parameters:

  • problem (UOVProblem) – An instance of the UOVProblem class.

  • **kwargs –

    Additional keyword arguments.

    w (int) - Linear algebra constant (default: 2).

    h (int) - External hybridization parameter (default: 0).

    excluded_algorithms (list) - A list/tuple of MQ algorithms to be excluded (default: [Lokshtanov]).

    memory_access (int) - 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).

    complexity_type (int) - Complexity type to consider (0: estimate, 1: tilde O complexity, default: 0).

    bit_complexities (int) - Determines if complexity is given in bit operations or basic operations (default 1: in bit).

property attack_type

Returns the attack type of the algorithm.

property complexity_type

Returns the attribute _complexity_type.

get_fastest_mq_algorithm()
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
linear_algebra_constant()

Return the linear algebra constant.

Tests:
>>> from cryptographic_estimators.UOVEstimator.uov_algorithm import UOVAlgorithm
>>> from cryptographic_estimators.UOVEstimator.uov_problem import UOVProblem
>>> UOVAlgorithm(UOVProblem(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.

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.