uov_problem

class cryptographic_estimators.UOVEstimator.uov_problem.UOVProblem(n: int, m: int, q: int, **kwargs)

Bases: BaseProblem

Construct an instance of UOVProblem.

Parameters:

• n (int) – Number of variables

• m (int) – Number of polynomials

• q (int) – Order of the finite field

• **kwargs –

  Additional keyword arguments

  theta (float, optional) - Exponent of the conversion factor. Defaults to 2. If 0 <= theta <= 2, every multiplication in GF(q) is counted as log2(q) ^ theta binary operation. If theta = None, every multiplication in GF(q) is counted as 2 * log2(q) ^ 2 + log2(q) binary operation.

  cost_one_hash (int, optional) - Bit complexity of computing one hash value. Defaults to 17.

  memory_bound (float, optional) - Maximum allowed memory to use for solving the problem. Defaults to inf.

property cost_one_hash

Returns the bit-complexity of computing one hash.

expected_number_solutions()

Returns the expected number of existing solutions to the problem.

get_parameters()

Return the optimizations parameters.

Tests:

>>> from cryptographic_estimators.UOVEstimator.uov_problem import UOVProblem
>>> E = UOVProblem(n=14, m=8, q=4)
>>> E.get_parameters()
[14, 8, 4]

hashes_to_basic_operations(number_of_hashes: float)

Return the number basic operations corresponding to a certain amount of hashes.

Parameters:

number_of_hashes (float) – Number of hashes (logarithmic)

npolynomials()

Return the number of polynomials.

nvariables()

Return the number of variables.

order_of_the_field()

Return the order of the field.

property theta

Returns the runtime of the algorithm.

to_bitcomplexity_memory(elements_to_store: float)

Return the memory bit-complexity associated to a given number of elements to store.

Parameters:

elements_to_store (float) – Number of memory operations (logarithmic)

to_bitcomplexity_time(basic_operations: float)

Return the bit-complexity corresponding to a certain amount of basic operations.

Parameters:

basic_operations (float) – Number of basic operations (logarithmic)