sboxUv2 package

sboxUv2 is a package providing both all the algorithms relevant to the study of vectorial Boolean functions, in particular those intended to be used as S-boxes within symmetric cryptographic primitives.

A particular focus is put on efficiency: large parts of this library are written in C++, and multi-threading is used as much as possible.

Subpackages

• sboxUv2.algorithms package
  • Submodules
  • sboxUv2.algorithms.cython_functions module
    • BinLinearBasis
      • BinLinearBasis.add_to_span()
      • BinLinearBasis.basis_vectors()
      • BinLinearBasis.is_in_span()
      • BinLinearBasis.rank()
      • BinLinearBasis.span()
    • BinLinearMap_from_masks()
    • BinLinearMap_from_range_and_image()
    • F2LinearSystem
      • F2LinearSystem.add_equation()
      • F2LinearSystem.kernel_as_bits()
      • F2LinearSystem.kernel_as_bytes()
      • F2LinearSystem.rank()
      • F2LinearSystem.remove_solution()
    • complete_basis()
    • complete_basis_reversed()
    • extract_affine_bases()
    • extract_bases()
    • generating_BinLinearMap()
    • generating_BinLinearMap_r()
    • is_affine()
• sboxUv2.apn package
  • Subpackages
    • sboxUv2.apn.knownFunctions package
  • Submodules
  • sboxUv2.apn.cython_functions module
    • apn_ea_mugshot()
    • apn_ea_mugshot_from_spectra()
    • automorphisms_from_ortho_derivative()
    • ccz_equivalent_quadratic_function()
    • ea_mappings_from_ortho_derivative()
    • enumerate_ea_classes_apn_quadratic()
    • get_WalshZeroesSpaces_quadratic_apn()
    • ortho_derivative()
    • ortho_integral()
    • sigma_multiplicities()
  • sboxUv2.apn.database module
    • APNFunctions
      • APNFunctions.insert_full_ccz_equivalence_class()
      • APNFunctions.is_new()
      • APNFunctions.parse_function_from_row()
• sboxUv2.biblio package
  • Submodules
  • sboxUv2.biblio.references module
    • cite()
    • cite_as()
    • format_to_rst()
    • gen_full_biblio_rst()
    • open_bibliography()
    • who_to_cite()
• sboxUv2.ccz package
  • Subpackages
    • sboxUv2.ccz.affine_equivalence package
      • Submodules
      • sboxUv2.ccz.affine_equivalence.cython_functions module
  • Submodules
  • sboxUv2.ccz.cython_functions module
    • EA_mapping()
    • WalshZeroesSpaces
      • WalshZeroesSpaces.get_bases()
      • WalshZeroesSpaces.get_mappings()
      • WalshZeroesSpaces.image_by()
      • WalshZeroesSpaces.init_mappings()
      • WalshZeroesSpaces.thickness_spectrum()
    • affine_equivalences()
    • are_affine_equivalent()
    • are_ccz_equivalent()
    • are_cczl_equivalent()
    • are_ea_equivalent()
    • are_el_equivalent()
    • are_linear_equivalent()
    • ccz_block_decomposition()
    • ccz_equivalences()
    • ccz_equivalent_function()
    • cczl_equivalences()
    • ea_equivalences()
    • el_equivalences()
    • enumerate_ea_classes()
    • equivalences_from_lat()
    • get_WalshZeroesSpaces()
    • linear_equivalences()
    • thickness_spectrum()
    • up_to_constant_equivalences()
    • verify_up_to_constant_equivalence()
  • sboxUv2.ccz.equivalences_from_code module
    • are_ccz_equivalent_from_code()
    • are_code_equivalent()
    • are_ea_equivalent_from_code()
    • ccz_matrix()
    • ea_matrix()
  • sboxUv2.ccz.tu_decompositions module
    • TUdecomposition
      • TUdecomposition.core()
      • TUdecomposition.get_S_box()
      • TUdecomposition.insert_after_T()
      • TUdecomposition.insert_after_U()
      • TUdecomposition.insert_before_T()
      • TUdecomposition.insert_before_U()
      • TUdecomposition.twist()
    • get_tu_decompositions()
    • swap_Blm()
    • thickness()
    • tu_decomposition_from_space_basis()
• sboxUv2.core package
  • Subpackages
    • sboxUv2.core.anf package
      • Submodules
      • sboxUv2.core.anf.cython_functions module
    • sboxUv2.core.building_blocks package
      • Submodules
      • sboxUv2.core.building_blocks.butterflies module
      • sboxUv2.core.building_blocks.cython_functions module
      • sboxUv2.core.building_blocks.one_round_functions module
    • sboxUv2.core.f2functions package
      • Submodules
      • sboxUv2.core.f2functions.cython_functions module
      • sboxUv2.core.f2functions.field_arithmetic module
    • sboxUv2.core.sbox package
      • Submodules
      • sboxUv2.core.sbox.cython_functions module
      • sboxUv2.core.sbox.misc module
    • sboxUv2.core.spectrum package
      • Submodules
      • sboxUv2.core.spectrum.cython_functions module
• sboxUv2.databases package
  • Submodules
  • sboxUv2.databases.database module
    • FunctionsDB
      • FunctionsDB.__init__()
      • FunctionsDB.create()
      • FunctionsDB.insert_function()
      • FunctionsDB.parse_function_from_row()
      • FunctionsDB.query_functions()
  • sboxUv2.databases.literatureDB module
    • LiteratureSBoxes
      • LiteratureSBoxes.insert_function_from_lut()
      • LiteratureSBoxes.parse_function_from_row()
• sboxUv2.display package
  • Submodules
  • sboxUv2.display.output module
    • Chronograph
    • Experiment
      • Experiment.section()
      • Experiment.subsection()
    • pprint()
    • section()
    • subsection()
  • sboxUv2.display.pollock module
    • TableCursor
      • TableCursor.on_mouse_move()
      • TableCursor.set_cross_hair_visible()
    • bct_interactive_view()
    • ddt_interactive_view()
    • fbct_interactive_view()
    • interactive_distribution_comparison()
    • interactive_distribution_comparison_bct()
    • interactive_distribution_comparison_ddt()
    • interactive_distribution_comparison_lat()
    • lat_interactive_view()
    • table_interactive_view()
• sboxUv2.exploration package
  • Submodules
  • sboxUv2.exploration.cython_functions module
    • non_trivial_sn()
• sboxUv2.random_objects package
  • Submodules
  • sboxUv2.random_objects.random_objects module
    • rand_Sbox()
    • rand_invertible_Sbox()
    • rand_linear_function()
    • rand_linear_permutation()
• sboxUv2.scripts package
  • Subpackages
    • sboxUv2.scripts.apnDB package
      • Submodules
      • sboxUv2.scripts.apnDB.BeierleLeander module
      • sboxUv2.scripts.apnDB.eightBitAPN module
      • sboxUv2.scripts.apnDB.firstQAM module
      • sboxUv2.scripts.apnDB.generate module
      • sboxUv2.scripts.apnDB.reprs6 module
      • sboxUv2.scripts.apnDB.reprs7 module
      • sboxUv2.scripts.apnDB.reprs8 module
      • sboxUv2.scripts.apnDB.secondQAM module
• sboxUv2.statistics package
  • Submodules
  • sboxUv2.statistics.anomalies module
    • bct_coeff_probability()
    • ddt_coeff_probability()
    • expected_boomerang_uniformity_distribution_permutation()
    • expected_differential_uniformity_distribution_permutation()
    • expected_linearity_distribution_function()
    • expected_linearity_distribution_permutation()
    • expected_maximum_distribution()
    • get_proba_func()
    • lat_coeff_probability_function()
    • lat_coeff_probability_permutation()
    • probability_of_max_and_occurrences()
    • table_anomaly()
    • table_negative_anomaly()
  • sboxUv2.statistics.cython_functions module
    • absolute_walsh_spectrum()
    • bct()
    • boomerang_spectrum()
    • boomerang_uniformity()
    • ddt()
    • differential_spectrum()
    • differential_uniformity()
    • fbct()
    • fbct_spectrum()
    • invert_lat()
    • is_differential_uniformity_smaller_than()
    • lat()
    • linear_structures()
    • linear_structures_vectorial()
    • linear_structures_vectorial_spectrum()
    • linearity()
    • walsh_spectrum()
    • walsh_transform()
    • xddt()
    • yddt()
    • zddt()

Submodules

sboxUv2.config module

The maximum number of threads used in each function.

sboxUv2.config.n_threads_from_sbox_size(n)

Customize this function to adjust the number of threads used by multi-threaded functions.

The idea is to prevent the use of many threads when each of them actually has very little to do.

Parameters:

n (-) – the bitlength of an S-box input.

Returns:

The number of threads to use. The higher the input, the higher the number of threads.