Cp xor differential model¶

class CpXorDifferentialModel(cipher)¶

Bases: CpModel

add_solution_to_components_values(component_id, component_solution, components_values, j, output_to_parse, solution_number, string)¶

add_solutions_from_components_values(components_values, memory, model_type, solutions, solve_time, solver_name, solver_output, total_weight)¶

build_mix_column_truncated_table(component)¶

Return a model that generates the list of possible input/output couples for the given mix column.

INPUT:

component – Component object; the mix column component in Cipher

EXAMPLES:

sage: from claasp.cipher_modules.models.cp.cp_model import CpModel
sage: from claasp.ciphers.block_ciphers.aes_block_cipher import AESBlockCipher
sage: aes = AESBlockCipher(number_of_rounds=3)
sage: cp = CpModel(aes)
sage: mix_column = aes.component_from(0, 21)
sage: cp.build_mix_column_truncated_table(mix_column)
'array[0..93, 1..8] of int: mix_column_truncated_table_mix_column_0_21 = array2d(0..93, 1..8, [0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,0,0,1,0,1,1,1,1,0,0,1,1,0,1,1,1,0,0,1,1,1,0,1,1,0,0,1,1,1,1,0,1,0,0,1,1,1,1,1,0,0,0,1,1,1,1,1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,1,1,1,0,1,0,1,1,0,1,1,0,1,0,1,1,1,0,1,0,1,0,1,1,1,1,0,0,1,0,1,1,1,1,1,0,1,1,0,0,1,1,1,0,1,1,0,1,0,1,1,0,1,1,0,1,1,0,1,0,1,1,0,1,1,1,0,0,1,1,0,1,1,1,1,0,1,1,1,0,0,1,1,0,1,1,1,0,1,0,1,0,1,1,1,0,1,1,0,0,1,1,1,0,1,1,1,0,1,1,1,1,0,0,1,0,1,1,1,1,0,1,0,0,1,1,1,1,0,1,1,0,1,1,1,1,1,0,0,0,1,1,1,1,1,0,1,0,1,1,1,1,1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,1,1,1,1,1,0,0,1,0,1,1,1,1,0,0,1,1,0,1,1,1,0,0,1,1,1,0,1,1,0,0,1,1,1,1,0,1,0,0,1,1,1,1,1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,1,1,1,0,1,0,1,1,0,1,1,0,1,0,1,1,1,0,1,0,1,0,1,1,1,1,1,0,1,1,0,0,1,1,1,0,1,1,0,1,0,1,1,0,1,1,0,1,1,0,1,0,1,1,0,1,1,1,1,0,1,1,1,0,0,1,1,0,1,1,1,0,1,0,1,0,1,1,1,0,1,1,1,0,1,1,1,1,0,0,1,0,1,1,1,1,0,1,1,0,1,1,1,1,1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,1,1,1,1,1,0,0,1,0,1,1,1,1,0,0,1,1,0,1,1,1,0,0,1,1,1,0,1,1,0,0,1,1,1,1,1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,1,1,1,0,1,0,1,1,0,1,1,0,1,0,1,1,1,1,1,0,1,1,0,0,1,1,1,0,1,1,0,1,0,1,1,0,1,1,0,1,1,1,1,0,1,1,1,0,0,1,1,0,1,1,1,0,1,1,1,0,1,1,1,1,0,1,1,0,1,1,1,1,1,1,1,1,0,0,0,1,1,1,1,1,0,0,1,0,1,1,1,1,0,0,1,1,0,1,1,1,0,0,1,1,1,1,1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,1,1,1,0,1,0,1,1,1,1,1,0,1,1,0,0,1,1,1,0,1,1,0,1,1,1,1,0,1,1,1,0,1,1,1,0,1,1,1,1,1,1,1,1,0,0,0,1,1,1,1,1,0,0,1,0,1,1,1,1,0,0,1,1,1,1,1,1,0,1,0,0,1,1,1,1,0,1,0,1,1,1,1,1,0,1,1,0,1,1,1,1,0,1,1,1,1,1,1,1,1,0,0,0,1,1,1,1,1,0,0,1,1,1,1,1,1,0,1,0,1,1,1,1,1,0,1,1,1,1,1,1,1,1,0,0,1,1,1,1,1,1,0,1,1,1,1,1,1,1,1,0,1,1,1,1,1,1,1,1]);'

build_xor_differential_trail_model(weight=- 1, fixed_variables=[])¶

Build the CP model for the search of XOR differential trails.

INPUT:

weight – integer (default: 1); a specific weight. If set to non-negative integer, fixes the XOR trail weight
fixed_variables – list (default: []); dictionaries containing the variables to be fixed in standard format

EXAMPLES:

sage: from claasp.cipher_modules.models.cp.cp_models.cp_xor_differential_model import (CpXorDifferentialModel)
sage: from claasp.ciphers.block_ciphers.speck_block_cipher import SpeckBlockCipher
sage: speck = SpeckBlockCipher(block_bit_size=32, key_bit_size=64, number_of_rounds=4)
sage: cp = CpXorDifferentialModel(speck)
sage: cp.build_xor_differential_trail_model(-1, fixed_variables)

build_xor_differential_trail_model_template(weight, fixed_variables)¶

calculate_bit_positions(bit_positions, input_length)¶

calculate_bit_values(bit_values, input_length)¶

calculate_input_bit_positions(word_index, input_name_1, input_name_2, new_input_bit_positions_1, new_input_bit_positions_2)¶

property cipher¶

property cipher_id¶

final_xor_differential_constraints(weight)¶

Return a CP constraints list for the cipher outputs and solving indications for single or second step model.

INPUT:

weight – integer; a specific weight. If set to non-negative integer, fixes the XOR trail weight

EXAMPLES:

sage: from claasp.cipher_modules.models.cp.cp_models.cp_xor_differential_model import (CpXorDifferentialModel)
sage: from claasp.ciphers.block_ciphers.speck_block_cipher import SpeckBlockCipher
sage: speck = SpeckBlockCipher(block_bit_size=32, key_bit_size=64, number_of_rounds=4)
sage: cp = CpXorDifferentialModel(speck)
sage: cp.build_xor_differential_trail_model(-1)
sage: cp.final_xor_differential_constraints(-1)[:-1]
['solve:: int_search(p, smallest, indomain_min, complete) minimize weight;']

find_all_xor_differential_trails_with_fixed_weight(fixed_weight, fixed_values=[], solver_name='Chuffed')¶

Return a list of solutions containing all the differential trails having the fixed_weight weight. By default, the search is set in the single-key setting.

INPUT:

fixed_weight – integer; the weight to be fixed
fixed_values – list (default: []); can be created using set_fixed_variables method
solver_name – string (default: Chuffed); the name of the solver. Available values are:
- 'Chuffed'
- 'Gecode'
- 'COIN-BC'

EXAMPLES:

# single-key setting
sage: from claasp.cipher_modules.models.cp.cp_models.cp_xor_differential_model import (CpXorDifferentialModel)
sage: from claasp.ciphers.block_ciphers.speck_block_cipher import SpeckBlockCipher
sage: speck = SpeckBlockCipher(number_of_rounds=5)
sage: cp = CpXorDifferentialModel(speck)
sage: trails = cp.find_all_xor_differential_trails_with_fixed_weight(9, solver_name='Chuffed')
sage: len(trails)
2

# related-key setting
sage: from claasp.cipher_modules.models.cp.cp_models.cp_xor_differential_model import (CpXorDifferentialModel)
sage: from claasp.ciphers.block_ciphers.speck_block_cipher import SpeckBlockCipher
sage: from claasp.cipher_modules.models.utils import set_fixed_variables
sage: speck = SpeckBlockCipher( number_of_rounds=5)
sage: cp = CpXorDifferentialModel(speck)
sage: key = set_fixed_variables('key', 'not_equal', list(range(64)), [0] * 64)
sage: trails = cp.find_all_xor_differential_trails_with_fixed_weight(2, fixed_values=[key], solver_name='Chuffed')
sage: len(trails)
2

find_all_xor_differential_trails_with_weight_at_most(min_weight, max_weight=64, fixed_values=[], solver_name='Chuffed')¶

Return a list of solutions containing all the differential trails. By default, the search is set in the single-key setting. The differential trails having the weight of correlation lying in the interval [min_weight, max_weight].

INPUT:

min_weight – integer; the weight from which to start the search
max_weight – integer (default: 64); the weight at which the search stops
fixed_values – list (default: []); can be created using set_fixed_variables method
solver_name – string (default: Chuffed); the name of the solver. Available values are:
- 'Chuffed'
- 'Gecode'
- 'COIN-BC'

EXAMPLES:

# single-key setting
sage: from claasp.cipher_modules.models.cp.cp_models.cp_xor_differential_model import (CpXorDifferentialModel)
sage: from claasp.ciphers.block_ciphers.speck_block_cipher import SpeckBlockCipher
sage: speck = SpeckBlockCipher(number_of_rounds=5)
sage: cp = CpXorDifferentialModel(speck)
sage: trails = cp.find_all_xor_differential_trails_with_weight_at_most(9,10, solver_name='Chuffed')
sage: len(trails)
28

# related-key setting
sage: from claasp.cipher_modules.models.cp.cp_models.cp_xor_differential_model import (CpXorDifferentialModel)
sage: from claasp.ciphers.block_ciphers.speck_block_cipher import SpeckBlockCipher
sage: from claasp.cipher_modules.models.utils import set_fixed_variables
sage: speck = SpeckBlockCipher(number_of_rounds=5)
sage: cp = CpXorDifferentialModel(speck)
sage: key = set_fixed_variables('key', 'not_equal', list(range(64)), [0] * 64)
sage: trails = cp.find_all_xor_differential_trails_with_weight_at_most(2,3, fixed_values=[key], solver_name='Chuffed') # long
sage: len(trails)
9

find_differential_weight(fixed_values=[], solver_name='Chuffed')¶

find_lowest_weight_xor_differential_trail(fixed_values=[], solver_name='Chuffed')¶

Return the solution representing a differential trail with the lowest probability weight. By default, the search is set in the single-key setting.

Note

There could be more than one trail with the lowest weight. In order to find all the lowest weight trail, run find_all_xor_differential_trails_with_fixed_weight().

INPUT:

fixed_values – list (default: []); can be created using set_fixed_variables method
solver_name – string (default: Chuffed); the name of the solver. Available values are:
- 'Chuffed'
- 'Gecode'
- 'COIN-BC'

EXAMPLES:

# single-key setting
sage: from claasp.cipher_modules.models.cp.cp_models.cp_xor_differential_model import (CpXorDifferentialModel)
sage: from claasp.ciphers.block_ciphers.speck_block_cipher import SpeckBlockCipher
sage: speck = SpeckBlockCipher(number_of_rounds=5)
sage: cp = CpXorDifferentialModel(speck)
sage: cp.find_lowest_weight_xor_differential_trail(solver_name='Chuffed') # random
{'building_time': 0.007165431976318359,
 'cipher_id': 'speck_p32_k64_o32_r4',
 'components_values': {'cipher_output_4_12': {'value': '850a9520',
 'weight': 0},
  ...
 'total_weight': '9.0'}

# related-key setting
sage: from claasp.cipher_modules.models.cp.cp_models.cp_xor_differential_model import (CpXorDifferentialModel)
sage: from claasp.ciphers.block_ciphers.speck_block_cipher import SpeckBlockCipher
sage: from claasp.cipher_modules.models.utils import set_fixed_variables
sage: speck = SpeckBlockCipher(number_of_rounds=5)
sage: cp = CpXorDifferentialModel(speck)
sage: key = set_fixed_variables('key', 'not_equal', list(range(32)), [0] * 32)
sage: trail = cp.find_lowest_weight_xor_differential_trail(fixed_values=[key], solver_name='Chuffed')
sage: trail['total_weight']
'1.0'

find_one_xor_differential_trail(fixed_values=[], solver_name='Chuffed')¶

Return the solution representing a differential trail with any weight. By default, the search is set in the single-key setting.

INPUT:

fixed_values – list (default: []); can be created using set_fixed_variables method
solver_name – string (default: Chuffed); the name of the solver. Available values are:
- 'Chuffed'
- 'Gecode'
- 'COIN-BC'

EXAMPLES:

# single-key setting
sage: from claasp.cipher_modules.models.cp.cp_models.cp_xor_differential_model import (CpXorDifferentialModel)
sage: from claasp.ciphers.block_ciphers.speck_block_cipher import SpeckBlockCipher
sage: speck = SpeckBlockCipher(number_of_rounds=2)
sage: cp = CpXorDifferentialModel(speck)
sage: cp.find_one_xor_differential_trail(solver_name=Chuffed') # random
{'cipher_id': 'speck_p32_k64_o32_r2',
 'model_type': 'xor_differential_one_solution',
  ...
 'cipher_output_1_12': {'value': 'ffff0000', 'weight': 0}},
 'total_weight': '18.0'}

# related-key setting
sage: from claasp.cipher_modules.models.cp.cp_models.cp_xor_differential_model import (CpXorDifferentialModel)
sage: from claasp.ciphers.block_ciphers.speck_block_cipher import SpeckBlockCipher
sage: from claasp.cipher_modules.models.utils import set_fixed_variables
sage: speck = SpeckBlockCipher(number_of_rounds=2)
sage: cp = CpXorDifferentialModel(speck)
sage: key = set_fixed_variables('key', 'not_equal', list(range(32)), [0] * 32)
sage: trail = cp.find_one_xor_differential_trail(fixed_values=[key], solver_name='Chuffed') # random

find_one_xor_differential_trail_with_fixed_weight(fixed_weight=- 1, fixed_values=[], solver_name='Chuffed')¶

Return the solution representing a differential trail with the weight of probability equal to fixed_weight. By default, the search is set in the single-key setting.

INPUT:

fixed_weight – integer; the value to which the weight is fixed, if non-negative
fixed_values – list (default: []); can be created using set_fixed_variables method
solver_name – string (default: Chuffed); the name of the solver. Available values are:
- 'Chuffed'
- 'Gecode'
- 'COIN-BC'

EXAMPLES:

# single-key setting
sage: from claasp.cipher_modules.models.cp.cp_models.cp_xor_differential_model import (CpXorDifferentialModel)
sage: from claasp.ciphers.block_ciphers.speck_block_cipher import SpeckBlockCipher
sage: speck = SpeckBlockCipher(number_of_rounds=3)
sage: cp = CpXorDifferentialModel(speck)
sage: trail = cp.find_one_xor_differential_trail_with_fixed_weight(3, solver_name='Chuffed') # random
sage: trail['total_weight']
'3.0'

# related-key setting
sage: from claasp.cipher_modules.models.cp.cp_models.cp_xor_differential_model import (CpXorDifferentialModel)
sage: from claasp.ciphers.block_ciphers.speck_block_cipher import SpeckBlockCipher
sage: from claasp.cipher_modules.models.utils import set_fixed_variables
sage: speck = SpeckBlockCipher(number_of_rounds=3)
sage: cp = CpXorDifferentialModel(speck)
sage: key = set_fixed_variables('key', 'not_equal', list(range(64)), [0] * 64)
sage: trail = cp.find_one_xor_differential_trail_with_fixed_weight(3, fixed_values=[key], solver_name='Chuffed')
sage: trail['total_weight']
'3.0'

find_possible_number_of_active_sboxes(weight)¶

Return a set whose numbers are the possible numbers of active S-boxes.

INPUT:

weight – integer; the fixed weight that must be able to be obtained with the found numbers of active S-boxes

EXAMPLES:

sage: from claasp.ciphers.block_ciphers.midori_block_cipher import MidoriBlockCipher
sage: from claasp.cipher_modules.models.cp.cp_model import CpModel
sage: midori = MidoriBlockCipher()
sage: cp = CpModel(midori)
sage: model = cp.find_possible_number_of_active_sboxes(9)
sage: model
{3, 4}

fix_variables_value_constraints(fixed_variables=[], step='full_model')¶

Return a list of CP constraints that fix the input variables to a specific value.

INPUT:

fixed_variables – list (default: []); dictionaries containing name, bit_size, value (as integer) for the variables that need to be fixed to a certain value:

{
‘component_id’: ‘plaintext’,

‘constraint_type’: ‘equal’/’not_equal’

‘bit_size’: 32,

‘value’: 753

}
step – string (default: full_model)

EXAMPLES:

sage: from claasp.cipher_modules.models.cp.cp_model import CpModel
sage: from claasp.ciphers.block_ciphers.speck_block_cipher import SpeckBlockCipher
sage: from claasp.cipher_modules.models.utils import set_fixed_variables, integer_to_bit_list
sage: speck = SpeckBlockCipher(block_bit_size=32, key_bit_size=64, number_of_rounds=4)
sage: cp = CpModel(speck)
sage: cp.fix_variables_value_constraints([set_fixed_variables('plaintext', 'equal', range(4), integer_to_bit_list(5, 4, 'big'))])
['constraint plaintext[0] = 0 /\\ plaintext[1] = 1 /\\ plaintext[2] = 0 /\\ plaintext[3] = 1;']
sage: cp.fix_variables_value_constraints([set_fixed_variables('plaintext', 'not_equal', list(range(4)), integer_to_bit_list(5, 4, 'big'))])
['constraint plaintext[0] != 0 \\/ plaintext[1] != 1 \\/ plaintext[2] != 0 \\/ plaintext[3] != 1;']

property float_and_lat_values¶

format_component_value(component_id, string)¶

get_command_for_solver_process(input_file_path, model_type, solver_name, num_of_processors, timelimit)¶

get_mix_column_all_inputs(input_bit_positions_1, input_id_link_1, numb_of_inp_1)¶

get_total_weight(string_total_weight)¶

get_word_operation_xor_differential_constraints(component, new_constraint)¶

initialise_model()¶

input_xor_differential_constraints()¶

Return a list of CP declarations and a list of Cp constraints for the first part of the xor differential model.

INPUT:

None

EXAMPLES:

sage: from claasp.ciphers.block_ciphers.speck_block_cipher import SpeckBlockCipher
sage: from claasp.cipher_modules.models.cp.cp_models.cp_xor_differential_model import (CpXorDifferentialModel)
sage: speck = SpeckBlockCipher(block_bit_size=32, key_bit_size=64, number_of_rounds=4)
sage: cp = CpXorDifferentialModel(speck)
sage: cp.input_xor_differential_constraints()
(['array[0..31] of var 0..1: plaintext;',
  'array[0..63] of var 0..1: key;',
   ...
  'array[0..31] of var 0..1: cipher_output_3_12;',
  'array[0..6] of var {0, 900, 200, 1100, 400, 1300, 600, 1500, 800, 100, 1000, 300, 1200, 500, 1400, 700}: p;',
  'var int: weight = sum(p);'],
 [])

property model_constraints¶

Return the model specified by model_type.

INPUT:

model_type – string; the model to retrieve

EXAMPLES:

sage: from claasp.ciphers.block_ciphers.speck_block_cipher import SpeckBlockCipher
sage: from claasp.cipher_modules.models.cp.cp_model import CpModel
sage: speck = SpeckBlockCipher(number_of_rounds=4)
sage: cp = CpModel(speck)
sage: cp.model_constraints()
Traceback (most recent call last):
...
ValueError: No model generated

parse_solver_information(output_to_parse, truncated)¶

set_component_solution_value(component_solution, truncated, value)¶

solve(model_type, solver_name='Chuffed', num_of_processors=None, timelimit=None)¶

Return the solution of the model.

INPUT:

model_type – string; the model to solve:
- ‘cipher’
- ‘xor_differential’
- ‘xor_differential_one_solution’
- ‘xor_linear’
- ‘xor_linear_one_solution’
- ‘deterministic_truncated_xor_differential’
- ‘deterministic_truncated_xor_differential_one_solution’
- ‘impossible_xor_differential’
solver_name – string (default: None); the name of the solver. Available values are:
- 'Chuffed'
- 'Gecode'
- 'COIN-BC'
num_of_processors – integer; the number of processors to be used
timelimit – integer; time limit to output a result

EXAMPLES:

sage: from claasp.cipher_modules.models.cp.cp_models.cp_xor_differential_trail_search_model import CpXorDifferentialTrailSearchModel
sage: from claasp.ciphers.block_ciphers.speck_block_cipher import SpeckBlockCipher
sage: from claasp.cipher_modules.models.utils import set_fixed_variables, integer_to_bit_list
sage: speck = SpeckBlockCipher(block_bit_size=32, key_bit_size=64, number_of_rounds=4)
sage: cp = CpXorDifferentialTrailSearchModel(speck)
sage: fixed_variables = [set_fixed_variables('key', 'equal', list(range(64)), integer_to_bit_list(0, 64, 'little')), set_fixed_variables('plaintext', 'not_equal', list(range(32)), integer_to_bit_list(0, 32, 'little'))]
sage: cp.build_xor_differential_trail_model(-1, fixed_variables)
sage: cp.solve('xor_differential', 'Chuffed') # random
[{'cipher_id': 'speck_p32_k64_o32_r4',
  ...
  'total_weight': '7'},
 {'cipher_id': 'speck_p32_k64_o32_r4',
   ...
  'total_weight': '5'}]

solver_names(verbose=False)¶

update_sbox_ddt_valid_probabilities(component, valid_probabilities)¶

weight_constraints(weight)¶

Return a list of CP constraints that fix the total weight to a specific value.

INPUT:

weight – integer; a specific weight. If set to non-negative integer, fixes the XOR trail weight

EXAMPLES:

sage: from claasp.ciphers.block_ciphers.speck_block_cipher import SpeckBlockCipher
sage: from claasp.cipher_modules.models.cp.cp_model import CpModel
sage: speck = SpeckBlockCipher(block_bit_size=32, key_bit_size=64, number_of_rounds=4)
sage: cp = CpModel(speck)
sage: cp.weight_constraints(10)
(['constraint weight = 1000;'], [])

and_xor_differential_probability_ddt(numadd)¶

Return the ddt of the and operation.

INPUT:

numadd – integer; the number of addenda

EXAMPLES:

sage: from claasp.cipher_modules.models.cp.cp_models.cp_xor_differential_model import (
....:     and_xor_differential_probability_ddt)
sage: from claasp.ciphers.block_ciphers.simon_block_cipher import SimonBlockCipher
sage: simon = SimonBlockCipher()
sage: and_xor_differential_probability_ddt(2)
[4, 0, 2, 2, 2, 2, 2, 2]

update_and_or_ddt_valid_probabilities(and_already_added, component, cp_declarations, valid_probabilities)¶

Cp xor differential model¶

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