Modular component

class Modular(current_round_number, current_round_number_of_components, input_id_links, input_bit_positions, output_bit_size, operation, modulus)

Bases: Component

as_python_dictionary()
check_output_size(available_word_sizes, fixed, word_size)
cms_xor_differential_propagation_constraints(model)
cms_xor_linear_mask_propagation_constraints(model=None)

Return a list of variables and a list of clauses for fixing variables in CMS XOR LINEAR model.

See also

CMS XOR LINEAR model for the format, [LWR2016] for the algorithm.

Warning

This method heavily relies on the fact that modular addition/substration is always performed using two addenda.

INPUT:

  • model – model object (default: None); a model instance

EXAMPLES:

sage: from claasp.ciphers.block_ciphers.speck_block_cipher import SpeckBlockCipher
sage: speck = SpeckBlockCipher(number_of_rounds=3)
sage: modadd_component = speck.component_from(0, 1)
sage: modadd_component.cms_xor_linear_mask_propagation_constraints()
(['modadd_0_1_0_i',
  'modadd_0_1_1_i',
  'modadd_0_1_2_i',
  ...
  'hw_modadd_0_1_14_o -modadd_0_1_14_o modadd_0_1_30_i',
  'hw_modadd_0_1_15_o modadd_0_1_15_o -modadd_0_1_31_i',
  'hw_modadd_0_1_15_o -modadd_0_1_15_o modadd_0_1_31_i'])
cp_deterministic_truncated_xor_differential_constraints()

Return lists of variables and constraints for Modular Addition/Substraction in CP deterministic truncated XOR differential model.

INPUT:

  • inverse – boolean (default: False)

EXAMPLES:

sage: from claasp.ciphers.block_ciphers.speck_block_cipher import SpeckBlockCipher
sage: speck = SpeckBlockCipher(number_of_rounds=3)
sage: modadd_component = speck.component_from(0 ,1)
sage: modadd_component.cp_deterministic_truncated_xor_differential_constraints()
(['array[0..15] of var 0..2: pre_modadd_0_1_0;',
  'array[0..15] of var 0..2: pre_modadd_0_1_1;'],
 ['constraint pre_modadd_0_1_0[0] = rot_0_0[0];',
   ...
  'constraint pre_modadd_0_1_1[15] = plaintext[31];',
  'constraint modular_addition_word(pre_modadd_0_1_1, pre_modadd_0_1_0, modadd_0_1);'])
cp_deterministic_truncated_xor_differential_trail_constraints()
cp_twoterms_xor_differential_probability(input_1, input_2, out, input_length, cp_constraints, cp_declarations, c, model)
cp_wordwise_deterministic_truncated_xor_differential_constraints(model)

Return lists declarations and constraints for XOR component CP wordwise deterministic truncated XOR differential model.

INPUT:

  • model – model object; a model instance

EXAMPLES:

sage: from claasp.ciphers.block_ciphers.aes_block_cipher import AESBlockCipher
sage: from claasp.cipher_modules.models.cp.mzn_model import MznModel
sage: aes = AESBlockCipher(number_of_rounds=5)
sage: cp = MznModel(aes)
sage: xor_component = aes.component_from(0, 0)
sage: xor_component.cp_wordwise_deterministic_truncated_xor_differential_constraints(cp)
(['var -2..255: xor_0_0_temp_0_0_value;',
  ...
  'var 0..9: xor_0_0_bound_value_0_15 = if xor_0_0_temp_0_15_value + xor_0_0_temp_1_15_value > 0 then ceil(log2(xor_0_0_temp_0_15_value + xor_0_0_temp_1_15_value)) else 0 endif;'],
 ['constraint xor_0_0_temp_0_0_value = key_value[0] /\ xor_0_0_temp_0_0_active = key_active[0];',
  ...
  'constraint if xor_0_0_temp_0_15_active + xor_0_0_temp_1_15_active > 2 then xor_0_0_active[15] == 3 /\ xor_0_0_value[15] = -2 elseif xor_0_0_temp_0_15_active + xor_0_0_temp_1_15_active == 1 then xor_0_0_active[15] = 1 /\ xor_0_0_value[15] = xor_0_0_temp_0_15_value + xor_0_0_temp_1_15_value elseif xor_0_0_temp_0_15_active + xor_0_0_temp_1_15_active == 0 then xor_0_0_active[15] = 0 /\ xor_0_0_value[15] = 0 elseif xor_0_0_temp_0_15_value + xor_0_0_temp_1_15_value < 0 then xor_0_0_active[15] = 2 /\ xor_0_0_value[15] = -1 elseif xor_0_0_temp_0_15_value == xor_0_0_temp_1_15_value then xor_0_0_active[15] = 0 /\ xor_0_0_value[15] = 0 else xor_0_0_active[15] = 1 /\ xor_0_0_value[15] = sum([(((floor(xor_0_0_temp_0_15_value/pow(2,j)) + floor(xor_0_0_temp_1_15_value/pow(2,j))) mod 2) * pow(2,j)) | j in 0..xor_0_0_bound_value_0_15]) endif;'])
cp_xor_differential_propagation_constraints(model)

Return lists of declarations and constraints for the probability of Modular Addition/Substraction component for CP xor differential probability.

INPUT:

  • model – model object; a model instance

EXAMPLES:

sage: from claasp.ciphers.block_ciphers.speck_block_cipher import SpeckBlockCipher
sage: from claasp.cipher_modules.models.cp.mzn_model import MznModel
sage: speck = SpeckBlockCipher(number_of_rounds=3)
sage: cp = MznModel(speck)
sage: modadd_component = speck.component_from(0, 1)
sage: modadd_component.cp_xor_differential_propagation_constraints(cp)
(['array[0..15] of var 0..1: pre_modadd_0_1_0;',
  ...
  'array[0..15] of var 0..1: eq_modadd_0_1 = Eq(Shi_pre_modadd_0_1_1, Shi_pre_modadd_0_1_0, Shi_modadd_0_1);'],
 ['constraint pre_modadd_0_1_0[0] = rot_0_0[0];',
  ...
  'constraint pre_modadd_0_1_1[15] = plaintext[31];',
  'constraint forall(j in 0..15)(if eq_modadd_0_1[j] = 1 then (sum([pre_modadd_0_1_1[j], pre_modadd_0_1_0[j], modadd_0_1[j]]) mod 2) = Shi_pre_modadd_0_1_0[j] else true endif) /\\ p[0] = 1600-100 * sum(eq_modadd_0_1);'])
cp_xor_differential_propagation_constraints_arx_optimized(model)

Return variables and constraints for the component Modular Addition/Substraction for MINIZINC xor differential probability.

INPUT:

  • model – model object; a model instance

EXAMPLES:

sage: from claasp.ciphers.toys.fancy_block_cipher import FancyBlockCipher
sage: from claasp.cipher_modules.models.cp.mzn_models.mzn_xor_differential_model_arx_optimized import MznXorDifferentialModelARXOptimized
sage: fancy = FancyBlockCipher(number_of_rounds=2)
sage: minizinc = MznXorDifferentialModelARXOptimized(fancy, sat_or_milp="milp")
sage: modadd_component = fancy.component_from(1, 9)
sage: _, constraints = modadd_component.cp_xor_differential_propagation_constraints_arx_optimized(minizinc)
sage: constraints[6]
'constraint pre_modadd_1_9_1[0] = sbox_1_0[0];'
cp_xor_linear_mask_propagation_constraints(model)

Return lists of declarations and constraints for the probability of Modular Addition/Substraction for CP xor linear model.

INPUT:

  • model – model object; a model instance

EXAMPLES:

sage: from claasp.ciphers.block_ciphers.speck_block_cipher import SpeckBlockCipher
sage: from claasp.cipher_modules.models.cp.mzn_model import MznModel
sage: speck = SpeckBlockCipher(block_bit_size=32, key_bit_size=64, number_of_rounds=22)
sage: modadd_component = speck.component_from(0, 1)
sage: cp = MznModel(speck)
sage: modadd_component.cp_xor_linear_mask_propagation_constraints(cp)
(['array[0..31] of var 0..1: modadd_0_1_i;',
  'array[0..15] of var 0..1: modadd_0_1_o;',
  ...
  'constraint pre_modadd_0_1_1[15]=modadd_0_1_i[31];',
  'constraint modadd_linear(pre_modadd_0_1_1, pre_modadd_0_1_0, modadd_0_1_o, p[0]);'])
create_bct_mzn_constraint_from_component_ids()
property description
get_graph_representation()
get_word_operation_sign(sign, solution)
property id
property input_bit_positions
property input_bit_size
is_forbidden(forbidden_types, forbidden_descriptions)
is_id_equal_to(component_id)
is_power_of_2_word_based(dto)
milp_bitwise_deterministic_truncated_xor_differential_binary_constraints(model)

Returns a list of variables and a list of constraints for modular addition component in deterministic truncated XOR differential model.

INPUTS:

  • component – dict, the modular addition component in Graph Representation

EXAMPLES:

sage: from claasp.ciphers.block_ciphers.speck_block_cipher import SpeckBlockCipher
sage: cipher = SpeckBlockCipher(block_bit_size=32, key_bit_size=64, number_of_rounds=2)
sage: from claasp.cipher_modules.models.milp.milp_models.milp_bitwise_deterministic_truncated_xor_differential_model import MilpBitwiseDeterministicTruncatedXorDifferentialModel
sage: milp = MilpBitwiseDeterministicTruncatedXorDifferentialModel(cipher)
sage: milp.init_model_in_sage_milp_class()
sage: modadd_component = cipher.get_component_from_id("modadd_0_1")
sage: variables, constraints = modadd_component.milp_bitwise_deterministic_truncated_xor_differential_binary_constraints(milp)
...
sage: variables
[('x[rot_0_0_0_class_bit_0]', x_0),
 ('x[rot_0_0_0_class_bit_1]', x_1),
...
 ('x[modadd_0_1_15_class_bit_0]', x_94),
 ('x[modadd_0_1_15_class_bit_1]', x_95)]
sage: constraints
[x_96 == 2*x_0 + x_1,
 x_97 == 2*x_2 + x_3,
...
 1 <= 18 - x_30 + x_94 - 17*x_159,
 1 <= 19 - x_62 - x_63 - 17*x_159]
milp_bitwise_deterministic_truncated_xor_differential_constraints(model)

Returns a list of variables and a list of constraints for modular addition component in deterministic truncated XOR differential model.

INPUTS:

  • component – dict, the modular addition component in Graph Representation

EXAMPLES:

sage: from claasp.ciphers.block_ciphers.speck_block_cipher import SpeckBlockCipher
sage: cipher = SpeckBlockCipher(block_bit_size=32, key_bit_size=64, number_of_rounds=2)
sage: from claasp.cipher_modules.models.milp.milp_models.milp_bitwise_deterministic_truncated_xor_differential_model import MilpBitwiseDeterministicTruncatedXorDifferentialModel
sage: milp = MilpBitwiseDeterministicTruncatedXorDifferentialModel(cipher)
sage: milp.init_model_in_sage_milp_class()
sage: modadd_component = cipher.get_component_from_id("modadd_0_1")
sage: variables, constraints = modadd_component.milp_bitwise_deterministic_truncated_xor_differential_constraints(milp)
...
sage: constraints
[x_48 <= 15,
 0 <= x_48,
 0 <= 16 + x_48 - 17*x_49,
 x_48 - 17*x_49 <= 0,
 ...
 2 <= 4 + x_47 - 4*x_157 + 4*x_160,
 x_157 <= x_15 + x_31]
 sage: len(constraints)
 430
milp_xor_differential_propagation_constraints(model)

Return a list of variables and a list of constrains modeling a component of type MODADD/MODSUB for MILP xor differential probability.

The constraints are extracted from [FWGSH2016].

INPUT:

  • model – model object; a model instance

EXAMPLES:

sage: from claasp.ciphers.block_ciphers.speck_block_cipher import SpeckBlockCipher
sage: from claasp.cipher_modules.models.milp.milp_models.milp_xor_differential_model import MilpXorDifferentialModel
sage: speck = SpeckBlockCipher(block_bit_size=32, key_bit_size=64, number_of_rounds=2)
sage: modadd_component = speck.component_from(0, 1)
sage: milp = MilpXorDifferentialModel(speck)
sage: milp.init_model_in_sage_milp_class()
sage: variables, constraints = modadd_component.milp_xor_differential_propagation_constraints(milp)
sage: variables
[('x[rot_0_0_0]', x_0),
('x[rot_0_0_1]', x_1),
...
('x[modadd_0_1_14]', x_46),
('x[modadd_0_1_15]', x_47)]
sage: constraints
[x_47 <= x_48,
x_15 <= x_48,
...
-2 <= -1*x_0 - x_16 - x_17 + x_32 + x_63,
x_64 == 100*x_49 + 100*x_50 + 100*x_51 + 100*x_52 + 100*x_53 + 100*x_54 + 100*x_55 + 100*x_56 + 100*x_57 + 100*x_58 + 100*x_59 + 100*x_60 + 100*x_61 + 100*x_62 + 100*x_63]
milp_xor_linear_mask_propagation_constraints(model)

Return lists of variables and constraints for probability of Modular Addition/Substraction for MILP xor linear model, for any arbitrary number of inputs.

INPUT:

  • model – model object; a model instance

EXAMPLES:

sage: from claasp.ciphers.block_ciphers.speck_block_cipher import SpeckBlockCipher
sage: from claasp.cipher_modules.models.milp.milp_models.milp_xor_linear_model import MilpXorLinearModel
sage: speck = SpeckBlockCipher(block_bit_size=32, key_bit_size=64, number_of_rounds=2)
sage: milp = MilpXorLinearModel(speck)
sage: milp.init_model_in_sage_milp_class()
sage: modadd_component = speck.component_from(0, 1)
sage: variables, constraints = modadd_component.milp_xor_linear_mask_propagation_constraints(milp)
sage: variables
[('x[modadd_0_1_0_i]', x_0),
 ('x[modadd_0_1_1_i]', x_1),
...
 ('x[modadd_0_1_14_o]', x_46),
 ('x[modadd_0_1_15_o]', x_47)]
sage: constraints
[x_48 == 0,
0 <= -1*x_0 - x_16 + x_32 + x_48 + x_49,
0 <= x_0 + x_16 - x_32 + x_48 - x_49,
...
 x_15 + x_31 + x_47 + x_63 + x_64 <= 4,
 x_65 == x_48 + x_49 + x_50 + x_51 + x_52 + x_53 + x_54 + x_55 + x_56 + x_57 + x_58 + x_59 + x_60 + x_61 + x_62 + x_63,
 x_66 == 100*x_65]
minizinc_xor_differential_propagation_constraints(model)

Return variables and constraints for the component Modular Addition/Substraction for MINIZINC xor differential probability.

INPUT:

  • model – model object; a model instance

EXAMPLES:

sage: from claasp.ciphers.toys.fancy_block_cipher import FancyBlockCipher
sage: from claasp.cipher_modules.models.cp.mzn_models.mzn_xor_differential_model_arx_optimized import MznXorDifferentialModelARXOptimized
sage: fancy = FancyBlockCipher(number_of_rounds=2)
sage: minizinc = MznXorDifferentialModelARXOptimized(fancy, sat_or_milp="milp")
sage: modadd_component = fancy.component_from(1, 9)
sage: _, constraints = modadd_component.minizinc_xor_differential_propagation_constraints(minizinc)
sage: constraints[6]
'constraint modular_addition_word(array1d(0..6-1, [modadd_1_9_x0,modadd_1_9_x1,modadd_1_9_x2,modadd_1_9_x3,modadd_1_9_x4,modadd_1_9_x5]),array1d(0..6-1, [modadd_1_9_x6,modadd_1_9_x7,modadd_1_9_x8,modadd_1_9_x9,modadd_1_9_x10,modadd_1_9_x11]),array1d(0..6-1, [modadd_1_9_y0_0,modadd_1_9_y1_0,modadd_1_9_y2_0,modadd_1_9_y3_0,modadd_1_9_y4_0,modadd_1_9_y5_0]), p_modadd_1_9_0, dummy_modadd_1_9_0, -1)=1;\nconstraint carry_modadd_1_9_0 = XOR3(array1d(0..6-1, [modadd_1_9_x0,modadd_1_9_x1,modadd_1_9_x2,modadd_1_9_x3,modadd_1_9_x4,modadd_1_9_x5]),array1d(0..6-1, [modadd_1_9_x6,modadd_1_9_x7,modadd_1_9_x8,modadd_1_9_x9,modadd_1_9_x10,modadd_1_9_x11]),array1d(0..6-1, [modadd_1_9_y0_0,modadd_1_9_y1_0,modadd_1_9_y2_0,modadd_1_9_y3_0,modadd_1_9_y4_0,modadd_1_9_y5_0]));\n'
property output_bit_size
output_size_for_concatenate(available_word_sizes, fixed, word_size)
print()
print_as_python_dictionary()
print_values(code)
print_word_values(code)
sat_bitwise_deterministic_truncated_xor_differential_constraints()

Return a list of variables and a list of clauses representing MODULAR ADDITION/SUBTRACTION for SAT DETERMINISTIC TRUNCATED XOR DIFFERENTIAL model

The model is built using the pivot constraint. The constraints are:

  • 0, for both the inputs and the output on the right of the pivot;

  • the usual XOR differential constraint in the pivot position;

  • ? (unknown), for both the inputs and the output on the left of the pivot.

See also

SAT standard of Cipher for the format.

INPUT:

  • None

EXAMPLES:

sage: from claasp.ciphers.block_ciphers.speck_block_cipher import SpeckBlockCipher
sage: speck = SpeckBlockCipher(number_of_rounds=3)
sage: modadd_component = speck.component_from(0, 1)
sage: modadd_component.sat_bitwise_deterministic_truncated_xor_differential_constraints()
(['modadd_0_1_0_0',
  'modadd_0_1_1_0',
  ...
  'carry_modadd_0_1_14_1_1',
  'carry_modadd_0_1_15_1_1'],
 ['-carry_modadd_0_1_15_0_0 -carry_modadd_0_1_15_1_1',
  'modadd_0_1_0_0 -carry_modadd_0_1_0_0_0',
  ...
  'plaintext_31_1 modadd_0_1_15_0 modadd_0_1_15_1 -rot_0_0_15_1',
  'modadd_0_1_15_0 -rot_0_0_15_1 -plaintext_31_1 -modadd_0_1_15_1'])
sat_semi_deterministic_truncated_xor_differential_constraints()

Return a list of variables and a list of clauses representing MODULAR ADDITION/SUBTRACTION for SAT SEMI-DETERMINISTIC TRUNCATED XOR DIFFERENTIAL model

sat_xor_differential_propagation_constraints(model=None)

Return a list of variables and a list of clauses representing MODULAR ADDITION/SUBTRACTION for SAT XOR DIFFERENTIAL model

See also

SAT standard of Cipher for the format, [LM2001] for the algorithm.

Warning

This method heavily relies on the fact that modular addition is always performed using two addenda.

INPUT:

  • model – model object; a model instance

EXAMPLES:

sage: from claasp.ciphers.block_ciphers.speck_block_cipher import SpeckBlockCipher
sage: from claasp.cipher_modules.models.sat.sat_model import SatModel
sage: speck = SpeckBlockCipher(number_of_rounds=3)
sage: sat = SatModel(speck)
sage: modadd_component = speck.component_from(0, 1)
sage: modadd_component.sat_xor_differential_propagation_constraints(sat)
(['modadd_0_1_0',
  'modadd_0_1_1',
  ...
  'hw_modadd_0_1_14',
  'hw_modadd_0_1_15'],
 ['rot_0_0_1 -modadd_0_1_1 hw_modadd_0_1_0',
  'plaintext_17 -rot_0_0_1 hw_modadd_0_1_0',
  ...
  'modadd_0_1_15 rot_0_0_15 -plaintext_31',
  '-modadd_0_1_15 -rot_0_0_15 -plaintext_31'])
sat_xor_linear_mask_propagation_constraints(model=None)

Return a list of variables and a list of clauses representing MODULAR ADDITION/SUBTRACTION for SAT XOR LINEAR model

See also

SAT standard of Cipher for the format, [LWR2016] for the algorithm.

Warning

This method heavily relies on the fact that modular addition is always performed using two addenda.

INPUT:

  • model – model object (default: None); a model instance

EXAMPLES:

sage: from claasp.ciphers.block_ciphers.speck_block_cipher import SpeckBlockCipher
sage: speck = SpeckBlockCipher(number_of_rounds=3)
sage: modadd_component = speck.component_from(0, 1)
sage: modadd_component.sat_xor_linear_mask_propagation_constraints()
(['modadd_0_1_0_i',
  'modadd_0_1_1_i',
  ...
  'hw_modadd_0_1_14_o',
  'hw_modadd_0_1_15_o'],
 ['-hw_modadd_0_1_0_o',
  '-hw_modadd_0_1_1_o modadd_0_1_0_o modadd_0_1_0_i modadd_0_1_16_i',
  ...
  'hw_modadd_0_1_15_o modadd_0_1_15_o -modadd_0_1_31_i',
  'hw_modadd_0_1_15_o -modadd_0_1_15_o modadd_0_1_31_i'])
select_bits(code)
select_words(code, word_size, input=True)
set_description(description)
set_id(id_string)
set_input_bit_positions(bit_positions)
smt_xor_differential_propagation_constraints(model=None)

Return a variable list and SMT-LIB list asserts representing MODULAR ADDITION/SUBTRACTION for SMT XOR DIFFERENTIAL model

See also

The algorithm is found in [LM2001].

Warning

This method heavily relies on the fact that modular addition is always performed using two addenda.

INPUT:

  • model – model object (default: None); a model instance

EXAMPLES:

sage: from claasp.ciphers.block_ciphers.tea_block_cipher import TeaBlockCipher
sage: tea = TeaBlockCipher(number_of_rounds=3)
sage: modadd_component = tea.component_from(0, 1)
sage: modadd_component.smt_xor_differential_propagation_constraints()
(['modadd_0_1_0',
  'modadd_0_1_1',
  ...
  'hw_modadd_0_1_30',
  'hw_modadd_0_1_31'],
 ['(assert (= (not hw_modadd_0_1_0) (= shift_0_0_1 key_1 modadd_0_1_1)))',
  '(assert (= (not hw_modadd_0_1_1) (= shift_0_0_2 key_2 modadd_0_1_2)))',
  ...
  '(assert (or hw_modadd_0_1_30 (not (xor shift_0_0_30 key_30 modadd_0_1_30 key_31))))',
  '(assert (not (xor modadd_0_1_31 shift_0_0_31 key_31)))'])
smt_xor_linear_mask_propagation_constraints(model=None)

Return a variable list and SMT-LIB list asserts representing MODULAR ADDITION/SUBTRACTION for SMT XOR LINEAR model

See also

The algorithm is found in [LWR2016].

Warning

This method heavily relies on the fact that modular addition is always performed using two addenda.

INPUT:

  • model – model object (default: None); a model instance

EXAMPLES:

sage: from claasp.ciphers.block_ciphers.tea_block_cipher import TeaBlockCipher
sage: tea = TeaBlockCipher(number_of_rounds=3)
sage: modadd_component = tea.component_from(0, 1)
sage: modadd_component.smt_xor_linear_mask_propagation_constraints()
(['modadd_0_1_0_i',
  'modadd_0_1_1_i',
  ...
  'hw_modadd_0_1_30_o',
  'hw_modadd_0_1_31_o'],
 ['(assert (not hw_modadd_0_1_0_o))',
  '(assert (= hw_modadd_0_1_1_o (xor modadd_0_1_0_o modadd_0_1_0_i modadd_0_1_32_i)))',
  ...
  '(assert (=> (xor modadd_0_1_30_o modadd_0_1_62_i) hw_modadd_0_1_30_o))',
  '(assert (=> (xor modadd_0_1_31_o modadd_0_1_63_i) hw_modadd_0_1_31_o))'])
property suffixes
twoterms_milp_probability_xor_linear_constraints(binary_variable, integer_variable, input_vars, output_vars, chunk_number)

Return lists of variables and constraints for the probability of Modular Addition/Substraction for two inputs MILP xor linear model.

Note

Using the 8 inequalities as described in Fu2016 https://eprint.iacr.org/2016/407.pdf

https://github.com/fukai6/milp_speck/blob/master/speck_diff_find.py

INPUT:

  • binary_variable – boolean MIPVariable

  • integer_variable – integer MIPVariable

  • input_vars – list

  • output_vars – list

  • chunk_number – integer

property type
generic_sign_linear_constraints(inputs, outputs)

Return the constraints for finding the sign of a MODADD/MODSUB component.

INPUT:

  • inputs – list; a list representing the inputs to the modadd/modsub

  • outputs – list; a list representing the output to the modadd/modsub

EXAMPLES:

sage: from claasp.components.modular_component import generic_sign_linear_constraints
sage: input = [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0]
sage: output = [0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
sage: generic_sign_linear_constraints(input, output)
-1
milp_n_window_heuristic(input_vars, output_vars, component_id, window_size, mip, x)