Struct SmallBooleanFunction

pub struct SmallBooleanFunction { /* private fields */ }

Struct representing a boolean function with a big truth table.

The struct internally stores the truth table as an u64, meaning that the maximum number of variables is 6.

For more than 6 variables, use the crate::BigBooleanFunction struct, or the crate::BooleanFunction type to store both small and big boolean functions.

Implementations

impl SmallBooleanFunction

pub fn from_truth_table( truth_table: u64, variables_count: usize, ) -> Result<Self, BooleanFunctionError>

Creates a new SmallBooleanFunction from a truth table and the number of variables.

Parameters

• truth_table - The truth table of the Boolean function, where the lower bit represents the output of the Boolean function for the input 0.
• variables_count - The number of variables of the Boolean function.

Returns

A SmallBooleanFunction instance from the truth table and the number of variables or an error if:

• The number of variables is greater than 6.
• The truth table is too big for the number of variables, and the unsafe_disable_safety_checks feature is not enabled.

pub fn get_truth_table_u64(&self) -> u64

Returns the truth table of the Boolean function, as an u64.

pub fn derivative_inner( &self, direction: u32, ) -> Result<Self, BooleanFunctionError>

Computes the derivative of the Boolean function for a given direction.

Parameters

• direction - The direction of the derivative.

Returns

The derivative of the Boolean function for the given direction, or an error if the direction is greater than the maximum input value and the unsafe_disable_safety_checks feature is not enabled.

pub fn reverse_inner(&self) -> Self

Computes the reverse of the Boolean function.

Returns

The reverse of the Boolean function.

pub fn annihilator_inner( &self, max_degree: Option<usize>, ) -> Option<(SmallBooleanFunction, usize, usize)>

Computes the annihilator of the Boolean function for a given maximum degree.

Parameters

• max_degree - An optional maximum degree of the annihilator to search for. If set to None, the value is set to the variable count.

Returns

A tuple containing the annihilator function, its degree and the dimension of the annihilator vector space, or None no annihilator was found.

pub fn from_walsh_hadamard_values( walsh_values: &[i32], ) -> Result<Self, BooleanFunctionError>

Computes a SmallBooleanFunction from Walsh-Hadamard values, by applying the inverse Walsh-Hadamard transform.

Parameters

• walsh_values - The Walsh-Hadamard values of the Boolean function.

Returns

The Boolean function created from the Walsh-Hadamard values list, or an error if:

• the list length is less than 4
• the list length is not a power of 2.
• the number of variables is greater than 6 (meaning that the list length is greater than 64).

pub fn from_walsh_fourier_values( walsh_values: &[i32], ) -> Result<Self, BooleanFunctionError>

Computes a SmallBooleanFunction from Walsh-Fourier values, by applying the inverse Walsh-Fourier transform.

Parameters

• walsh_values - The Walsh-Hadamard values of the Boolean function.

Returns

The Boolean function created from the Walsh-Hadamard values list, or an error if:

• the list length is less than 4
• the list length is not a power of 2.
• the number of variables is greater than 6 (meaning that the list length is greater than 64).

pub fn get_1_local_neighbor_inner(&self, position: u32) -> Self

Returns a 1-local neighbor of the Boolean function, at a specific position

Parameters

• position: The position $i$ at which to compute the 1-local neighbor.

Returns

The 1-local neighbor of the Boolean function at the given position.

Panics

If the position is greater than the maximum input value, and the unsafe_disable_safety_checks feature is not enabled.

pub fn close_balanced_functions_iterator_inner( &self, ) -> Result<SmallCloseBalancedFunctionIterator, BooleanFunctionError>

Returns an iterator over the closest possible balanced Boolean functions.

See BooleanFunctionImpl::close_balanced_functions_iterator for more details.

Returns

An iterator over close balanced Boolean functions, or an error if the function is already balanced.

Note

It is assumed that the function truth table is correctly sanitized, so be careful if you generated it with unsafe_disable_safety_checks feature activated.

pub fn from_anf_polynomial_str_inner( anf_polynomial: &str, num_variables: usize, ) -> Result<Self, BooleanFunctionError>

Computes SmallBooleanFunction from string ANF representation

The ANF string representation must be in exact form “x0*x2*x3 + x2*x3 + x1 + 1”.

X’s index starts at 0, meaning the maximum index is variable count - 1.

Parameters:

• anf_polynomial: The string representation of the ANF form
• num_variables: Variable count of the polynomial

Returns

The SmallBooleanFunction corresponding to the ANF string representation, or an error if:

• the input string doesn’t respect the format and unsafe_disable_safety_checks feature is not activated.
• the polynomial variable count is greater than 6

pub fn from_anf_polynomial_inner( anf_polynomial: &AnfPolynomial, ) -> Result<Self, BooleanFunctionError>

Computes SmallBooleanFunction from ANF polynomial

Parameters:

• anf_polynomial: The polynomial in Algebraic Normal Form

Returns

The SmallBooleanFunction corresponding to the ANF polynomial, or an error if polynomial variable count > 6

Trait Implementations

impl Add for SmallBooleanFunction

ADD operator for Boolean functions truth tables.

It is equivalent to crate::SmallBooleanFunction::bitxor operator.

Panics

If the Boolean functions have different number of variables, and the unsafe_disable_safety_checks feature is not enabled.

type Output = SmallBooleanFunction

The resulting type after applying the + operator.

fn add(self, rhs: Self) -> Self::Output

Performs the + operation.

impl AddAssign for SmallBooleanFunction

In-place ADD operator for Boolean functions truth tables.

It is equivalent to crate::SmallBooleanFunction::bitxor_assign operator.

Panics

If the Boolean functions have different number of variables, and the unsafe_disable_safety_checks feature is not enabled.

fn add_assign(&mut self, rhs: Self)

Performs the += operation.

impl BitAnd for SmallBooleanFunction

AND operator for Boolean functions truth tables.

Panics

If the Boolean functions have different number of variables, and the unsafe_disable_safety_checks feature is not enabled.

type Output = SmallBooleanFunction

The resulting type after applying the & operator.

fn bitand(self, rhs: Self) -> Self::Output

Performs the & operation.

impl BitAndAssign for SmallBooleanFunction

In-place AND operator for Boolean functions truth tables.

Panics

If the Boolean functions have different number of variables, and the unsafe_disable_safety_checks feature is not enabled.

fn bitand_assign(&mut self, rhs: Self)

Performs the &= operation.

impl BitXor for SmallBooleanFunction

XOR operator for Boolean functions truth tables.

Panics

If the Boolean functions have different number of variables, and the unsafe_disable_safety_checks feature is not enabled.

type Output = SmallBooleanFunction

The resulting type after applying the ^ operator.

fn bitxor(self, rhs: Self) -> Self::Output

Performs the ^ operation.

impl BitXorAssign for SmallBooleanFunction

In-place XOR operator for Boolean functions truth tables.

Panics

If the Boolean functions have different number of variables, and the unsafe_disable_safety_checks feature is not enabled.

fn bitxor_assign(&mut self, rhs: Self)

Performs the ^= operation.

impl BooleanFunctionImpl for SmallBooleanFunction

fn variables_count(&self) -> usize

Variable count of the Boolean function.

fn get_boolean_function_type(&self) -> BooleanFunctionType

Internal type of the Boolean function abstraction:

fn is_balanced(&self) -> bool

Returns true if the Boolean function is balanced, ie it has an equal number of 0 and 1 outputs.

fn compute_cellular_automata_rule(&self, input_bits: u32) -> bool

Computes the value of the Boolean function for a given input, as a 32-bit unsigned integer.

fn derivative( &self, direction: u32, ) -> Result<BooleanFunction, BooleanFunctionError>

Computes the derivative of the Boolean function for a given direction.

fn is_linear(&self) -> bool

Returns true if the Boolean function is linear, ie its algebraic degree is 0 or 1.

fn reverse(&self) -> BooleanFunction

Reverse the Boolean function, ie swap 0 and 1 outputs.

fn algebraic_normal_form(&self) -> AnfPolynomial

Returns the Algebraic Normal Form of the Boolean function, in the form of an AnfPolynomial.

fn annihilator( &self, max_degree: Option<usize>, ) -> Option<(BooleanFunction, usize, usize)>

Returns, if it exists, an annihilator function, its degree and the dimension of annihilator vector space.

fn get_1_local_neighbor(&self, position: u32) -> BooleanFunction

Returns a 1-local neighbor of the Boolean function, at a specific position

fn iter(&self) -> BooleanFunctionIterator

Returns an iterator over the values of the Boolean function.

fn printable_hex_truth_table(&self) -> String

Returns the truth table of the Boolean function as a hexadecimal string.

fn biguint_truth_table(&self) -> BigUint

Returns the truth table of the Boolean function as a BigUint.

fn close_balanced_functions_iterator( &self, ) -> Result<CloseBalancedFunctionIterator, BooleanFunctionError>

Returns an iterator over the closest possible balanced Boolean functions.

fn get_max_input_value(&self) -> u32

Maximum input value for the Boolean function, as unsigned 32-bit integer.

fn walsh_hadamard_transform(&self, w: u32) -> i32

Computes the Walsh-Hadamard transform of the Boolean function for a given point.

fn walsh_hadamard_values(&self) -> Vec<i32>

Computes the Walsh-Hadamard values for all points.

fn absolute_walsh_hadamard_spectrum(&self) -> HashMap<u32, usize>

Computes the absolute Walsh-Hadamard spectrum of the Boolean function.

fn walsh_fourier_transform(&self, w: u32) -> i32

Computes the Walsh-Fourier transform of the Boolean function for a given point.

fn walsh_fourier_values(&self) -> Vec<i32>

Computes the Walsh-Fourier values for all points.

fn auto_correlation_transform(&self, w: u32) -> i32

Computes the autocorrelation transform of the Boolean function for a given point. The autocorrelation transform of a Boolean function $f$, for a given point $\omega$, is defined as:

fn absolute_autocorrelation(&self) -> HashMap<u32, usize>

Computes the absolute autocorrelation spectrum of the Boolean function.

fn absolute_indicator(&self) -> u32

Returns the absolute indicator of the Boolean function.

fn algebraic_degree(&self) -> usize

Returns the algebraic degree of the Boolean function.

fn is_symmetric(&self) -> bool

Returns true if the Boolean function is symmetric.

fn nonlinearity(&self) -> u32

Returns the nonlinearity of the Boolean function.

fn is_bent(&self) -> bool

Returns true if the Boolean function is bent, meaning maximally nonlinear, or perfectly nonlinear.

fn is_near_bent(&self) -> bool

Returns true if the Boolean function is near-bent.

fn algebraic_immunity(&self) -> usize

Returns the algebraic immunity of the Boolean function.

fn is_plateaued(&self) -> bool

Returns true if the Boolean function is plateaued.

fn sum_of_square_indicator(&self) -> usize

Returns the sum of the square of the indicator of the Boolean function.

fn has_linear_structure(&self) -> bool

Returns true if the Boolean function has a linear structure.

fn is_linear_structure(&self, value: u32) -> bool

Checks if the parameter is a linear structure of the Boolean function.

fn linear_structures(&self) -> Vec<u32>

List of all linear structures of the Boolean function.

fn correlation_immunity(&self) -> usize

Returns the correlation immunity order of the Boolean function (calculated using Xiao Massey theorem).

fn resiliency_order(&self) -> Option<usize>

Returns the resiliency order of the Boolean function.

fn support(&self) -> HashSet<u32>

Returns the support of the Boolean function.

fn propagation_criterion(&self) -> usize

Returns the maximum propagation criterion of the Boolean function.

fn try_u64_truth_table(&self) -> Option<u64>

Returns the truth table of the Boolean function as an unsigned 64-bit integer, if it fits (meaning the Boolean function has 6 or less input variables).

impl Clone for SmallBooleanFunction

fn clone(&self) -> SmallBooleanFunction

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Debug for SmallBooleanFunction

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl Deref for SmallBooleanFunction

type Target = dyn Fn(u32) -> bool

The resulting type after dereferencing.

fn deref(&self) -> &Self::Target

Dereferences the value.

impl From<SmallBooleanFunction> for BooleanFunction

fn from(v: SmallBooleanFunction) -> BooleanFunction

Converts to this type from the input type.

impl Mul for SmallBooleanFunction

MUL operator for Boolean functions truth tables.

It is equivalent to crate::SmallBooleanFunction::bitand operator.

Panics

If the Boolean functions have different number of variables, and the unsafe_disable_safety_checks feature is not enabled.

type Output = SmallBooleanFunction

The resulting type after applying the * operator.

fn mul(self, rhs: Self) -> Self::Output

Performs the * operation.

impl MulAssign for SmallBooleanFunction

In-place MUL operator for Boolean functions truth tables.

It is equivalent to crate::SmallBooleanFunction::bitand_assign operator.

Panics

If the Boolean functions have different number of variables, and the unsafe_disable_safety_checks feature is not enabled.

fn mul_assign(&mut self, rhs: Self)

Performs the *= operation.

impl Not for SmallBooleanFunction

NOT operator for Boolean functions.

This is equivalent to the crate::BooleanFunctionImpl::reverse operation: it reverses each output of the Boolean function.

type Output = SmallBooleanFunction

The resulting type after applying the ! operator.

fn not(self) -> Self::Output

Performs the unary ! operation.

impl PartialEq for SmallBooleanFunction

fn eq(&self, other: &SmallBooleanFunction) -> bool

Tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl TryInto<SmallBooleanFunction> for BooleanFunction

type Error = &'static str

The type returned in the event of a conversion error.

fn try_into( self, ) -> Result<SmallBooleanFunction, <Self as TryInto<SmallBooleanFunction>>::Error>

Performs the conversion.

impl Copy for SmallBooleanFunction

impl Eq for SmallBooleanFunction

impl StructuralPartialEq for SmallBooleanFunction