Namespaces
	curves

	detail

	fields

	pairing

	policies

Classes
struct	is_complex

struct	is_complex< std::complex< T > >

struct	is_curve

struct	is_curve_group

struct	is_extended_field

struct	is_field

struct	is_g1_group_element

struct	is_g2_group_element

struct	is_group_element

struct	matrix
	A container representing a matrix. More...

struct	remove_complex

struct	remove_complex< std::complex< T > >

struct	vector
	A container representing a vector. More...

Typedefs
template<typename T >
using	remove_complex_t = typename remove_complex< T >::type

template<typename GroupType >
using	window_table = std::vector< std::vector< typename GroupType::value_type > >

Functions
template<typename T , std::size_t N>
constexpr vector< nil::crypto3::detail::remove_complex_t< T >, N >	abs (const vector< T, N > &v)
	computes the elementwise absolute value More...

template<typename T >
constexpr nil::crypto3::detail::remove_complex_t< T >	abs (T x)
	computes the absolute value More...

template<typename T , std::size_t N, typename F , typename U >
constexpr U	accumulate (const vector< T, N > &v, U init, F &&f)
	accumulates an operation across a vector More...

template<typename T , std::size_t N>
constexpr matrix< T, N, 1 >	as_column (const vector< T, N > &v)
	converts a vector into a column vector More...

template<typename T , std::size_t N>
constexpr matrix< T, 1, N >	as_row (const vector< T, N > &v)
	converts a vector into a row vector More...

template<typename GroupType , typename FieldType , typename InputRange , typename = typename std::enable_if< std::is_same<typename InputRange::value_type, typename FieldType::value_type>::value>::type>
std::vector< typename GroupType::value_type >	batch_exp (const std::size_t scalar_size, const std::size_t window, const window_table< GroupType > &table, const InputRange &v)

template<typename GroupType , typename FieldType , typename InputRange , typename = typename std::enable_if< std::is_same<typename InputRange::value_type, typename FieldType::value_type>::value>::type>
std::vector< typename GroupType::value_type >	batch_exp_with_coeff (const std::size_t scalar_size, const std::size_t window, const window_table< GroupType > &table, const typename FieldType::value_type &coeff, const InputRange &v)

template<typename GroupType , typename InputRange >
std::enable_if< std::is_same< typename InputRange::value_type, typename GroupType::value_type >::value, void >::type	batch_to_special (InputRange &vec)

template<typename T , typename U , std::size_t N, std::size_t M>
constexpr matrix< T, N, M >	cast (const matrix< U, N, M > &m)
	casts a vector to another type More...

template<typename T , typename U , std::size_t N>
constexpr vector< T, N >	cast (const vector< U, N > &v)
	casts a vector to another type More...

template<typename T , std::size_t N, std::size_t M>
constexpr vector< T, N+M >	concat (vector< T, N > a, vector< T, M > b)
	concatenates two vectors More...

template<typename T , std::size_t M, std::size_t N>
constexpr matrix< T, M, N >	conj (const matrix< T, M, N > &m)
	computes the elementwise complex conjugate More...

template<typename T , std::size_t N>
constexpr vector< T, N >	conj (const vector< T, N > &v)
	computes the elementwise complex conjugate More...

template<typename T >
constexpr T	conj (T x)
	computes the complex conjugate More...

template<typename T , std::size_t M>
constexpr T	det (const matrix< T, M, M > &m)
	Compute the determinant. More...

template<typename T , std::size_t N>
constexpr T	dot (const vector< T, N > &a, const vector< T, N > &b)
	computes the dot product More...

template<typename PairingCurveType , typename PairingPolicy = pairing::pairing_policy<PairingCurveType>>
PairingCurveType::gt_type::value_type	double_miller_loop (const typename PairingPolicy::g1_precomputed_type &prec_P1, const typename PairingPolicy::g2_precomputed_type &prec_Q1, const typename PairingPolicy::g1_precomputed_type &prec_P2, const typename PairingPolicy::g2_precomputed_type &prec_Q2)

template<typename F , typename T , typename... Matrices, typename U = std::invoke_result_t<F, T, typename Matrices::value_type...>, std::size_t N = detail::all_same_value<std::size_t, Matrices::column_size...>::value, std::size_t M = detail::all_same_value<std::size_t, Matrices::row_size...>::value>
constexpr matrix< U, N, M >	elementwise (F f, const matrix< T, N, M > &m, const Matrices &...matrices)
	applies a function elementwise between many matrices More...

template<typename F , typename T , typename... Vectors, typename U = std::invoke_result_t<F, T, typename Vectors::value_type...>, std::size_t N = detail::all_same_value<std::size_t, Vectors::size...>::value>
constexpr vector< U, N >	elementwise (F f, const vector< T, N > &v, const Vectors &...vectors)
	applies a function elementwise between many vectors More...

constexpr double	exponentiate (double x, int n)
	computes exponents More...

template<std::size_t N, std::size_t M, typename T >
constexpr matrix< T, N, M >	fill (T value)
	generates a matrix containing a single value More...

template<std::size_t N, typename T >
constexpr vector< T, N >	fill (T value)
	generates a vector containing a single value More...

template<typename PairingCurveType , typename PairingPolicy = pairing::pairing_policy<PairingCurveType>>
PairingCurveType::gt_type::value_type	final_exponentiation (const typename PairingCurveType::gt_type::value_type &elt)

template<typename BaseValueType , typename Backend , multiprecision::expression_template_option ExpressionTemplates>
BaseValueType	fixed_window_wnaf_exp (const std::size_t window_size, const BaseValueType &base, const multiprecision::number< Backend, ExpressionTemplates > &scalar)

template<std::size_t N, std::size_t M, typename F >
constexpr decltype(auto)	generate (F &&f)
	generates a matrix as a function of its indices More...

template<std::size_t N, typename F >
constexpr decltype(auto)	generate (F &&f)
	generates a vector as a function of its index More...

template<typename GroupType >
std::size_t	get_exp_window_size (const std::size_t num_scalars)

template<typename T , std::size_t N>
constexpr matrix< T, N, N >	get_identity ()

template<typename GroupType >
window_table< GroupType >	get_window_table (const std::size_t scalar_size, const std::size_t window, const typename GroupType::value_type &g)

template<typename T , std::size_t M, std::size_t N>
constexpr matrix< T, N, M >	hermitian (const matrix< T, M, N > &m)
	computes the Hermitian transpose More...

template<std::size_t M, std::size_t N, std::size_t P, typename T >
constexpr matrix< T, M, N+P >	horzcat (const matrix< T, M, N > &a, const matrix< T, M, P > &b)
	horizontally concatenates two matrices More...

template<typename T , std::size_t M, std::size_t N>
constexpr matrix< nil::crypto3::detail::remove_complex_t< T >, M, N >	imag (const matrix< T, M, N > &m)
	computes the elementwise imag More...

template<typename T , std::size_t N>
constexpr vector< nil::crypto3::detail::remove_complex_t< T >, N >	imag (const vector< T, N > &v)
	computes the elementwise imag More...

template<typename InputBaseIterator >
std::iterator_traits< InputBaseIterator >::value_type	inner_product (InputBaseIterator a_begin, InputBaseIterator a_end, InputBaseIterator b_begin, InputBaseIterator b_end)

template<typename T , std::size_t M>
constexpr matrix< T, M, M >	inverse (const matrix< T, M, M > &m)
	computes the matrix inverse More...

template<std::size_t N, typename T >
constexpr vector< T, N >	iota (T value=T())
	generates a vector containing consecutive elements More...

template<typename T , std::size_t M, std::size_t N, std::size_t P, std::size_t Q>
constexpr matrix< T, M P, N Q >	kron (const matrix< T, M, N > &a, const matrix< T, P, Q > &b)
	Computes the kronecker tensor product. More...

template<std::size_t N, typename T >
constexpr vector< T, N >	linspace (T min, T max)
	generates a vector of equally spaced elements More...

template<typename T , std::size_t M, std::size_t N>
constexpr T	macs (const matrix< T, M, N > &m)
	Computes the maximum absolute column sum norm. More...

template<typename... Args>
constexpr decltype(auto)	make_vector (Args... args)
	constructs a `vector` from arguments More...

template<typename T , std::size_t M, std::size_t N>
constexpr T	mars (const matrix< T, M, N > &m)
	Computes the maximum absolute row sum norm. More...

template<typename T , std::size_t M, std::size_t N, std::size_t P>
constexpr matrix< T, M, P >	matmul (const matrix< T, M, N > &a, const matrix< T, N, P > &b)
	computes the matrix product More...

template<typename T , std::size_t M, std::size_t N>
constexpr vector< T, M >	matvectmul (const matrix< T, M, N > &m, const vector< T, N > &v)
	computes the product of matrix and vector More...

template<typename T , std::size_t N>
constexpr T	max (const vector< T, N > &v)
	computes the maximum valued element More...

template<typename T , std::size_t N>
constexpr std::size_t	max_index (const vector< T, N > &v)
	computes the index of the maximum valued element More...

template<typename PairingCurveType , typename PairingPolicy = pairing::pairing_policy<PairingCurveType>>
PairingCurveType::gt_type::value_type	miller_loop (const typename PairingPolicy::g1_precomputed_type &prec_P, const typename PairingPolicy::g2_precomputed_type &prec_Q)

template<typename T , std::size_t N>
constexpr T	min (const vector< T, N > &v)
	computes the minimum valued element More...

template<typename T , std::size_t N>
constexpr std::size_t	min_index (const vector< T, N > &v)
	computes the index of the minimum valued element More...

template<typename MultiexpMethod , typename InputBaseIterator , typename InputFieldIterator >
std::iterator_traits< InputBaseIterator >::value_type	multiexp (InputBaseIterator vec_start, InputBaseIterator vec_end, InputFieldIterator scalar_start, InputFieldIterator scalar_end, const std::size_t chunks_count)

template<typename MultiexpMethod , typename InputBaseIterator , typename InputFieldIterator >
std::iterator_traits< InputBaseIterator >::value_type	multiexp_with_mixed_addition (InputBaseIterator vec_start, InputBaseIterator vec_end, InputFieldIterator scalar_start, InputFieldIterator scalar_end, const std::size_t chunks_count)

constexpr double	nthroot (double x, int n)
	computes the th root More...

template<typename T , std::size_t N, std::size_t M>
constexpr bool	operator!= (const matrix< T, N, M > &a, const matrix< T, N, M > &b)
	checks inequality of two matrices More...

template<typename T , std::size_t N>
constexpr bool	operator!= (const vector< T, N > &a, const vector< T, N > &b)
	checks inequality of two vectors More...

template<typename T , std::size_t N, std::size_t M>
constexpr matrix< T, N, M >	operator* (const matrix< T, N, M > &a, const matrix< T, N, M > &b)
	computes the Hadamard product More...

template<typename T , std::size_t N, std::size_t M>
constexpr matrix< T, N, M >	operator* (const matrix< T, N, M > &m, T a)
	computes the product of a matrix and a scalar More...

template<typename T , std::size_t N>
constexpr vector< T, N >	operator* (const vector< T, N > &a, const vector< T, N > &b)
	computes the Hadamard product More...

template<typename T , std::size_t N>
constexpr vector< T, N >	operator* (const vector< T, N > &v, T a)
	computes the product of a vector and a scalar More...

template<typename T , std::size_t N, std::size_t M>
constexpr matrix< T, N, M >	operator* (T a, const matrix< T, N, M > &m)
	computes the product of a matrix and a scalar More...

template<typename T , std::size_t N>
constexpr vector< T, N >	operator* (T a, const vector< T, N > &v)
	computes the product of a vector and a scalar More...

template<typename T , std::size_t N, std::size_t M>
constexpr matrix< T, N, M >	operator+ (const matrix< T, N, M > &a, const matrix< T, N, M > &b)
	computes the matrix sum More...

template<typename T , std::size_t N, std::size_t M>
constexpr matrix< T, N, M >	operator+ (const matrix< T, N, M > &m, T a)
	computes the sum of a matrix and a scalar More...

template<typename T , std::size_t N>
constexpr vector< T, N >	operator+ (const vector< T, N > &a, const vector< T, N > &b)
	computes the vector sum More...

template<typename T , std::size_t N>
constexpr vector< T, N >	operator+ (const vector< T, N > &v, T a)
	computes the sum of a vector and a scalar More...

template<typename T , std::size_t N, std::size_t M>
constexpr matrix< T, N, M >	operator+ (T a, const matrix< T, N, M > &m)
	computes the sum of a matrix and a scalar More...

template<typename T , std::size_t N>
constexpr vector< T, N >	operator+ (T a, const vector< T, N > &v)
	computes the sum of a vector and a scalar More...

template<typename T , std::size_t N, std::size_t M>
constexpr matrix< T, N, M >	operator/ (const matrix< T, N, M > &a, const matrix< T, N, M > &b)
	computes the elementwise matrix quotient More...

template<typename T , std::size_t N>
constexpr vector< T, N >	operator/ (const vector< T, N > &a, const vector< T, N > &b)
	computes the elementwise vector quotient More...

template<typename T , std::size_t N, std::size_t M>
constexpr matrix< T, N, M >	operator/ (T a, const matrix< T, N, M > &m)
	computes the quotient between a matrix and a scalar More...

template<typename T , std::size_t N>
constexpr vector< T, N >	operator/ (T a, const vector< T, N > &v)
	computes the quotient between a vector and a scalar More...

template<typename T , std::size_t N, std::size_t M>
constexpr bool	operator== (const matrix< T, N, M > &a, const matrix< T, N, M > &b)
	checks equality of two matrices More...

template<typename T , std::size_t N>
constexpr bool	operator== (const vector< T, N > &a, const vector< T, N > &b)
	checks equality of two vectors More...

template<typename CurveGroupValueType , typename Backend , multiprecision::expression_template_option ExpressionTemplates>
CurveGroupValueType	opt_window_wnaf_exp (const CurveGroupValueType &base, const multiprecision::number< Backend, ExpressionTemplates > &scalar, const std::size_t scalar_bits)

template<typename PairingCurveType , typename PairingPolicy = pairing::pairing_policy<PairingCurveType>>
PairingCurveType::gt_type::value_type	pair (const typename PairingCurveType::template g1_type<>::value_type &v1, const typename PairingCurveType::template g2_type<>::value_type &v2)

template<typename PairingCurveType , typename PairingPolicy = pairing::pairing_policy<PairingCurveType>>
PairingCurveType::gt_type::value_type	pair_reduced (const typename PairingCurveType::template g1_type<>::value_type &v1, const typename PairingCurveType::template g2_type<>::value_type &v2)

template<typename PairingCurveType , typename PairingPolicy = pairing::pairing_policy<PairingCurveType>>
PairingPolicy::g1_precomputed_type	precompute_g1 (const typename PairingCurveType::template g1_type<>::value_type &P)

template<typename PairingCurveType , typename PairingPolicy = pairing::pairing_policy<PairingCurveType>>
PairingPolicy::g2_precomputed_type	precompute_g2 (const typename PairingCurveType::template g2_type<>::value_type &P)

template<typename FieldType , typename DistributionType = boost::random::uniform_int_distribution<typename FieldType::integral_type>, typename GeneratorType = boost::random::mt19937>
std::enable_if< is_field< FieldType >::value &&!(is_extended_field< FieldType >::value), typename FieldType::value_type >::type	random_element ()

template<typename FieldType , typename DistributionType = boost::random::uniform_int_distribution<typename FieldType::integral_type>, typename GeneratorType = boost::random::mt19937>
std::enable_if< is_field< FieldType >::value &&is_extended_field< FieldType >::value, typename FieldType::value_type >::type	random_element ()

template<typename CurveGroupType , typename DistributionType = boost::random::uniform_int_distribution<typename CurveGroupType::field_type::integral_type>, typename GeneratorType = boost::random::mt19937>
std::enable_if< is_curve_group< CurveGroupType >::value, typename CurveGroupType::value_type >::type	random_element ()

template<typename T , std::size_t M, std::size_t N>
constexpr std::size_t	rank (const matrix< T, M, N > &m)
	Compute the rank. More...

template<typename T , std::size_t M, std::size_t N>
constexpr matrix< nil::crypto3::detail::remove_complex_t< T >, M, N >	real (const matrix< T, M, N > &m)
	computes the elementwise real More...

template<typename T , std::size_t N>
constexpr vector< nil::crypto3::detail::remove_complex_t< T >, N >	real (const vector< T, N > &v)
	computes the elementwise real More...

template<std::size_t Row, std::size_t Col, std::size_t M, std::size_t N, typename T >
constexpr matrix< T, M Row, N Col >	repmat (const matrix< T, M, N > &m)
	repeats a matrix More...

template<std::size_t P, std::size_t Q, std::size_t M, std::size_t N, typename T >
constexpr matrix< T, P, Q >	reshape (const matrix< T, M, N > &m)
	reshapes a matrix More...

template<std::size_t N, typename T >
constexpr vector< T, N >	rotate (vector< T, N > v, int n)
	shifts vector elements More...

template<typename T , std::size_t M, std::size_t N>
constexpr matrix< T, M, N >	rref (const matrix< T, M, N > &m)
	Compute the reduced row echelon form. More...

template<typename T , std::size_t M, std::size_t N>
constexpr matrix< T, M, N >	rref (const matrix< T, M, N > &m, T tolerance)
	Compute the reduced row echelon form. More...

template<std::size_t M, typename T , std::size_t N>
constexpr vector< T, M >	slice (vector< T, N > v, std::size_t start=0)
	slices a vector into a subvector More...

template<typename T , std::size_t N>
constexpr vector< T, N >	sqrt (const vector< T, N > &v)
	computes the elementwise square root More...

constexpr double	sqrt (double x)
	computes the square root More...

constexpr float	sqrt (float x)
	computes the square root More...

template<typename InputType , typename OutputType >
constexpr void	strxor (const InputType &in1, const InputType &in2, OutputType &out)

template<typename InputIterator1 , typename InputIterator2 , typename OutputIterator >
constexpr std::enable_if< std::is_same< typename std::iterator_traits< InputIterator1 >::value_type, typename std::iterator_traits< InputIterator2 >::value_type >::value, OutputIterator >::type	strxor (InputIterator1 first1, InputIterator1 last1, InputIterator2 first2, InputIterator2 last2, OutputIterator out)

template<std::size_t P, std::size_t Q, std::size_t M, std::size_t N, typename T >
constexpr matrix< T, P, Q >	submat (const matrix< T, M, N > &m, std::size_t a, std::size_t b)
	extracts the submatrix of a matrix More...

template<typename T , std::size_t N>
constexpr T	sum (const vector< T, N > &v)
	computes the sum of elements More...

template<std::size_t M, std::size_t N, typename T >
constexpr matrix< T, M, N >	swapcol (matrix< T, M, N > m, std::size_t a, std::size_t b)
	swaps columns of a matrix More...

template<std::size_t M, std::size_t N, typename T >
constexpr matrix< T, M, N >	swaprow (matrix< T, M, N > m, std::size_t a, std::size_t b)
	swaps rows of a matrix More...

template<typename T , std::size_t M>
constexpr T	trace (const matrix< T, M, M > &m)
	computes the trace More...

template<typename T , std::size_t M, std::size_t N>
constexpr matrix< T, N, M >	transpose (const matrix< T, M, N > &m)
	computes the transpose More...

template<typename T , std::size_t M, std::size_t N>
constexpr vector< T, N >	vectmatmul (const vector< T, M > &v, const matrix< T, M, N > &m)
	computes the product of vector and matrix More...

template<std::size_t M, std::size_t N, std::size_t P, typename T >
constexpr matrix< T, M+N, P >	vertcat (const matrix< T, M, P > &a, const matrix< T, N, P > &b)
	vertically concatenates two matrices More...

template<typename GroupType , typename FieldType >
GroupType::value_type	windowed_exp (const std::size_t scalar_size, const std::size_t window, const window_table< GroupType > &powers_of_g, const typename FieldType::value_type &pow)

matrix deduction guides
template<typename T , std::size_t M, std::size_t N>
	matrix (const T(&)[M][N]) -> matrix< T, M, N >
	deduction guide for aggregate initialization More...

vector deduction guides
template<typename T , typename... U>
	vector (T, U...) -> vector< std::enable_if_t<(std::is_same_v< T, U > &&...), T >, 1+sizeof...(U)>
	deduction guide for uniform initialization More...

template<typename T , std::size_t N>
	vector (const T(&)[N]) -> vector< T, N >
	deduction guide for aggregate initialization More...

Variables
template<typename T , std::size_t N>
const matrix< T, N, N >	identity
	the matrix identity More...

template<typename T >
constexpr bool	is_complex_v = is_complex<T>::value

Typedef Documentation

◆ remove_complex_t

template<typename T >

using nil::crypto3::algebra::remove_complex_t = typedef typename remove_complex<T>::type

◆ window_table

template<typename GroupType >

using nil::crypto3::algebra::window_table = typedef std::vector<std::vector<typename GroupType::value_type> >

A window table stores window sizes for different instance sizes for fixed-base multi-scalar multiplications.

Function Documentation

◆ batch_exp()

template<typename GroupType , typename FieldType , typename InputRange , typename = typename std::enable_if< std::is_same<typename InputRange::value_type, typename FieldType::value_type>::value>::type>

std::vector<typename GroupType::value_type> nil::crypto3::algebra::batch_exp	(	const std::size_t	scalar_size,
		const std::size_t	window,
		const window_table< GroupType > &	table,
		const InputRange &	v
	)

◆ batch_exp_with_coeff()

template<typename GroupType , typename FieldType , typename InputRange , typename = typename std::enable_if< std::is_same<typename InputRange::value_type, typename FieldType::value_type>::value>::type>

std::vector<typename GroupType::value_type> nil::crypto3::algebra::batch_exp_with_coeff	(	const std::size_t	scalar_size,
		const std::size_t	window,
		const window_table< GroupType > &	table,
		const typename FieldType::value_type &	coeff,
		const InputRange &	v
	)

◆ batch_to_special()

template<typename GroupType , typename InputRange >

std::enable_if< std::is_same<typename InputRange::value_type, typename GroupType::value_type>::value, void>::type nil::crypto3::algebra::batch_to_special ( InputRange & vec )

◆ double_miller_loop()

template<typename PairingCurveType , typename PairingPolicy = pairing::pairing_policy<PairingCurveType>>

PairingCurveType::gt_type::value_type nil::crypto3::algebra::double_miller_loop	(	const typename PairingPolicy::g1_precomputed_type &	prec_P1,
		const typename PairingPolicy::g2_precomputed_type &	prec_Q1,
		const typename PairingPolicy::g1_precomputed_type &	prec_P2,
		const typename PairingPolicy::g2_precomputed_type &	prec_Q2
	)

◆ final_exponentiation()

template<typename PairingCurveType , typename PairingPolicy = pairing::pairing_policy<PairingCurveType>>

PairingCurveType::gt_type::value_type nil::crypto3::algebra::final_exponentiation ( const typename PairingCurveType::gt_type::value_type & elt )

◆ fixed_window_wnaf_exp()

template<typename BaseValueType , typename Backend , multiprecision::expression_template_option ExpressionTemplates>

BaseValueType nil::crypto3::algebra::fixed_window_wnaf_exp	(	const std::size_t	window_size,
		const BaseValueType &	base,
		const multiprecision::number< Backend, ExpressionTemplates > &	scalar
	)

◆ get_exp_window_size()

template<typename GroupType >

std::size_t nil::crypto3::algebra::get_exp_window_size ( const std::size_t num_scalars )

◆ get_window_table()

template<typename GroupType >

window_table<GroupType> nil::crypto3::algebra::get_window_table	(	const std::size_t	scalar_size,
		const std::size_t	window,
		const typename GroupType::value_type &	g
	)

◆ inner_product()

template<typename InputBaseIterator >

std::iterator_traits<InputBaseIterator>::value_type nil::crypto3::algebra::inner_product	(	InputBaseIterator	a_begin,
		InputBaseIterator	a_end,
		InputBaseIterator	b_begin,
		InputBaseIterator	b_end
	)

inline

◆ miller_loop()

template<typename PairingCurveType , typename PairingPolicy = pairing::pairing_policy<PairingCurveType>>

PairingCurveType::gt_type::value_type nil::crypto3::algebra::miller_loop	(	const typename PairingPolicy::g1_precomputed_type &	prec_P,
		const typename PairingPolicy::g2_precomputed_type &	prec_Q
	)

◆ multiexp()

template<typename MultiexpMethod , typename InputBaseIterator , typename InputFieldIterator >

std::iterator_traits<InputBaseIterator>::value_type nil::crypto3::algebra::multiexp	(	InputBaseIterator	vec_start,
		InputBaseIterator	vec_end,
		InputFieldIterator	scalar_start,
		InputFieldIterator	scalar_end,
		const std::size_t	chunks_count
	)

◆ multiexp_with_mixed_addition()

template<typename MultiexpMethod , typename InputBaseIterator , typename InputFieldIterator >

std::iterator_traits<InputBaseIterator>::value_type nil::crypto3::algebra::multiexp_with_mixed_addition	(	InputBaseIterator	vec_start,
		InputBaseIterator	vec_end,
		InputFieldIterator	scalar_start,
		InputFieldIterator	scalar_end,
		const std::size_t	chunks_count
	)

◆ opt_window_wnaf_exp()

template<typename CurveGroupValueType , typename Backend , multiprecision::expression_template_option ExpressionTemplates>

CurveGroupValueType nil::crypto3::algebra::opt_window_wnaf_exp	(	const CurveGroupValueType &	base,
		const multiprecision::number< Backend, ExpressionTemplates > &	scalar,
		const std::size_t	scalar_bits
	)

◆ pair()

template<typename PairingCurveType , typename PairingPolicy = pairing::pairing_policy<PairingCurveType>>

PairingCurveType::gt_type::value_type nil::crypto3::algebra::pair	(	const typename PairingCurveType::template g1_type<>::value_type &	v1,
		const typename PairingCurveType::template g2_type<>::value_type &	v2
	)

◆ pair_reduced()

template<typename PairingCurveType , typename PairingPolicy = pairing::pairing_policy<PairingCurveType>>

PairingCurveType::gt_type::value_type nil::crypto3::algebra::pair_reduced	(	const typename PairingCurveType::template g1_type<>::value_type &	v1,
		const typename PairingCurveType::template g2_type<>::value_type &	v2
	)

◆ precompute_g1()

template<typename PairingCurveType , typename PairingPolicy = pairing::pairing_policy<PairingCurveType>>

PairingPolicy::g1_precomputed_type nil::crypto3::algebra::precompute_g1 ( const typename PairingCurveType::template g1_type<>::value_type & P )

◆ precompute_g2()

template<typename PairingCurveType , typename PairingPolicy = pairing::pairing_policy<PairingCurveType>>

PairingPolicy::g2_precomputed_type nil::crypto3::algebra::precompute_g2 ( const typename PairingCurveType::template g2_type<>::value_type & P )

◆ random_element() [1/3]

template<typename FieldType , typename DistributionType = boost::random::uniform_int_distribution<typename FieldType::integral_type>, typename GeneratorType = boost::random::mt19937>

std::enable_if<is_field<FieldType>::value && !(is_extended_field<FieldType>::value), typename FieldType::value_type>::type nil::crypto3::algebra::random_element ( )

◆ random_element() [2/3]

template<typename FieldType , typename DistributionType = boost::random::uniform_int_distribution<typename FieldType::integral_type>, typename GeneratorType = boost::random::mt19937>

std::enable_if<is_field<FieldType>::value && is_extended_field<FieldType>::value, typename FieldType::value_type>::type nil::crypto3::algebra::random_element ( )

◆ random_element() [3/3]

template<typename CurveGroupType , typename DistributionType = boost::random::uniform_int_distribution<typename CurveGroupType::field_type::integral_type>, typename GeneratorType = boost::random::mt19937>

std::enable_if<is_curve_group<CurveGroupType>::value, typename CurveGroupType::value_type>::type nil::crypto3::algebra::random_element ( )

◆ strxor() [1/2]

template<typename InputType , typename OutputType >

constexpr void nil::crypto3::algebra::strxor	(	const InputType &	in1,
		const InputType &	in2,
		OutputType &	out
	)

inlineconstexpr

◆ strxor() [2/2]

template<typename InputIterator1 , typename InputIterator2 , typename OutputIterator >

constexpr std::enable_if<std::is_same<typename std::iterator_traits<InputIterator1>::value_type, typename std::iterator_traits<InputIterator2>::value_type>::value, OutputIterator>::type nil::crypto3::algebra::strxor	(	InputIterator1	first1,
		InputIterator1	last1,
		InputIterator2	first2,
		InputIterator2	last2,
		OutputIterator	out
	)

inlineconstexpr

◆ windowed_exp()

template<typename GroupType , typename FieldType >

GroupType::value_type nil::crypto3::algebra::windowed_exp	(	const std::size_t	scalar_size,
		const std::size_t	window,
		const window_table< GroupType > &	powers_of_g,
		const typename FieldType::value_type &	pow
	)

Variable Documentation

◆ is_complex_v

template<typename T >

constexpr bool nil::crypto3::algebra::is_complex_v = is_complex<T>::value

constexpr

Namespaces

Classes

Typedefs

Functions

Variables

Typedef Documentation

◆ remove_complex_t

◆ window_table

Function Documentation

◆ batch_exp()

◆ batch_exp_with_coeff()

◆ batch_to_special()

◆ double_miller_loop()

◆ final_exponentiation()

◆ fixed_window_wnaf_exp()

◆ get_exp_window_size()

◆ get_window_table()

◆ inner_product()

◆ miller_loop()

◆ multiexp()

◆ multiexp_with_mixed_addition()

◆ opt_window_wnaf_exp()

◆ pair()

◆ pair_reduced()

◆ precompute_g1()

◆ precompute_g2()

◆ random_element() [1/3]

◆ random_element() [2/3]

◆ random_element() [3/3]

◆ strxor() [1/2]

◆ strxor() [2/2]

◆ windowed_exp()

Variable Documentation

◆ is_complex_v