Field element modulo the backend scalar field used by this implementation. More...

#include <numeric.hpp>

Public Member Functions
	FieldElement ()

UInt256	to_uint256 () const
	Exports the field element as a canonical 256-bit unsigned integer.

std::array< unsigned char, 32 >	to_bytes_be () const
	Serializes the field element in big-endian form.

std::array< unsigned char, 32 >	to_bytes_le () const
	Serializes the field element in little-endian form.

std::string	to_hex () const
	Formats the field element as lowercase hexadecimal.

std::string	to_decimal () const
	Formats the field element as an unsigned decimal string.

bool	is_zero () const
	Returns true when the element is zero.

bool	is_one () const
	Returns true when the element is one.

bool	is_odd () const
	Returns true when the canonical representative is odd.

bool	is_square () const
	Returns true when the element is a quadratic residue in the field.

FieldElement	negate () const
	Returns the additive inverse modulo the field prime.

void	conditional_assign (const FieldElement &other, bool flag)
	Conditionally assigns `other` into `*this` when `flag` is true.

FieldElement	inverse_consttime () const
	Returns the multiplicative inverse modulo the field prime in constant time.

FieldElement	inverse () const
	Returns the multiplicative inverse modulo the field prime using the faster variable-time backend.

std::optional< FieldElement >	sqrt () const
	Computes a square root when one exists, otherwise returns `std::nullopt`.

FieldElement	pow (const UInt256 &exponent) const
	Raises the element to an unsigned exponent via square-and-multiply.

Static Public Member Functions
static FieldElement	zero ()
	Returns the additive identity of the scalar field.

static FieldElement	one ()
	Returns the multiplicative identity of the scalar field.

static FieldElement	from_u64 (std::uint64_t value)
	Constructs a field element from an unsigned 64-bit integer.

static FieldElement	from_int (std::int64_t value)
	Constructs a field element from a signed integer, reducing negatives modulo the field.

static Result< FieldElement >	try_from_bytes32 (const std::array< unsigned char, 32 > &bytes)
	Decodes a canonical 32-byte big-endian field element.

static FieldElement	from_bytes32 (const std::array< unsigned char, 32 > &bytes)
	Decodes a 32-byte big-endian field element.

static Result< FieldElement >	try_from_uint256 (const UInt256 &value)
	Converts a canonical 256-bit unsigned integer into the scalar field representation.

static FieldElement	from_uint256 (const UInt256 &value)
	Converts a 256-bit unsigned integer into the scalar field representation.

Friends
struct	detail::FieldElementAccess

bool	operator== (const FieldElement &lhs, const FieldElement &rhs)
	Compares two field elements for exact equality.

bool	operator!= (const FieldElement &lhs, const FieldElement &rhs)
	Compares two field elements for inequality.

FieldElement	operator+ (const FieldElement &lhs, const FieldElement &rhs)
	Adds two field elements modulo the field prime.

FieldElement	operator- (const FieldElement &lhs, const FieldElement &rhs)
	Subtracts two field elements modulo the field prime.

FieldElement	operator* (const FieldElement &lhs, const FieldElement &rhs)
	Multiplies two field elements modulo the field prime.