field.h File Reference

#include "util.h"
#include "field_10x26.h"

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Functions
static void	secp256k1_fe_normalize (secp256k1_fe *r)
	Normalize a field element. More...
static void	secp256k1_fe_normalize_weak (secp256k1_fe *r)
	Weakly normalize a field element: reduce its magnitude to 1, but don't fully normalize. More...
static void	secp256k1_fe_normalize_var (secp256k1_fe *r)
	Normalize a field element, without constant-time guarantee. More...
static int	secp256k1_fe_normalizes_to_zero (const secp256k1_fe *r)
	Verify whether a field element represents zero i.e. More...
static int	secp256k1_fe_normalizes_to_zero_var (const secp256k1_fe *r)
	Verify whether a field element represents zero i.e. More...
static void	secp256k1_fe_set_int (secp256k1_fe *r, int a)
	Set a field element equal to a small (not greater than 0x7FFF), non-negative integer. More...
static void	secp256k1_fe_clear (secp256k1_fe *a)
	Sets a field element equal to zero, initializing all fields. More...
static int	secp256k1_fe_is_zero (const secp256k1_fe *a)
	Verify whether a field element is zero. More...
static int	secp256k1_fe_is_odd (const secp256k1_fe *a)
	Check the "oddness" of a field element. More...
static int	secp256k1_fe_equal (const secp256k1_fe *a, const secp256k1_fe *b)
	Compare two field elements. More...
static int	secp256k1_fe_equal_var (const secp256k1_fe *a, const secp256k1_fe *b)
	Same as secp256k1_fe_equal, but may be variable time. More...
static int	secp256k1_fe_cmp_var (const secp256k1_fe *a, const secp256k1_fe *b)
	Compare two field elements. More...
static int	secp256k1_fe_set_b32 (secp256k1_fe *r, const unsigned char *a)
	Set a field element equal to 32-byte big endian value. More...
static void	secp256k1_fe_get_b32 (unsigned char *r, const secp256k1_fe *a)
	Convert a field element to a 32-byte big endian value. More...
static void	secp256k1_fe_negate (secp256k1_fe *r, const secp256k1_fe *a, int m)
	Set a field element equal to the additive inverse of another. More...
static void	secp256k1_fe_mul_int (secp256k1_fe *r, int a)
	Multiplies the passed field element with a small integer constant. More...
static void	secp256k1_fe_add (secp256k1_fe *r, const secp256k1_fe *a)
	Adds a field element to another. More...
static void	secp256k1_fe_mul (secp256k1_fe *r, const secp256k1_fe *a, const secp256k1_fe *SECP256K1_RESTRICT b)
	Sets a field element to be the product of two others. More...
static void	secp256k1_fe_sqr (secp256k1_fe *r, const secp256k1_fe *a)
	Sets a field element to be the square of another. More...
static int	secp256k1_fe_sqrt (secp256k1_fe *r, const secp256k1_fe *a)
	If a has a square root, it is computed in r and 1 is returned. More...
static void	secp256k1_fe_inv (secp256k1_fe *r, const secp256k1_fe *a)
	Sets a field element to be the (modular) inverse of another. More...
static void	secp256k1_fe_inv_var (secp256k1_fe *r, const secp256k1_fe *a)
	Potentially faster version of secp256k1_fe_inv, without constant-time guarantee. More...
static void	secp256k1_fe_to_storage (secp256k1_fe_storage *r, const secp256k1_fe *a)
	Convert a field element to the storage type. More...
static void	secp256k1_fe_from_storage (secp256k1_fe *r, const secp256k1_fe_storage *a)
	Convert a field element back from the storage type. More...
static void	secp256k1_fe_storage_cmov (secp256k1_fe_storage *r, const secp256k1_fe_storage *a, int flag)
	If flag is true, set *r equal to *a; otherwise leave it. More...
static void	secp256k1_fe_cmov (secp256k1_fe *r, const secp256k1_fe *a, int flag)
	If flag is true, set *r equal to *a; otherwise leave it. More...
static void	secp256k1_fe_half (secp256k1_fe *r)
	Halves the value of a field element modulo the field prime. More...
static void	secp256k1_fe_get_bounds (secp256k1_fe *r, int m)
	Sets each limb of 'r' to its upper bound at magnitude 'm'. More...

Variables
static const secp256k1_fe	secp256k1_fe_one = SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 1)
	Field element module. More...
static const secp256k1_fe	secp256k1_const_beta

Function Documentation

secp256k1_fe_add()

static void secp256k1_fe_add ( secp256k1_fe *  r, const secp256k1_fe *  a  )

static

Adds a field element to another.

The result has the sum of the inputs' magnitudes as magnitude.

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secp256k1_fe_clear()

static void secp256k1_fe_clear ( secp256k1_fe *  a )

static

Sets a field element equal to zero, initializing all fields.

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secp256k1_fe_cmov()

static void secp256k1_fe_cmov ( secp256k1_fe *  r, const secp256k1_fe *  a, int  flag  )

static

If flag is true, set *r equal to *a; otherwise leave it.

Constant-time. Both *r and *a must be initialized.

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secp256k1_fe_cmp_var()

static int secp256k1_fe_cmp_var ( const secp256k1_fe *  a, const secp256k1_fe *  b  )

static

Compare two field elements.

Requires both inputs to be normalized

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secp256k1_fe_equal()

static int secp256k1_fe_equal ( const secp256k1_fe *  a, const secp256k1_fe *  b  )

static

Compare two field elements.

Requires magnitude-1 inputs.

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secp256k1_fe_equal_var()

static int secp256k1_fe_equal_var ( const secp256k1_fe *  a, const secp256k1_fe *  b  )

static

Same as secp256k1_fe_equal, but may be variable time.

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secp256k1_fe_from_storage()

static void secp256k1_fe_from_storage ( secp256k1_fe *  r, const secp256k1_fe_storage *  a  )

static

Convert a field element back from the storage type.

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secp256k1_fe_get_b32()

static void secp256k1_fe_get_b32 ( unsigned char *  r, const secp256k1_fe *  a  )

static

Convert a field element to a 32-byte big endian value.

Requires the input to be normalized

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secp256k1_fe_get_bounds()

static void secp256k1_fe_get_bounds ( secp256k1_fe *  r, int  m  )

static

Sets each limb of 'r' to its upper bound at magnitude 'm'.

The output will also have its magnitude set to 'm' and is normalized if (and only if) 'm' is zero.

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secp256k1_fe_half()

static void secp256k1_fe_half ( secp256k1_fe *  r )

static

Halves the value of a field element modulo the field prime.

Constant-time. For an input magnitude 'm', the output magnitude is set to 'floor(m/2) + 1'. The output is not guaranteed to be normalized, regardless of the input.

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secp256k1_fe_inv()

static void secp256k1_fe_inv ( secp256k1_fe *  r, const secp256k1_fe *  a  )

static

Sets a field element to be the (modular) inverse of another.

Requires the input's magnitude to be at most 8. The output magnitude is 1 (but not guaranteed to be normalized).

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secp256k1_fe_inv_var()

static void secp256k1_fe_inv_var ( secp256k1_fe *  r, const secp256k1_fe *  a  )

static

Potentially faster version of secp256k1_fe_inv, without constant-time guarantee.

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secp256k1_fe_is_odd()

static int secp256k1_fe_is_odd ( const secp256k1_fe *  a )

static

Check the "oddness" of a field element.

Requires the input to be normalized.

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secp256k1_fe_is_zero()

static int secp256k1_fe_is_zero ( const secp256k1_fe *  a )

static

Verify whether a field element is zero.

Requires the input to be normalized.

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secp256k1_fe_mul()

static void secp256k1_fe_mul ( secp256k1_fe *  r, const secp256k1_fe *  a, const secp256k1_fe *SECP256K1_RESTRICT  b  )

static

Sets a field element to be the product of two others.

Requires the inputs' magnitudes to be at most 8. The output magnitude is 1 (but not guaranteed to be normalized).

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secp256k1_fe_mul_int()

static void secp256k1_fe_mul_int ( secp256k1_fe *  r, int  a  )

static

Multiplies the passed field element with a small integer constant.

Multiplies the magnitude by that small integer.

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secp256k1_fe_negate()

static void secp256k1_fe_negate ( secp256k1_fe *  r, const secp256k1_fe *  a, int  m  )

static

Set a field element equal to the additive inverse of another.

Takes a maximum magnitude of the input as an argument. The magnitude of the output is one higher.

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secp256k1_fe_normalize()

static void secp256k1_fe_normalize ( secp256k1_fe *  r )

static

Normalize a field element.

This brings the field element to a canonical representation, reduces its magnitude to 1, and reduces it modulo field size p.

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secp256k1_fe_normalize_var()

static void secp256k1_fe_normalize_var ( secp256k1_fe *  r )

static

Normalize a field element, without constant-time guarantee.

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secp256k1_fe_normalize_weak()

static void secp256k1_fe_normalize_weak ( secp256k1_fe *  r )

static

Weakly normalize a field element: reduce its magnitude to 1, but don't fully normalize.

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secp256k1_fe_normalizes_to_zero()

static int secp256k1_fe_normalizes_to_zero ( const secp256k1_fe *  r )

static

Verify whether a field element represents zero i.e.

would normalize to a zero value.

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secp256k1_fe_normalizes_to_zero_var()

static int secp256k1_fe_normalizes_to_zero_var ( const secp256k1_fe *  r )

static

Verify whether a field element represents zero i.e.

would normalize to a zero value, without constant-time guarantee.

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secp256k1_fe_set_b32()

static int secp256k1_fe_set_b32 ( secp256k1_fe *  r, const unsigned char *  a  )

static

Set a field element equal to 32-byte big endian value.

If successful, the resulting field element is normalized.

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secp256k1_fe_set_int()

static void secp256k1_fe_set_int ( secp256k1_fe *  r, int  a  )

static

Set a field element equal to a small (not greater than 0x7FFF), non-negative integer.

Resulting field element is normalized; it has magnitude 0 if a == 0, and magnitude 1 otherwise.

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secp256k1_fe_sqr()

static void secp256k1_fe_sqr ( secp256k1_fe *  r, const secp256k1_fe *  a  )

static

Sets a field element to be the square of another.

Requires the input's magnitude to be at most 8. The output magnitude is 1 (but not guaranteed to be normalized).

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secp256k1_fe_sqrt()

static int secp256k1_fe_sqrt ( secp256k1_fe *  r, const secp256k1_fe *  a  )

static

If a has a square root, it is computed in r and 1 is returned.

If a does not have a square root, the root of its negation is computed and 0 is returned. The input's magnitude can be at most 8. The output magnitude is 1 (but not guaranteed to be normalized). The result in r will always be a square itself.

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secp256k1_fe_storage_cmov()

static void secp256k1_fe_storage_cmov ( secp256k1_fe_storage *  r, const secp256k1_fe_storage *  a, int  flag  )

static

If flag is true, set *r equal to *a; otherwise leave it.

Constant-time. Both *r and *a must be initialized.

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secp256k1_fe_to_storage()

static void secp256k1_fe_to_storage ( secp256k1_fe_storage *  r, const secp256k1_fe *  a  )

static

Convert a field element to the storage type.

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Variable Documentation

secp256k1_const_beta

const secp256k1_fe secp256k1_const_beta

static

Initial value:

= SECP256K1_FE_CONST(
    0x7ae96a2bul, 0x657c0710ul, 0x6e64479eul, 0xac3434e9ul,
    0x9cf04975ul, 0x12f58995ul, 0xc1396c28ul, 0x719501eeul
)

Definition at line 36 of file field.h.

secp256k1_fe_one

const secp256k1_fe secp256k1_fe_one = SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 1)

static

Field element module.

Field elements can be represented in several ways, but code accessing it (and implementations) need to take certain properties into account:

• Each field element can be normalized or not.
• Each field element has a magnitude, which represents how far away its representation is away from normalization. Normalized elements always have a magnitude of 0 or 1, but a magnitude of 1 doesn't imply normality.

Definition at line 35 of file field.h.