field.h File Reference

#include "util.h"

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Functions
static void	secp256k1_fe_normalize (secp256k1_fe *r)
	Field element module. More...
static void	secp256k1_fe_normalize_weak (secp256k1_fe *r)
	Weakly normalize a field element: reduce it 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 (secp256k1_fe *r)
	Verify whether a field element represents zero i.e. More...
static int	secp256k1_fe_normalizes_to_zero_var (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 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 int	secp256k1_fe_is_quad_var (const secp256k1_fe *a)
	Checks whether a field element is a quadratic residue. 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_inv_all_var (secp256k1_fe *r, const secp256k1_fe *a, size_t len)
	Calculate the (modular) inverses of a batch of field elements. 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...

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.

Referenced by bench_field_inverse(), bench_field_inverse_var(), bench_field_sqrt(), random_field_element_magnitude(), run_field_misc(), secp256k1_ecdsa_sig_recover(), secp256k1_ecdsa_sig_verify(), secp256k1_ecmult_odd_multiples_table_storage_var(), secp256k1_fe_equal(), secp256k1_fe_equal_var(), secp256k1_fe_inv_var(), secp256k1_ge_is_valid_var(), secp256k1_ge_set_xquad(), secp256k1_gej_add_ge(), secp256k1_gej_add_ge_var(), secp256k1_gej_add_var(), secp256k1_gej_add_zinv_var(), secp256k1_gej_double_var(), secp256k1_gej_is_valid_var(), and test_sqrt().

secp256k1_fe_clear()

static void secp256k1_fe_clear ( secp256k1_fe *  a )

static

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

Referenced by random_field_element_magnitude(), secp256k1_ecmult_gen_blind(), secp256k1_ge_clear(), secp256k1_ge_set_infinity(), secp256k1_gej_clear(), and secp256k1_gej_set_infinity().

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.

Referenced by run_field_misc(), and secp256k1_gej_add_ge().

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

Referenced by gej_xyz_equals_gej(), run_field_misc(), secp256k1_ecdsa_sig_recover(), and secp256k1_ecdsa_sig_verify().

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.

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.

Referenced by check_fe_equal(), ge_equals_ge(), ge_equals_gej(), main(), run_field_convert(), run_field_misc(), run_point_times_order(), secp256k1_ge_is_valid_var(), secp256k1_gej_eq_x_var(), secp256k1_gej_is_valid_var(), test_ge(), and test_group_decompress().

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.

Referenced by run_field_convert(), run_field_misc(), and secp256k1_ge_from_storage().

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

Referenced by r_from_k(), run_field_convert(), secp256k1_ecdh(), secp256k1_ecdsa_sig_sign(), secp256k1_ecdsa_sig_verify(), secp256k1_eckey_pubkey_serialize(), secp256k1_fe_inv_var(), secp256k1_fe_is_quad_var(), and secp256k1_pubkey_save().

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).

Referenced by bench_field_inverse(), run_field_inv(), secp256k1_ge_set_gej(), and test_exhaustive_addition().

secp256k1_fe_inv_all_var()

static void secp256k1_fe_inv_all_var ( secp256k1_fe *  r, const secp256k1_fe *  a, size_t  len  )

static

Calculate the (modular) inverses of a batch of field elements.

Requires the inputs' magnitudes to be at most 8. The output magnitudes are 1 (but not guaranteed to be normalized). The inputs and outputs must not overlap in memory.

Referenced by run_field_inv_all_var(), and test_ge().

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.

Referenced by bench_field_inverse_var(), run_field_inv_var(), secp256k1_ecmult_odd_multiples_table_storage_var(), secp256k1_ge_set_all_gej_var(), secp256k1_ge_set_gej_var(), and test_ge().

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.

Referenced by secp256k1_ecdsa_sig_sign(), secp256k1_eckey_pubkey_parse(), secp256k1_eckey_pubkey_serialize(), secp256k1_ge_set_xo_var(), test_ge(), and test_group_decompress().

secp256k1_fe_is_quad_var()

static int secp256k1_fe_is_quad_var ( const secp256k1_fe *  a )

static

Checks whether a field element is a quadratic residue.

Referenced by secp256k1_gej_has_quad_y_var(), and test_group_decompress().

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.

Referenced by random_fe_non_zero(), random_group_element_jacobian_test(), secp256k1_ecmult_gen_blind(), secp256k1_gej_rescale(), secp256k1_pubkey_load(), test_ge(), test_group_decompress(), and test_sqrt().

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).

Referenced by bench_field_mul(), check_fe_inverse(), ge_equals_gej(), random_group_element_jacobian_test(), run_field_misc(), run_sqrt(), secp256k1_ecmult_const(), secp256k1_ecmult_odd_multiples_table(), secp256k1_ecmult_odd_multiples_table_storage_var(), secp256k1_ecmult_strauss_wnaf(), secp256k1_fe_inv(), secp256k1_fe_inv_all_var(), secp256k1_fe_inv_var(), secp256k1_fe_sqrt(), secp256k1_ge_globalz_set_table_gej(), secp256k1_ge_is_valid_var(), secp256k1_ge_set_all_gej_var(), secp256k1_ge_set_gej(), secp256k1_ge_set_gej_var(), secp256k1_ge_set_gej_zinv(), secp256k1_ge_set_xquad(), secp256k1_gej_add_ge(), secp256k1_gej_add_ge_var(), secp256k1_gej_add_var(), secp256k1_gej_add_zinv_var(), secp256k1_gej_double_var(), secp256k1_gej_eq_x_var(), secp256k1_gej_has_quad_y_var(), secp256k1_gej_is_valid_var(), secp256k1_gej_rescale(), and test_ge().

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.

Referenced by random_field_element_magnitude(), run_field_misc(), run_sqr(), secp256k1_gej_add_ge(), secp256k1_gej_add_ge_var(), secp256k1_gej_add_var(), secp256k1_gej_add_zinv_var(), secp256k1_gej_double_var(), and secp256k1_gej_is_valid_var().

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.

Referenced by random_fe_non_square(), random_field_element_magnitude(), run_field_misc(), run_sqr(), run_sqrt(), secp256k1_ecmult_odd_multiples_table_storage_var(), secp256k1_fe_equal(), secp256k1_fe_equal_var(), secp256k1_ge_neg(), secp256k1_ge_set_xo_var(), secp256k1_gej_add_ge(), secp256k1_gej_add_ge_var(), secp256k1_gej_add_var(), secp256k1_gej_add_zinv_var(), secp256k1_gej_double_var(), secp256k1_gej_neg(), and test_sqrt().

secp256k1_fe_normalize()

static void secp256k1_fe_normalize ( secp256k1_fe *  r )

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 1, but a magnitude of 1 doesn't imply normality.Normalize a field element.

Referenced by bench_field_normalize(), gej_xyz_equals_gej(), r_from_k(), random_fe_non_zero(), random_field_element_magnitude(), random_group_element_test(), run_sqr(), secp256k1_ecdh(), secp256k1_ecdsa_sig_sign(), secp256k1_ecdsa_sig_verify(), secp256k1_ge_to_storage(), and test_sqrt().

secp256k1_fe_normalize_var()

static void secp256k1_fe_normalize_var ( secp256k1_fe *  r )

static

Normalize a field element, without constant-time guarantee.

Referenced by check_fe_equal(), run_field_misc(), run_point_times_order(), secp256k1_eckey_pubkey_serialize(), secp256k1_ecmult_odd_multiples_table_storage_var(), secp256k1_ecmult_strauss_wnaf(), secp256k1_fe_inv_var(), secp256k1_fe_is_quad_var(), secp256k1_ge_set_xo_var(), secp256k1_pubkey_save(), and test_group_decompress().

secp256k1_fe_normalize_weak()

static void secp256k1_fe_normalize_weak ( secp256k1_fe *  r )

static

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

Referenced by bench_field_normalize_weak(), check_fe_equal(), ge_equals_gej(), secp256k1_ecmult_const(), secp256k1_ge_globalz_set_table_gej(), secp256k1_ge_is_valid_var(), secp256k1_ge_neg(), secp256k1_gej_add_ge(), secp256k1_gej_add_ge_var(), secp256k1_gej_add_zinv_var(), secp256k1_gej_double_var(), secp256k1_gej_eq_x_var(), secp256k1_gej_is_valid_var(), and secp256k1_gej_neg().

secp256k1_fe_normalizes_to_zero()

static int secp256k1_fe_normalizes_to_zero ( secp256k1_fe *  r )

static

Verify whether a field element represents zero i.e.

would normalize to a zero value. The field implementation may optionally normalize the input, but this should not be relied upon.

Referenced by secp256k1_fe_equal(), and secp256k1_gej_add_ge().

secp256k1_fe_normalizes_to_zero_var()

static int secp256k1_fe_normalizes_to_zero_var ( secp256k1_fe *  r )

static

Verify whether a field element represents zero i.e.

would normalize to a zero value. The field implementation may optionally normalize the input, but this should not be relied upon.

Referenced by secp256k1_fe_equal_var(), secp256k1_fe_inv_var(), secp256k1_gej_add_ge_var(), secp256k1_gej_add_var(), and secp256k1_gej_add_zinv_var().

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.

Referenced by bench_setup(), random_fe(), random_fe_test(), random_field_element_test(), run_field_convert(), secp256k1_ecdsa_sig_recover(), secp256k1_ecdsa_sig_verify(), secp256k1_eckey_pubkey_parse(), secp256k1_ecmult_gen_blind(), secp256k1_ecmult_gen_context_build(), secp256k1_fe_inv_var(), and secp256k1_pubkey_load().

secp256k1_fe_set_int()

static void secp256k1_fe_set_int ( secp256k1_fe *  r, int  a  )

static

Set a field element equal to a small integer.

Resulting field element is normalized.

Referenced by run_sqr(), run_sqrt(), secp256k1_ecmult_strauss_wnaf(), secp256k1_ge_is_valid_var(), secp256k1_ge_set_gej(), secp256k1_ge_set_gej_var(), secp256k1_ge_set_xquad(), secp256k1_gej_add_ge_var(), secp256k1_gej_add_var(), secp256k1_gej_add_zinv_var(), secp256k1_gej_double_var(), and secp256k1_gej_set_ge().

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).

Referenced by bench_field_sqr(), ge_equals_gej(), random_group_element_jacobian_test(), run_point_times_order(), run_sqr(), run_sqrt(), secp256k1_ecmult_odd_multiples_table_storage_var(), secp256k1_fe_inv(), secp256k1_fe_sqrt(), secp256k1_ge_is_valid_var(), secp256k1_ge_set_gej(), secp256k1_ge_set_gej_var(), secp256k1_ge_set_gej_zinv(), secp256k1_ge_set_xquad(), secp256k1_gej_add_ge(), secp256k1_gej_add_ge_var(), secp256k1_gej_add_var(), secp256k1_gej_add_zinv_var(), secp256k1_gej_double_var(), secp256k1_gej_eq_x_var(), secp256k1_gej_is_valid_var(), secp256k1_gej_rescale(), and test_ge().

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.

Referenced by bench_field_sqrt(), random_fe_non_square(), secp256k1_ge_set_xquad(), and test_sqrt().

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.

Referenced by run_field_misc(), and secp256k1_ge_storage_cmov().

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.

Referenced by run_field_convert(), run_field_misc(), secp256k1_ecmult_odd_multiples_table_storage_var(), and secp256k1_ge_to_storage().