field_impl.h File Reference

#include "util.h"
#include "num.h"

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Functions
static SECP256K1_INLINE int	secp256k1_fe_equal (const secp256k1_fe *a, const secp256k1_fe *b)
static SECP256K1_INLINE int	secp256k1_fe_equal_var (const secp256k1_fe *a, const secp256k1_fe *b)
static int	secp256k1_fe_sqrt (secp256k1_fe *r, const secp256k1_fe *a)
static void	secp256k1_fe_inv (secp256k1_fe *r, const secp256k1_fe *a)
static void	secp256k1_fe_inv_var (secp256k1_fe *r, const secp256k1_fe *a)
static void	secp256k1_fe_inv_all_var (secp256k1_fe *r, const secp256k1_fe *a, size_t len)
static int	secp256k1_fe_is_quad_var (const secp256k1_fe *a)

Function Documentation

secp256k1_fe_equal()

static SECP256K1_INLINE int secp256k1_fe_equal ( const secp256k1_fe *  a, const secp256k1_fe *  b  )

static

Definition at line 25 of file field_impl.h.

References secp256k1_fe_add(), secp256k1_fe_negate(), and secp256k1_fe_normalizes_to_zero().

Referenced by secp256k1_fe_sqrt().

secp256k1_fe_equal_var()

static SECP256K1_INLINE int secp256k1_fe_equal_var ( const secp256k1_fe *  a, const secp256k1_fe *  b  )

static

Definition at line 32 of file field_impl.h.

References secp256k1_fe_add(), secp256k1_fe_negate(), and secp256k1_fe_normalizes_to_zero_var().

secp256k1_fe_inv()

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

static

The binary representation of (p - 2) has 5 blocks of 1s, with lengths in { 1, 2, 22, 223 }. Use an addition chain to calculate 2^n - 1 for each block: [1], [2], 3, 6, 9, 11, [22], 44, 88, 176, 220, [223]

Definition at line 139 of file field_impl.h.

References secp256k1_fe_mul(), and secp256k1_fe_sqr().

Referenced by secp256k1_fe_inv_var().

secp256k1_fe_inv_all_var()

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

static

Definition at line 266 of file field_impl.h.

References secp256k1_fe_inv_var(), secp256k1_fe_mul(), and VERIFY_CHECK.

secp256k1_fe_inv_var()

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

static

Definition at line 229 of file field_impl.h.

References CHECK, secp256k1_fe_add(), SECP256K1_FE_CONST, secp256k1_fe_get_b32(), secp256k1_fe_inv(), secp256k1_fe_mul(), secp256k1_fe_normalize_var(), secp256k1_fe_normalizes_to_zero_var(), secp256k1_fe_set_b32(), secp256k1_num_get_bin(), secp256k1_num_mod_inverse(), secp256k1_num_set_bin(), and VERIFY_CHECK.

Referenced by secp256k1_fe_inv_all_var().

secp256k1_fe_is_quad_var()

static int secp256k1_fe_is_quad_var ( const secp256k1_fe *  a )

static

Definition at line 293 of file field_impl.h.

References secp256k1_fe_get_b32(), secp256k1_fe_normalize_var(), secp256k1_fe_sqrt(), secp256k1_num_jacobi(), and secp256k1_num_set_bin().

secp256k1_fe_sqrt()

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

static

Given that p is congruent to 3 mod 4, we can compute the square root of a mod p as the (p+1)/4'th power of a.

As (p+1)/4 is an even number, it will have the same result for a and for (-a). Only one of these two numbers actually has a square root however, so we test at the end by squaring and comparing to the input. Also because (p+1)/4 is an even number, the computed square root is itself always a square (a ** ((p+1)/4) is the square of a ** ((p+1)/8)).

The binary representation of (p + 1)/4 has 3 blocks of 1s, with lengths in { 2, 22, 223 }. Use an addition chain to calculate 2^n - 1 for each block: 1, [2], 3, 6, 9, 11, [22], 44, 88, 176, 220, [223]

Definition at line 39 of file field_impl.h.

References secp256k1_fe_equal(), secp256k1_fe_mul(), secp256k1_fe_sqr(), and VERIFY_CHECK.

Referenced by secp256k1_fe_is_quad_var().