143 lines
6.8 KiB
C
143 lines
6.8 KiB
C
/***********************************************************************
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* Copyright (c) 2013, 2014 Pieter Wuille *
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* Distributed under the MIT software license, see the accompanying *
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* file COPYING or https://www.opensource.org/licenses/mit-license.php.*
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***********************************************************************/
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#ifndef SECP256K1_FIELD_H
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#define SECP256K1_FIELD_H
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/** Field element module.
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*
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* Field elements can be represented in several ways, but code accessing
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* it (and implementations) need to take certain properties into account:
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* - Each field element can be normalized or not.
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* - Each field element has a magnitude, which represents how far away
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* its representation is away from normalization. Normalized elements
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* always have a magnitude of 0 or 1, but a magnitude of 1 doesn't
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* imply normality.
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*/
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#if defined HAVE_CONFIG_H
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#include "libsecp256k1-config.h"
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#endif
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#include "util.h"
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#if defined(SECP256K1_WIDEMUL_INT128)
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#include "field_5x52.h"
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#elif defined(SECP256K1_WIDEMUL_INT64)
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#include "field_10x26.h"
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#else
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#error "Please select wide multiplication implementation"
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#endif
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static const secp256k1_fe secp256k1_fe_one = SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 1);
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static const secp256k1_fe secp256k1_const_beta = SECP256K1_FE_CONST(
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0x7ae96a2bul, 0x657c0710ul, 0x6e64479eul, 0xac3434e9ul,
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0x9cf04975ul, 0x12f58995ul, 0xc1396c28ul, 0x719501eeul
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);
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/** Normalize a field element. This brings the field element to a canonical representation, reduces
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* its magnitude to 1, and reduces it modulo field size `p`.
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*/
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static void secp256k1_fe_normalize(secp256k1_fe *r);
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/** Weakly normalize a field element: reduce its magnitude to 1, but don't fully normalize. */
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static void secp256k1_fe_normalize_weak(secp256k1_fe *r);
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/** Normalize a field element, without constant-time guarantee. */
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static void secp256k1_fe_normalize_var(secp256k1_fe *r);
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/** Verify whether a field element represents zero i.e. would normalize to a zero value. */
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static int secp256k1_fe_normalizes_to_zero(const secp256k1_fe *r);
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/** Verify whether a field element represents zero i.e. would normalize to a zero value,
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* without constant-time guarantee. */
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static int secp256k1_fe_normalizes_to_zero_var(const secp256k1_fe *r);
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/** Set a field element equal to a small (not greater than 0x7FFF), non-negative integer.
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* Resulting field element is normalized; it has magnitude 0 if a == 0, and magnitude 1 otherwise.
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*/
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static void secp256k1_fe_set_int(secp256k1_fe *r, int a);
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/** Sets a field element equal to zero, initializing all fields. */
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static void secp256k1_fe_clear(secp256k1_fe *a);
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/** Verify whether a field element is zero. Requires the input to be normalized. */
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static int secp256k1_fe_is_zero(const secp256k1_fe *a);
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/** Check the "oddness" of a field element. Requires the input to be normalized. */
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static int secp256k1_fe_is_odd(const secp256k1_fe *a);
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/** Compare two field elements. Requires magnitude-1 inputs. */
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static int secp256k1_fe_equal(const secp256k1_fe *a, const secp256k1_fe *b);
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/** Same as secp256k1_fe_equal, but may be variable time. */
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static int secp256k1_fe_equal_var(const secp256k1_fe *a, const secp256k1_fe *b);
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/** Compare two field elements. Requires both inputs to be normalized */
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static int secp256k1_fe_cmp_var(const secp256k1_fe *a, const secp256k1_fe *b);
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/** Set a field element equal to 32-byte big endian value. If successful, the resulting field element is normalized. */
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static int secp256k1_fe_set_b32(secp256k1_fe *r, const unsigned char *a);
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/** Convert a field element to a 32-byte big endian value. Requires the input to be normalized */
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static void secp256k1_fe_get_b32(unsigned char *r, const secp256k1_fe *a);
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/** Set a field element equal to the additive inverse of another. Takes a maximum magnitude of the input
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* as an argument. The magnitude of the output is one higher. */
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static void secp256k1_fe_negate(secp256k1_fe *r, const secp256k1_fe *a, int m);
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/** Multiplies the passed field element with a small integer constant. Multiplies the magnitude by that
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* small integer. */
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static void secp256k1_fe_mul_int(secp256k1_fe *r, int a);
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/** Adds a field element to another. The result has the sum of the inputs' magnitudes as magnitude. */
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static void secp256k1_fe_add(secp256k1_fe *r, const secp256k1_fe *a);
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/** Sets a field element to be the product of two others. Requires the inputs' magnitudes to be at most 8.
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* The output magnitude is 1 (but not guaranteed to be normalized). */
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static void secp256k1_fe_mul(secp256k1_fe *r, const secp256k1_fe *a, const secp256k1_fe * SECP256K1_RESTRICT b);
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/** Sets a field element to be the square of another. Requires the input's magnitude to be at most 8.
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* The output magnitude is 1 (but not guaranteed to be normalized). */
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static void secp256k1_fe_sqr(secp256k1_fe *r, const secp256k1_fe *a);
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/** If a has a square root, it is computed in r and 1 is returned. If a does not
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* have a square root, the root of its negation is computed and 0 is returned.
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* The input's magnitude can be at most 8. The output magnitude is 1 (but not
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* guaranteed to be normalized). The result in r will always be a square
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* itself. */
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static int secp256k1_fe_sqrt(secp256k1_fe *r, const secp256k1_fe *a);
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/** Sets a field element to be the (modular) inverse of another. Requires the input's magnitude to be
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* at most 8. The output magnitude is 1 (but not guaranteed to be normalized). */
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static void secp256k1_fe_inv(secp256k1_fe *r, const secp256k1_fe *a);
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/** Potentially faster version of secp256k1_fe_inv, without constant-time guarantee. */
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static void secp256k1_fe_inv_var(secp256k1_fe *r, const secp256k1_fe *a);
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/** Convert a field element to the storage type. */
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static void secp256k1_fe_to_storage(secp256k1_fe_storage *r, const secp256k1_fe *a);
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/** Convert a field element back from the storage type. */
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static void secp256k1_fe_from_storage(secp256k1_fe *r, const secp256k1_fe_storage *a);
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/** 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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static void secp256k1_fe_storage_cmov(secp256k1_fe_storage *r, const secp256k1_fe_storage *a, int flag);
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/** 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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static void secp256k1_fe_cmov(secp256k1_fe *r, const secp256k1_fe *a, int flag);
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/** Halves the value of a field element modulo the field prime. Constant-time.
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* For an input magnitude 'm', the output magnitude is set to 'floor(m/2) + 1'.
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* The output is not guaranteed to be normalized, regardless of the input. */
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static void secp256k1_fe_half(secp256k1_fe *r);
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/** Sets each limb of 'r' to its upper bound at magnitude 'm'. The output will also have its
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* magnitude set to 'm' and is normalized if (and only if) 'm' is zero. */
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static void secp256k1_fe_get_bounds(secp256k1_fe *r, int m);
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#endif /* SECP256K1_FIELD_H */
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