


/**********************************************************************




* Copyright (c) 2013, 2014 Pieter Wuille *




* Distributed under the MIT software license, see the accompanying *




* file COPYING or http://www.opensource.org/licenses/mitlicense.php.*




**********************************************************************/








#ifndef _SECP256K1_FIELD_




#define _SECP256K1_FIELD_








/** 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.




*/








#if defined HAVE_CONFIG_H




#include "libsecp256k1config.h"




#endif








#if defined(USE_FIELD_10X26)




#include "field_10x26.h"




#elif defined(USE_FIELD_5X52)




#include "field_5x52.h"




#else




#error "Please select field implementation"




#endif








/** Normalize a field element. */




static void secp256k1_fe_normalize(secp256k1_fe *r);








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




static void secp256k1_fe_normalize_weak(secp256k1_fe *r);








/** Normalize a field element, without constanttime guarantee. */




static void secp256k1_fe_normalize_var(secp256k1_fe *r);








/** 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. */




static int secp256k1_fe_normalizes_to_zero(secp256k1_fe *r);








/** 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. */




static int secp256k1_fe_normalizes_to_zero_var(secp256k1_fe *r);








/** Set a field element equal to a small integer. Resulting field element is normalized. */




static void secp256k1_fe_set_int(secp256k1_fe *r, int a);








/** Verify whether a field element is zero. Requires the input to be normalized. */




static int secp256k1_fe_is_zero(const secp256k1_fe *a);








/** Check the "oddness" of a field element. Requires the input to be normalized. */




static int secp256k1_fe_is_odd(const secp256k1_fe *a);








/** Compare two field elements. Requires magnitude1 inputs. */




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








/** Compare two field elements. Requires both inputs to be normalized */




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








/** Set a field element equal to 32byte big endian value. If successful, the resulting field element is normalized. */




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








/** Convert a field element to a 32byte big endian value. Requires the input to be normalized */




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








/** 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. */




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








/** Multiplies the passed field element with a small integer constant. Multiplies the magnitude by that




* small integer. */




static void secp256k1_fe_mul_int(secp256k1_fe *r, int a);








/** Adds a field element to another. The result has the sum of the inputs' magnitudes as magnitude. */




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








/** 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). */




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 square of another. Requires the input's magnitude to be at most 8.




* The output magnitude is 1 (but not guaranteed to be normalized). */




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








/** 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. */




static int secp256k1_fe_sqrt_var(secp256k1_fe *r, const secp256k1_fe *a);








/** 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). */




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








/** Potentially faster version of secp256k1_fe_inv, without constanttime guarantee. */




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








/** 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. */




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








/** Convert a field element to the storage type. */




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








/** Convert a field element back from the storage type. */




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








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




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. Constanttime. */




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








#endif
