/*********************************************************************** * Copyright (c) 2013, 2014 Pieter Wuille * * Distributed under the MIT software license, see the accompanying * * file COPYING or https://www.opensource.org/licenses/mit-license.php.* ***********************************************************************/ #ifndef SECP256K1_FIELD_H #define SECP256K1_FIELD_H /** 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. */ #if defined HAVE_CONFIG_H #include "libsecp256k1-config.h" #endif #include "util.h" #if defined(SECP256K1_WIDEMUL_INT128) #include "field_5x52.h" #elif defined(SECP256K1_WIDEMUL_INT64) #include "field_10x26.h" #else #error "Please select wide multiplication implementation" #endif static const rustsecp256k1_v0_8_1_fe rustsecp256k1_v0_8_1_fe_one = SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 1); static const rustsecp256k1_v0_8_1_fe rustsecp256k1_v0_8_1_const_beta = SECP256K1_FE_CONST( 0x7ae96a2bul, 0x657c0710ul, 0x6e64479eul, 0xac3434e9ul, 0x9cf04975ul, 0x12f58995ul, 0xc1396c28ul, 0x719501eeul ); /** 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`. */ static void rustsecp256k1_v0_8_1_fe_normalize(rustsecp256k1_v0_8_1_fe *r); /** Weakly normalize a field element: reduce its magnitude to 1, but don't fully normalize. */ static void rustsecp256k1_v0_8_1_fe_normalize_weak(rustsecp256k1_v0_8_1_fe *r); /** Normalize a field element, without constant-time guarantee. */ static void rustsecp256k1_v0_8_1_fe_normalize_var(rustsecp256k1_v0_8_1_fe *r); /** Verify whether a field element represents zero i.e. would normalize to a zero value. */ static int rustsecp256k1_v0_8_1_fe_normalizes_to_zero(const rustsecp256k1_v0_8_1_fe *r); /** Verify whether a field element represents zero i.e. would normalize to a zero value, * without constant-time guarantee. */ static int rustsecp256k1_v0_8_1_fe_normalizes_to_zero_var(const rustsecp256k1_v0_8_1_fe *r); /** 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. */ static void rustsecp256k1_v0_8_1_fe_set_int(rustsecp256k1_v0_8_1_fe *r, int a); /** Sets a field element equal to zero, initializing all fields. */ static void rustsecp256k1_v0_8_1_fe_clear(rustsecp256k1_v0_8_1_fe *a); /** Verify whether a field element is zero. Requires the input to be normalized. */ static int rustsecp256k1_v0_8_1_fe_is_zero(const rustsecp256k1_v0_8_1_fe *a); /** Check the "oddness" of a field element. Requires the input to be normalized. */ static int rustsecp256k1_v0_8_1_fe_is_odd(const rustsecp256k1_v0_8_1_fe *a); /** Compare two field elements. Requires magnitude-1 inputs. */ static int rustsecp256k1_v0_8_1_fe_equal(const rustsecp256k1_v0_8_1_fe *a, const rustsecp256k1_v0_8_1_fe *b); /** Same as rustsecp256k1_v0_8_1_fe_equal, but may be variable time. */ static int rustsecp256k1_v0_8_1_fe_equal_var(const rustsecp256k1_v0_8_1_fe *a, const rustsecp256k1_v0_8_1_fe *b); /** Compare two field elements. Requires both inputs to be normalized */ static int rustsecp256k1_v0_8_1_fe_cmp_var(const rustsecp256k1_v0_8_1_fe *a, const rustsecp256k1_v0_8_1_fe *b); /** Set a field element equal to 32-byte big endian value. If successful, the resulting field element is normalized. */ static int rustsecp256k1_v0_8_1_fe_set_b32(rustsecp256k1_v0_8_1_fe *r, const unsigned char *a); /** Convert a field element to a 32-byte big endian value. Requires the input to be normalized */ static void rustsecp256k1_v0_8_1_fe_get_b32(unsigned char *r, const rustsecp256k1_v0_8_1_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 rustsecp256k1_v0_8_1_fe_negate(rustsecp256k1_v0_8_1_fe *r, const rustsecp256k1_v0_8_1_fe *a, int m); /** Multiplies the passed field element with a small integer constant. Multiplies the magnitude by that * small integer. */ static void rustsecp256k1_v0_8_1_fe_mul_int(rustsecp256k1_v0_8_1_fe *r, int a); /** Adds a field element to another. The result has the sum of the inputs' magnitudes as magnitude. */ static void rustsecp256k1_v0_8_1_fe_add(rustsecp256k1_v0_8_1_fe *r, const rustsecp256k1_v0_8_1_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 rustsecp256k1_v0_8_1_fe_mul(rustsecp256k1_v0_8_1_fe *r, const rustsecp256k1_v0_8_1_fe *a, const rustsecp256k1_v0_8_1_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 rustsecp256k1_v0_8_1_fe_sqr(rustsecp256k1_v0_8_1_fe *r, const rustsecp256k1_v0_8_1_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 rustsecp256k1_v0_8_1_fe_sqrt(rustsecp256k1_v0_8_1_fe *r, const rustsecp256k1_v0_8_1_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 rustsecp256k1_v0_8_1_fe_inv(rustsecp256k1_v0_8_1_fe *r, const rustsecp256k1_v0_8_1_fe *a); /** Potentially faster version of rustsecp256k1_v0_8_1_fe_inv, without constant-time guarantee. */ static void rustsecp256k1_v0_8_1_fe_inv_var(rustsecp256k1_v0_8_1_fe *r, const rustsecp256k1_v0_8_1_fe *a); /** Convert a field element to the storage type. */ static void rustsecp256k1_v0_8_1_fe_to_storage(rustsecp256k1_v0_8_1_fe_storage *r, const rustsecp256k1_v0_8_1_fe *a); /** Convert a field element back from the storage type. */ static void rustsecp256k1_v0_8_1_fe_from_storage(rustsecp256k1_v0_8_1_fe *r, const rustsecp256k1_v0_8_1_fe_storage *a); /** If flag is true, set *r equal to *a; otherwise leave it. Constant-time. Both *r and *a must be initialized.*/ static void rustsecp256k1_v0_8_1_fe_storage_cmov(rustsecp256k1_v0_8_1_fe_storage *r, const rustsecp256k1_v0_8_1_fe_storage *a, int flag); /** If flag is true, set *r equal to *a; otherwise leave it. Constant-time. Both *r and *a must be initialized.*/ static void rustsecp256k1_v0_8_1_fe_cmov(rustsecp256k1_v0_8_1_fe *r, const rustsecp256k1_v0_8_1_fe *a, int flag); /** 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. */ static void rustsecp256k1_v0_8_1_fe_half(rustsecp256k1_v0_8_1_fe *r); /** 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. */ static void rustsecp256k1_v0_8_1_fe_get_bounds(rustsecp256k1_v0_8_1_fe *r, int m); #endif /* SECP256K1_FIELD_H */