1 /********************************************************************** 2 * Copyright (c) 2014 Pieter Wuille * 3 * Distributed under the MIT software license, see the accompanying * 4 * file COPYING or http://www.opensource.org/licenses/mit-license.php.* 5 **********************************************************************/ 6 7 #ifndef _SECP256K1_SCALAR_ 8 #define _SECP256K1_SCALAR_ 9 10 #include "num.h" 11 12 #if defined HAVE_CONFIG_H 13 #include "libsecp256k1-config.h" 14 #endif 15 16 #if defined(USE_SCALAR_4X64) 17 #include "scalar_4x64.h" 18 #elif defined(USE_SCALAR_8X32) 19 #include "scalar_8x32.h" 20 #else 21 #error "Please select scalar implementation" 22 #endif 23 24 /** Clear a scalar to prevent the leak of sensitive data. */ 25 static void secp256k1_scalar_clear(secp256k1_scalar *r); 26 27 /** Access bits from a scalar. All requested bits must belong to the same 32-bit limb. */ 28 static unsigned int secp256k1_scalar_get_bits(const secp256k1_scalar *a, unsigned int offset, unsigned int count); 29 30 /** Access bits from a scalar. Not constant time. */ 31 static unsigned int secp256k1_scalar_get_bits_var(const secp256k1_scalar *a, unsigned int offset, unsigned int count); 32 33 /** Set a scalar from a big endian byte array. */ 34 static void secp256k1_scalar_set_b32(secp256k1_scalar *r, const unsigned char *bin, int *overflow); 35 36 /** Set a scalar to an unsigned integer. */ 37 static void secp256k1_scalar_set_int(secp256k1_scalar *r, unsigned int v); 38 39 /** Convert a scalar to a byte array. */ 40 static void secp256k1_scalar_get_b32(unsigned char *bin, const secp256k1_scalar* a); 41 42 /** Add two scalars together (modulo the group order). Returns whether it overflowed. */ 43 static int secp256k1_scalar_add(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b); 44 45 /** Conditionally add a power of two to a scalar. The result is not allowed to overflow. */ 46 static void secp256k1_scalar_cadd_bit(secp256k1_scalar *r, unsigned int bit, int flag); 47 48 /** Multiply two scalars (modulo the group order). */ 49 static void secp256k1_scalar_mul(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b); 50 51 /** Shift a scalar right by some amount strictly between 0 and 16, returning 52 * the low bits that were shifted off */ 53 static int secp256k1_scalar_shr_int(secp256k1_scalar *r, int n); 54 55 /** Compute the square of a scalar (modulo the group order). */ 56 static void secp256k1_scalar_sqr(secp256k1_scalar *r, const secp256k1_scalar *a); 57 58 /** Compute the inverse of a scalar (modulo the group order). */ 59 static void secp256k1_scalar_inverse(secp256k1_scalar *r, const secp256k1_scalar *a); 60 61 /** Compute the inverse of a scalar (modulo the group order), without constant-time guarantee. */ 62 static void secp256k1_scalar_inverse_var(secp256k1_scalar *r, const secp256k1_scalar *a); 63 64 /** Compute the complement of a scalar (modulo the group order). */ 65 static void secp256k1_scalar_negate(secp256k1_scalar *r, const secp256k1_scalar *a); 66 67 /** Check whether a scalar equals zero. */ 68 static int secp256k1_scalar_is_zero(const secp256k1_scalar *a); 69 70 /** Check whether a scalar equals one. */ 71 static int secp256k1_scalar_is_one(const secp256k1_scalar *a); 72 73 /** Check whether a scalar, considered as an nonnegative integer, is even. */ 74 static int secp256k1_scalar_is_even(const secp256k1_scalar *a); 75 76 /** Check whether a scalar is higher than the group order divided by 2. */ 77 static int secp256k1_scalar_is_high(const secp256k1_scalar *a); 78 79 /** Conditionally negate a number, in constant time. 80 * Returns -1 if the number was negated, 1 otherwise */ 81 static int secp256k1_scalar_cond_negate(secp256k1_scalar *a, int flag); 82 83 #ifndef USE_NUM_NONE 84 /** Convert a scalar to a number. */ 85 static void secp256k1_scalar_get_num(secp256k1_num *r, const secp256k1_scalar *a); 86 87 /** Get the order of the group as a number. */ 88 static void secp256k1_scalar_order_get_num(secp256k1_num *r); 89 #endif 90 91 /** Compare two scalars. */ 92 static int secp256k1_scalar_eq(const secp256k1_scalar *a, const secp256k1_scalar *b); 93 94 #ifdef USE_ENDOMORPHISM 95 /** Find r1 and r2 such that r1+r2*2^128 = a. */ 96 static void secp256k1_scalar_split_128(secp256k1_scalar *r1, secp256k1_scalar *r2, const secp256k1_scalar *a); 97 /** Find r1 and r2 such that r1+r2*lambda = a, and r1 and r2 are maximum 128 bits long (see secp256k1_gej_mul_lambda). */ 98 static void secp256k1_scalar_split_lambda(secp256k1_scalar *r1, secp256k1_scalar *r2, const secp256k1_scalar *a); 99 #endif 100 101 /** Multiply a and b (without taking the modulus!), divide by 2**shift, and round to the nearest integer. Shift must be at least 256. */ 102 static void secp256k1_scalar_mul_shift_var(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b, unsigned int shift); 103 104 #endif 105