Bitcoin Core  24.99.0
P2P Digital Currency
ecmult_const_impl.h
Go to the documentation of this file.
1 /***********************************************************************
2  * Copyright (c) 2015 Pieter Wuille, Andrew Poelstra *
3  * Distributed under the MIT software license, see the accompanying *
4  * file COPYING or https://www.opensource.org/licenses/mit-license.php.*
5  ***********************************************************************/
6 
7 #ifndef SECP256K1_ECMULT_CONST_IMPL_H
8 #define SECP256K1_ECMULT_CONST_IMPL_H
9 
10 #include "scalar.h"
11 #include "group.h"
12 #include "ecmult_const.h"
13 #include "ecmult_impl.h"
14 
23 
26 }
27 
28 /* This is like `ECMULT_TABLE_GET_GE` but is constant time */
29 #define ECMULT_CONST_TABLE_GET_GE(r,pre,n,w) do { \
30  int m = 0; \
31  /* Extract the sign-bit for a constant time absolute-value. */ \
32  int mask = (n) >> (sizeof(n) * CHAR_BIT - 1); \
33  int abs_n = ((n) + mask) ^ mask; \
34  int idx_n = abs_n >> 1; \
35  secp256k1_fe neg_y; \
36  VERIFY_CHECK(((n) & 1) == 1); \
37  VERIFY_CHECK((n) >= -((1 << ((w)-1)) - 1)); \
38  VERIFY_CHECK((n) <= ((1 << ((w)-1)) - 1)); \
39  VERIFY_SETUP(secp256k1_fe_clear(&(r)->x)); \
40  VERIFY_SETUP(secp256k1_fe_clear(&(r)->y)); \
41  /* Unconditionally set r->x = (pre)[m].x. r->y = (pre)[m].y. because it's either the correct one \
42  * or will get replaced in the later iterations, this is needed to make sure `r` is initialized. */ \
43  (r)->x = (pre)[m].x; \
44  (r)->y = (pre)[m].y; \
45  for (m = 1; m < ECMULT_TABLE_SIZE(w); m++) { \
46  /* This loop is used to avoid secret data in array indices. See
47  * the comment in ecmult_gen_impl.h for rationale. */ \
48  secp256k1_fe_cmov(&(r)->x, &(pre)[m].x, m == idx_n); \
49  secp256k1_fe_cmov(&(r)->y, &(pre)[m].y, m == idx_n); \
50  } \
51  (r)->infinity = 0; \
52  secp256k1_fe_negate(&neg_y, &(r)->y, 1); \
53  secp256k1_fe_cmov(&(r)->y, &neg_y, (n) != abs_n); \
54 } while(0)
55 
69 static int secp256k1_wnaf_const(int *wnaf, const secp256k1_scalar *scalar, int w, int size) {
70  int global_sign;
71  int skew;
72  int word = 0;
73 
74  /* 1 2 3 */
75  int u_last;
76  int u;
77 
78  int flip;
79  secp256k1_scalar s = *scalar;
80 
81  VERIFY_CHECK(w > 0);
82  VERIFY_CHECK(size > 0);
83 
84  /* Note that we cannot handle even numbers by negating them to be odd, as is
85  * done in other implementations, since if our scalars were specified to have
86  * width < 256 for performance reasons, their negations would have width 256
87  * and we'd lose any performance benefit. Instead, we use a variation of a
88  * technique from Section 4.2 of the Okeya/Tagaki paper, which is to add 1 to the
89  * number we are encoding when it is even, returning a skew value indicating
90  * this, and having the caller compensate after doing the multiplication.
91  *
92  * In fact, we _do_ want to negate numbers to minimize their bit-lengths (and in
93  * particular, to ensure that the outputs from the endomorphism-split fit into
94  * 128 bits). If we negate, the parity of our number flips, affecting whether
95  * we want to add to the scalar to ensure that it's odd. */
96  flip = secp256k1_scalar_is_high(&s);
97  skew = flip ^ secp256k1_scalar_is_even(&s);
98  secp256k1_scalar_cadd_bit(&s, 0, skew);
99  global_sign = secp256k1_scalar_cond_negate(&s, flip);
100 
101  /* 4 */
102  u_last = secp256k1_scalar_shr_int(&s, w);
103  do {
104  int even;
105 
106  /* 4.1 4.4 */
107  u = secp256k1_scalar_shr_int(&s, w);
108  /* 4.2 */
109  even = ((u & 1) == 0);
110  /* In contrast to the original algorithm, u_last is always > 0 and
111  * therefore we do not need to check its sign. In particular, it's easy
112  * to see that u_last is never < 0 because u is never < 0. Moreover,
113  * u_last is never = 0 because u is never even after a loop
114  * iteration. The same holds analogously for the initial value of
115  * u_last (in the first loop iteration). */
116  VERIFY_CHECK(u_last > 0);
117  VERIFY_CHECK((u_last & 1) == 1);
118  u += even;
119  u_last -= even * (1 << w);
120 
121  /* 4.3, adapted for global sign change */
122  wnaf[word++] = u_last * global_sign;
123 
124  u_last = u;
125  } while (word * w < size);
126  wnaf[word] = u * global_sign;
127 
129  VERIFY_CHECK(word == WNAF_SIZE_BITS(size, w));
130  return skew;
131 }
132 
133 static void secp256k1_ecmult_const(secp256k1_gej *r, const secp256k1_ge *a, const secp256k1_scalar *scalar, int size) {
135  secp256k1_ge tmpa;
136  secp256k1_fe Z;
137 
138  int skew_1;
140  int wnaf_lam[1 + WNAF_SIZE(WINDOW_A - 1)];
141  int skew_lam;
142  secp256k1_scalar q_1, q_lam;
143  int wnaf_1[1 + WNAF_SIZE(WINDOW_A - 1)];
144 
145  int i;
146 
147  /* build wnaf representation for q. */
148  int rsize = size;
149  if (size > 128) {
150  rsize = 128;
151  /* split q into q_1 and q_lam (where q = q_1 + q_lam*lambda, and q_1 and q_lam are ~128 bit) */
152  secp256k1_scalar_split_lambda(&q_1, &q_lam, scalar);
153  skew_1 = secp256k1_wnaf_const(wnaf_1, &q_1, WINDOW_A - 1, 128);
154  skew_lam = secp256k1_wnaf_const(wnaf_lam, &q_lam, WINDOW_A - 1, 128);
155  } else
156  {
157  skew_1 = secp256k1_wnaf_const(wnaf_1, scalar, WINDOW_A - 1, size);
158  skew_lam = 0;
159  }
160 
161  /* Calculate odd multiples of a.
162  * All multiples are brought to the same Z 'denominator', which is stored
163  * in Z. Due to secp256k1' isomorphism we can do all operations pretending
164  * that the Z coordinate was 1, use affine addition formulae, and correct
165  * the Z coordinate of the result once at the end.
166  */
167  VERIFY_CHECK(!a->infinity);
168  secp256k1_gej_set_ge(r, a);
170  for (i = 0; i < ECMULT_TABLE_SIZE(WINDOW_A); i++) {
171  secp256k1_fe_normalize_weak(&pre_a[i].y);
172  }
173  if (size > 128) {
174  for (i = 0; i < ECMULT_TABLE_SIZE(WINDOW_A); i++) {
175  secp256k1_ge_mul_lambda(&pre_a_lam[i], &pre_a[i]);
176  }
177 
178  }
179 
180  /* first loop iteration (separated out so we can directly set r, rather
181  * than having it start at infinity, get doubled several times, then have
182  * its new value added to it) */
183  i = wnaf_1[WNAF_SIZE_BITS(rsize, WINDOW_A - 1)];
184  VERIFY_CHECK(i != 0);
185  ECMULT_CONST_TABLE_GET_GE(&tmpa, pre_a, i, WINDOW_A);
186  secp256k1_gej_set_ge(r, &tmpa);
187  if (size > 128) {
188  i = wnaf_lam[WNAF_SIZE_BITS(rsize, WINDOW_A - 1)];
189  VERIFY_CHECK(i != 0);
190  ECMULT_CONST_TABLE_GET_GE(&tmpa, pre_a_lam, i, WINDOW_A);
191  secp256k1_gej_add_ge(r, r, &tmpa);
192  }
193  /* remaining loop iterations */
194  for (i = WNAF_SIZE_BITS(rsize, WINDOW_A - 1) - 1; i >= 0; i--) {
195  int n;
196  int j;
197  for (j = 0; j < WINDOW_A - 1; ++j) {
198  secp256k1_gej_double(r, r);
199  }
200 
201  n = wnaf_1[i];
202  ECMULT_CONST_TABLE_GET_GE(&tmpa, pre_a, n, WINDOW_A);
203  VERIFY_CHECK(n != 0);
204  secp256k1_gej_add_ge(r, r, &tmpa);
205  if (size > 128) {
206  n = wnaf_lam[i];
207  ECMULT_CONST_TABLE_GET_GE(&tmpa, pre_a_lam, n, WINDOW_A);
208  VERIFY_CHECK(n != 0);
209  secp256k1_gej_add_ge(r, r, &tmpa);
210  }
211  }
212 
213  {
214  /* Correct for wNAF skew */
215  secp256k1_gej tmpj;
216 
217  secp256k1_ge_neg(&tmpa, &pre_a[0]);
218  secp256k1_gej_add_ge(&tmpj, r, &tmpa);
219  secp256k1_gej_cmov(r, &tmpj, skew_1);
220 
221  if (size > 128) {
222  secp256k1_ge_neg(&tmpa, &pre_a_lam[0]);
223  secp256k1_gej_add_ge(&tmpj, r, &tmpa);
224  secp256k1_gej_cmov(r, &tmpj, skew_lam);
225  }
226  }
227 
228  secp256k1_fe_mul(&r->z, &r->z, &Z);
229 }
230 
231 #endif /* SECP256K1_ECMULT_CONST_IMPL_H */
#define ECMULT_TABLE_SIZE(w)
The number of entries a table with precomputed multiples needs to have.
Definition: ecmult.h:41
static void secp256k1_ecmult_odd_multiples_table_globalz_windowa(secp256k1_ge *pre, secp256k1_fe *globalz, const secp256k1_gej *a)
Fill a table 'pre' with precomputed odd multiples of a.
#define ECMULT_CONST_TABLE_GET_GE(r, pre, n, w)
static void secp256k1_ecmult_const(secp256k1_gej *r, const secp256k1_ge *a, const secp256k1_scalar *scalar, int size)
static int secp256k1_wnaf_const(int *wnaf, const secp256k1_scalar *scalar, int w, int size)
Convert a number to WNAF notation.
#define WNAF_SIZE(w)
Definition: ecmult_impl.h:46
#define WINDOW_A
Definition: ecmult_impl.h:32
#define WNAF_SIZE_BITS(bits, w)
Definition: ecmult_impl.h:45
static void secp256k1_ecmult_odd_multiples_table(int n, secp256k1_ge *pre_a, secp256k1_fe *zr, secp256k1_fe *z, const secp256k1_gej *a)
Fill a table 'pre_a' with precomputed odd multiples of a.
Definition: ecmult_impl.h:73
static void secp256k1_fe_normalize_weak(secp256k1_fe *r)
Weakly normalize a field element: reduce its magnitude to 1, but don't fully normalize.
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 product of two others.
static void secp256k1_ge_mul_lambda(secp256k1_ge *r, const secp256k1_ge *a)
Set r to be equal to lambda times a, where lambda is chosen in a way such that this is very fast.
static void secp256k1_gej_add_ge(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_ge *b)
Set r equal to the sum of a and b (with b given in affine coordinates, and not infinity).
static void secp256k1_ge_table_set_globalz(size_t len, secp256k1_ge *a, const secp256k1_fe *zr)
Bring a batch of inputs to the same global z "denominator", based on ratios between (omitted) z coord...
static void secp256k1_ge_neg(secp256k1_ge *r, const secp256k1_ge *a)
Set r equal to the inverse of a (i.e., mirrored around the X axis)
static void secp256k1_gej_double(secp256k1_gej *r, const secp256k1_gej *a)
Set r equal to the double of a.
static void secp256k1_gej_set_ge(secp256k1_gej *r, const secp256k1_ge *a)
Set a group element (jacobian) equal to another which is given in affine coordinates.
static void secp256k1_gej_cmov(secp256k1_gej *r, const secp256k1_gej *a, int flag)
If flag is true, set *r equal to *a; otherwise leave it.
static int secp256k1_scalar_is_even(const secp256k1_scalar *a)
Check whether a scalar, considered as an nonnegative integer, is even.
static int secp256k1_scalar_is_zero(const secp256k1_scalar *a)
Check whether a scalar equals zero.
static int secp256k1_scalar_cond_negate(secp256k1_scalar *a, int flag)
Conditionally negate a number, in constant time.
static int secp256k1_scalar_is_high(const secp256k1_scalar *a)
Check whether a scalar is higher than the group order divided by 2.
static void secp256k1_scalar_cadd_bit(secp256k1_scalar *r, unsigned int bit, int flag)
Conditionally add a power of two to a scalar.
static void secp256k1_scalar_split_lambda(secp256k1_scalar *r1, secp256k1_scalar *r2, const secp256k1_scalar *k)
Find r1 and r2 such that r1+r2*lambda = k, where r1 and r2 or their negations are maximum 128 bits lo...
static int secp256k1_scalar_shr_int(secp256k1_scalar *r, int n)
Shift a scalar right by some amount strictly between 0 and 16, returning the low bits that were shift...
#define VERIFY_CHECK(cond)
Definition: util.h:100
A group element in affine coordinates on the secp256k1 curve, or occasionally on an isomorphic curve ...
Definition: group.h:16
int infinity
Definition: group.h:19
A group element of the secp256k1 curve, in jacobian coordinates.
Definition: group.h:28
secp256k1_fe z
Definition: group.h:31
A scalar modulo the group order of the secp256k1 curve.
Definition: scalar_4x64.h:13