github.com/ethereum/go-ethereum@v1.16.1/crypto/secp256k1/libsecp256k1/src/field_impl.h (about)

     1  /***********************************************************************
     2   * Copyright (c) 2013, 2014 Pieter Wuille                              *
     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_FIELD_IMPL_H
     8  #define SECP256K1_FIELD_IMPL_H
     9  
    10  #include "field.h"
    11  #include "util.h"
    12  
    13  #if defined(SECP256K1_WIDEMUL_INT128)
    14  #include "field_5x52_impl.h"
    15  #elif defined(SECP256K1_WIDEMUL_INT64)
    16  #include "field_10x26_impl.h"
    17  #else
    18  #error "Please select wide multiplication implementation"
    19  #endif
    20  
    21  SECP256K1_INLINE static void secp256k1_fe_clear(secp256k1_fe *a) {
    22      secp256k1_memclear(a, sizeof(secp256k1_fe));
    23  }
    24  
    25  SECP256K1_INLINE static int secp256k1_fe_equal(const secp256k1_fe *a, const secp256k1_fe *b) {
    26      secp256k1_fe na;
    27      SECP256K1_FE_VERIFY(a);
    28      SECP256K1_FE_VERIFY(b);
    29      SECP256K1_FE_VERIFY_MAGNITUDE(a, 1);
    30      SECP256K1_FE_VERIFY_MAGNITUDE(b, 31);
    31  
    32      secp256k1_fe_negate(&na, a, 1);
    33      secp256k1_fe_add(&na, b);
    34      return secp256k1_fe_normalizes_to_zero(&na);
    35  }
    36  
    37  static int secp256k1_fe_sqrt(secp256k1_fe * SECP256K1_RESTRICT r, const secp256k1_fe * SECP256K1_RESTRICT a) {
    38      /** Given that p is congruent to 3 mod 4, we can compute the square root of
    39       *  a mod p as the (p+1)/4'th power of a.
    40       *
    41       *  As (p+1)/4 is an even number, it will have the same result for a and for
    42       *  (-a). Only one of these two numbers actually has a square root however,
    43       *  so we test at the end by squaring and comparing to the input.
    44       *  Also because (p+1)/4 is an even number, the computed square root is
    45       *  itself always a square (a ** ((p+1)/4) is the square of a ** ((p+1)/8)).
    46       */
    47      secp256k1_fe x2, x3, x6, x9, x11, x22, x44, x88, x176, x220, x223, t1;
    48      int j, ret;
    49  
    50      VERIFY_CHECK(r != a);
    51      SECP256K1_FE_VERIFY(a);
    52      SECP256K1_FE_VERIFY_MAGNITUDE(a, 8);
    53  
    54      /** The binary representation of (p + 1)/4 has 3 blocks of 1s, with lengths in
    55       *  { 2, 22, 223 }. Use an addition chain to calculate 2^n - 1 for each block:
    56       *  1, [2], 3, 6, 9, 11, [22], 44, 88, 176, 220, [223]
    57       */
    58  
    59      secp256k1_fe_sqr(&x2, a);
    60      secp256k1_fe_mul(&x2, &x2, a);
    61  
    62      secp256k1_fe_sqr(&x3, &x2);
    63      secp256k1_fe_mul(&x3, &x3, a);
    64  
    65      x6 = x3;
    66      for (j=0; j<3; j++) {
    67          secp256k1_fe_sqr(&x6, &x6);
    68      }
    69      secp256k1_fe_mul(&x6, &x6, &x3);
    70  
    71      x9 = x6;
    72      for (j=0; j<3; j++) {
    73          secp256k1_fe_sqr(&x9, &x9);
    74      }
    75      secp256k1_fe_mul(&x9, &x9, &x3);
    76  
    77      x11 = x9;
    78      for (j=0; j<2; j++) {
    79          secp256k1_fe_sqr(&x11, &x11);
    80      }
    81      secp256k1_fe_mul(&x11, &x11, &x2);
    82  
    83      x22 = x11;
    84      for (j=0; j<11; j++) {
    85          secp256k1_fe_sqr(&x22, &x22);
    86      }
    87      secp256k1_fe_mul(&x22, &x22, &x11);
    88  
    89      x44 = x22;
    90      for (j=0; j<22; j++) {
    91          secp256k1_fe_sqr(&x44, &x44);
    92      }
    93      secp256k1_fe_mul(&x44, &x44, &x22);
    94  
    95      x88 = x44;
    96      for (j=0; j<44; j++) {
    97          secp256k1_fe_sqr(&x88, &x88);
    98      }
    99      secp256k1_fe_mul(&x88, &x88, &x44);
   100  
   101      x176 = x88;
   102      for (j=0; j<88; j++) {
   103          secp256k1_fe_sqr(&x176, &x176);
   104      }
   105      secp256k1_fe_mul(&x176, &x176, &x88);
   106  
   107      x220 = x176;
   108      for (j=0; j<44; j++) {
   109          secp256k1_fe_sqr(&x220, &x220);
   110      }
   111      secp256k1_fe_mul(&x220, &x220, &x44);
   112  
   113      x223 = x220;
   114      for (j=0; j<3; j++) {
   115          secp256k1_fe_sqr(&x223, &x223);
   116      }
   117      secp256k1_fe_mul(&x223, &x223, &x3);
   118  
   119      /* The final result is then assembled using a sliding window over the blocks. */
   120  
   121      t1 = x223;
   122      for (j=0; j<23; j++) {
   123          secp256k1_fe_sqr(&t1, &t1);
   124      }
   125      secp256k1_fe_mul(&t1, &t1, &x22);
   126      for (j=0; j<6; j++) {
   127          secp256k1_fe_sqr(&t1, &t1);
   128      }
   129      secp256k1_fe_mul(&t1, &t1, &x2);
   130      secp256k1_fe_sqr(&t1, &t1);
   131      secp256k1_fe_sqr(r, &t1);
   132  
   133      /* Check that a square root was actually calculated */
   134  
   135      secp256k1_fe_sqr(&t1, r);
   136      ret = secp256k1_fe_equal(&t1, a);
   137  
   138  #ifdef VERIFY
   139      if (!ret) {
   140          secp256k1_fe_negate(&t1, &t1, 1);
   141          secp256k1_fe_normalize_var(&t1);
   142          VERIFY_CHECK(secp256k1_fe_equal(&t1, a));
   143      }
   144  #endif
   145      return ret;
   146  }
   147  
   148  #ifndef VERIFY
   149  static void secp256k1_fe_verify(const secp256k1_fe *a) { (void)a; }
   150  static void secp256k1_fe_verify_magnitude(const secp256k1_fe *a, int m) { (void)a; (void)m; }
   151  #else
   152  static void secp256k1_fe_impl_verify(const secp256k1_fe *a);
   153  static void secp256k1_fe_verify(const secp256k1_fe *a) {
   154      /* Magnitude between 0 and 32. */
   155      SECP256K1_FE_VERIFY_MAGNITUDE(a, 32);
   156      /* Normalized is 0 or 1. */
   157      VERIFY_CHECK((a->normalized == 0) || (a->normalized == 1));
   158      /* If normalized, magnitude must be 0 or 1. */
   159      if (a->normalized) SECP256K1_FE_VERIFY_MAGNITUDE(a, 1);
   160      /* Invoke implementation-specific checks. */
   161      secp256k1_fe_impl_verify(a);
   162  }
   163  
   164  static void secp256k1_fe_verify_magnitude(const secp256k1_fe *a, int m) {
   165      VERIFY_CHECK(m >= 0);
   166      VERIFY_CHECK(m <= 32);
   167      VERIFY_CHECK(a->magnitude <= m);
   168  }
   169  
   170  static void secp256k1_fe_impl_normalize(secp256k1_fe *r);
   171  SECP256K1_INLINE static void secp256k1_fe_normalize(secp256k1_fe *r) {
   172      SECP256K1_FE_VERIFY(r);
   173  
   174      secp256k1_fe_impl_normalize(r);
   175      r->magnitude = 1;
   176      r->normalized = 1;
   177  
   178      SECP256K1_FE_VERIFY(r);
   179  }
   180  
   181  static void secp256k1_fe_impl_normalize_weak(secp256k1_fe *r);
   182  SECP256K1_INLINE static void secp256k1_fe_normalize_weak(secp256k1_fe *r) {
   183      SECP256K1_FE_VERIFY(r);
   184  
   185      secp256k1_fe_impl_normalize_weak(r);
   186      r->magnitude = 1;
   187  
   188      SECP256K1_FE_VERIFY(r);
   189  }
   190  
   191  static void secp256k1_fe_impl_normalize_var(secp256k1_fe *r);
   192  SECP256K1_INLINE static void secp256k1_fe_normalize_var(secp256k1_fe *r) {
   193      SECP256K1_FE_VERIFY(r);
   194  
   195      secp256k1_fe_impl_normalize_var(r);
   196      r->magnitude = 1;
   197      r->normalized = 1;
   198  
   199      SECP256K1_FE_VERIFY(r);
   200  }
   201  
   202  static int secp256k1_fe_impl_normalizes_to_zero(const secp256k1_fe *r);
   203  SECP256K1_INLINE static int secp256k1_fe_normalizes_to_zero(const secp256k1_fe *r) {
   204      SECP256K1_FE_VERIFY(r);
   205  
   206      return secp256k1_fe_impl_normalizes_to_zero(r);
   207  }
   208  
   209  static int secp256k1_fe_impl_normalizes_to_zero_var(const secp256k1_fe *r);
   210  SECP256K1_INLINE static int secp256k1_fe_normalizes_to_zero_var(const secp256k1_fe *r) {
   211      SECP256K1_FE_VERIFY(r);
   212  
   213      return secp256k1_fe_impl_normalizes_to_zero_var(r);
   214  }
   215  
   216  static void secp256k1_fe_impl_set_int(secp256k1_fe *r, int a);
   217  SECP256K1_INLINE static void secp256k1_fe_set_int(secp256k1_fe *r, int a) {
   218      VERIFY_CHECK(0 <= a && a <= 0x7FFF);
   219  
   220      secp256k1_fe_impl_set_int(r, a);
   221      r->magnitude = (a != 0);
   222      r->normalized = 1;
   223  
   224      SECP256K1_FE_VERIFY(r);
   225  }
   226  
   227  static void secp256k1_fe_impl_add_int(secp256k1_fe *r, int a);
   228  SECP256K1_INLINE static void secp256k1_fe_add_int(secp256k1_fe *r, int a) {
   229      VERIFY_CHECK(0 <= a && a <= 0x7FFF);
   230      SECP256K1_FE_VERIFY(r);
   231  
   232      secp256k1_fe_impl_add_int(r, a);
   233      r->magnitude += 1;
   234      r->normalized = 0;
   235  
   236      SECP256K1_FE_VERIFY(r);
   237  }
   238  
   239  static int secp256k1_fe_impl_is_zero(const secp256k1_fe *a);
   240  SECP256K1_INLINE static int secp256k1_fe_is_zero(const secp256k1_fe *a) {
   241      SECP256K1_FE_VERIFY(a);
   242      VERIFY_CHECK(a->normalized);
   243  
   244      return secp256k1_fe_impl_is_zero(a);
   245  }
   246  
   247  static int secp256k1_fe_impl_is_odd(const secp256k1_fe *a);
   248  SECP256K1_INLINE static int secp256k1_fe_is_odd(const secp256k1_fe *a) {
   249      SECP256K1_FE_VERIFY(a);
   250      VERIFY_CHECK(a->normalized);
   251  
   252      return secp256k1_fe_impl_is_odd(a);
   253  }
   254  
   255  static int secp256k1_fe_impl_cmp_var(const secp256k1_fe *a, const secp256k1_fe *b);
   256  SECP256K1_INLINE static int secp256k1_fe_cmp_var(const secp256k1_fe *a, const secp256k1_fe *b) {
   257      SECP256K1_FE_VERIFY(a);
   258      SECP256K1_FE_VERIFY(b);
   259      VERIFY_CHECK(a->normalized);
   260      VERIFY_CHECK(b->normalized);
   261  
   262      return secp256k1_fe_impl_cmp_var(a, b);
   263  }
   264  
   265  static void secp256k1_fe_impl_set_b32_mod(secp256k1_fe *r, const unsigned char *a);
   266  SECP256K1_INLINE static void secp256k1_fe_set_b32_mod(secp256k1_fe *r, const unsigned char *a) {
   267      secp256k1_fe_impl_set_b32_mod(r, a);
   268      r->magnitude = 1;
   269      r->normalized = 0;
   270  
   271      SECP256K1_FE_VERIFY(r);
   272  }
   273  
   274  static int secp256k1_fe_impl_set_b32_limit(secp256k1_fe *r, const unsigned char *a);
   275  SECP256K1_INLINE static int secp256k1_fe_set_b32_limit(secp256k1_fe *r, const unsigned char *a) {
   276      if (secp256k1_fe_impl_set_b32_limit(r, a)) {
   277          r->magnitude = 1;
   278          r->normalized = 1;
   279          SECP256K1_FE_VERIFY(r);
   280          return 1;
   281      } else {
   282          /* Mark the output field element as invalid. */
   283          r->magnitude = -1;
   284          return 0;
   285      }
   286  }
   287  
   288  static void secp256k1_fe_impl_get_b32(unsigned char *r, const secp256k1_fe *a);
   289  SECP256K1_INLINE static void secp256k1_fe_get_b32(unsigned char *r, const secp256k1_fe *a) {
   290      SECP256K1_FE_VERIFY(a);
   291      VERIFY_CHECK(a->normalized);
   292  
   293      secp256k1_fe_impl_get_b32(r, a);
   294  }
   295  
   296  static void secp256k1_fe_impl_negate_unchecked(secp256k1_fe *r, const secp256k1_fe *a, int m);
   297  SECP256K1_INLINE static void secp256k1_fe_negate_unchecked(secp256k1_fe *r, const secp256k1_fe *a, int m) {
   298      SECP256K1_FE_VERIFY(a);
   299      VERIFY_CHECK(m >= 0 && m <= 31);
   300      SECP256K1_FE_VERIFY_MAGNITUDE(a, m);
   301  
   302      secp256k1_fe_impl_negate_unchecked(r, a, m);
   303      r->magnitude = m + 1;
   304      r->normalized = 0;
   305  
   306      SECP256K1_FE_VERIFY(r);
   307  }
   308  
   309  static void secp256k1_fe_impl_mul_int_unchecked(secp256k1_fe *r, int a);
   310  SECP256K1_INLINE static void secp256k1_fe_mul_int_unchecked(secp256k1_fe *r, int a) {
   311      SECP256K1_FE_VERIFY(r);
   312  
   313      VERIFY_CHECK(a >= 0 && a <= 32);
   314      VERIFY_CHECK(a*r->magnitude <= 32);
   315      secp256k1_fe_impl_mul_int_unchecked(r, a);
   316      r->magnitude *= a;
   317      r->normalized = 0;
   318  
   319      SECP256K1_FE_VERIFY(r);
   320  }
   321  
   322  static void secp256k1_fe_impl_add(secp256k1_fe *r, const secp256k1_fe *a);
   323  SECP256K1_INLINE static void secp256k1_fe_add(secp256k1_fe *r, const secp256k1_fe *a) {
   324      SECP256K1_FE_VERIFY(r);
   325      SECP256K1_FE_VERIFY(a);
   326      VERIFY_CHECK(r->magnitude + a->magnitude <= 32);
   327  
   328      secp256k1_fe_impl_add(r, a);
   329      r->magnitude += a->magnitude;
   330      r->normalized = 0;
   331  
   332      SECP256K1_FE_VERIFY(r);
   333  }
   334  
   335  static void secp256k1_fe_impl_mul(secp256k1_fe *r, const secp256k1_fe *a, const secp256k1_fe * SECP256K1_RESTRICT b);
   336  SECP256K1_INLINE static void secp256k1_fe_mul(secp256k1_fe *r, const secp256k1_fe *a, const secp256k1_fe * SECP256K1_RESTRICT b) {
   337      SECP256K1_FE_VERIFY(a);
   338      SECP256K1_FE_VERIFY(b);
   339      SECP256K1_FE_VERIFY_MAGNITUDE(a, 8);
   340      SECP256K1_FE_VERIFY_MAGNITUDE(b, 8);
   341      VERIFY_CHECK(r != b);
   342      VERIFY_CHECK(a != b);
   343  
   344      secp256k1_fe_impl_mul(r, a, b);
   345      r->magnitude = 1;
   346      r->normalized = 0;
   347  
   348      SECP256K1_FE_VERIFY(r);
   349  }
   350  
   351  static void secp256k1_fe_impl_sqr(secp256k1_fe *r, const secp256k1_fe *a);
   352  SECP256K1_INLINE static void secp256k1_fe_sqr(secp256k1_fe *r, const secp256k1_fe *a) {
   353      SECP256K1_FE_VERIFY(a);
   354      SECP256K1_FE_VERIFY_MAGNITUDE(a, 8);
   355  
   356      secp256k1_fe_impl_sqr(r, a);
   357      r->magnitude = 1;
   358      r->normalized = 0;
   359  
   360      SECP256K1_FE_VERIFY(r);
   361  }
   362  
   363  static void secp256k1_fe_impl_cmov(secp256k1_fe *r, const secp256k1_fe *a, int flag);
   364  SECP256K1_INLINE static void secp256k1_fe_cmov(secp256k1_fe *r, const secp256k1_fe *a, int flag) {
   365      VERIFY_CHECK(flag == 0 || flag == 1);
   366      SECP256K1_FE_VERIFY(a);
   367      SECP256K1_FE_VERIFY(r);
   368  
   369      secp256k1_fe_impl_cmov(r, a, flag);
   370      if (a->magnitude > r->magnitude) r->magnitude = a->magnitude;
   371      if (!a->normalized) r->normalized = 0;
   372  
   373      SECP256K1_FE_VERIFY(r);
   374  }
   375  
   376  static void secp256k1_fe_impl_to_storage(secp256k1_fe_storage *r, const secp256k1_fe *a);
   377  SECP256K1_INLINE static void secp256k1_fe_to_storage(secp256k1_fe_storage *r, const secp256k1_fe *a) {
   378      SECP256K1_FE_VERIFY(a);
   379      VERIFY_CHECK(a->normalized);
   380  
   381      secp256k1_fe_impl_to_storage(r, a);
   382  }
   383  
   384  static void secp256k1_fe_impl_from_storage(secp256k1_fe *r, const secp256k1_fe_storage *a);
   385  SECP256K1_INLINE static void secp256k1_fe_from_storage(secp256k1_fe *r, const secp256k1_fe_storage *a) {
   386      secp256k1_fe_impl_from_storage(r, a);
   387      r->magnitude = 1;
   388      r->normalized = 1;
   389  
   390      SECP256K1_FE_VERIFY(r);
   391  }
   392  
   393  static void secp256k1_fe_impl_inv(secp256k1_fe *r, const secp256k1_fe *x);
   394  SECP256K1_INLINE static void secp256k1_fe_inv(secp256k1_fe *r, const secp256k1_fe *x) {
   395      int input_is_zero = secp256k1_fe_normalizes_to_zero(x);
   396      SECP256K1_FE_VERIFY(x);
   397  
   398      secp256k1_fe_impl_inv(r, x);
   399      r->magnitude = x->magnitude > 0;
   400      r->normalized = 1;
   401  
   402      VERIFY_CHECK(secp256k1_fe_normalizes_to_zero(r) == input_is_zero);
   403      SECP256K1_FE_VERIFY(r);
   404  }
   405  
   406  static void secp256k1_fe_impl_inv_var(secp256k1_fe *r, const secp256k1_fe *x);
   407  SECP256K1_INLINE static void secp256k1_fe_inv_var(secp256k1_fe *r, const secp256k1_fe *x) {
   408      int input_is_zero = secp256k1_fe_normalizes_to_zero(x);
   409      SECP256K1_FE_VERIFY(x);
   410  
   411      secp256k1_fe_impl_inv_var(r, x);
   412      r->magnitude = x->magnitude > 0;
   413      r->normalized = 1;
   414  
   415      VERIFY_CHECK(secp256k1_fe_normalizes_to_zero(r) == input_is_zero);
   416      SECP256K1_FE_VERIFY(r);
   417  }
   418  
   419  static int secp256k1_fe_impl_is_square_var(const secp256k1_fe *x);
   420  SECP256K1_INLINE static int secp256k1_fe_is_square_var(const secp256k1_fe *x) {
   421      int ret;
   422      secp256k1_fe tmp = *x, sqrt;
   423      SECP256K1_FE_VERIFY(x);
   424  
   425      ret = secp256k1_fe_impl_is_square_var(x);
   426      secp256k1_fe_normalize_weak(&tmp);
   427      VERIFY_CHECK(ret == secp256k1_fe_sqrt(&sqrt, &tmp));
   428      return ret;
   429  }
   430  
   431  static void secp256k1_fe_impl_get_bounds(secp256k1_fe* r, int m);
   432  SECP256K1_INLINE static void secp256k1_fe_get_bounds(secp256k1_fe* r, int m) {
   433      VERIFY_CHECK(m >= 0);
   434      VERIFY_CHECK(m <= 32);
   435  
   436      secp256k1_fe_impl_get_bounds(r, m);
   437      r->magnitude = m;
   438      r->normalized = (m == 0);
   439  
   440      SECP256K1_FE_VERIFY(r);
   441  }
   442  
   443  static void secp256k1_fe_impl_half(secp256k1_fe *r);
   444  SECP256K1_INLINE static void secp256k1_fe_half(secp256k1_fe *r) {
   445      SECP256K1_FE_VERIFY(r);
   446      SECP256K1_FE_VERIFY_MAGNITUDE(r, 31);
   447  
   448      secp256k1_fe_impl_half(r);
   449      r->magnitude = (r->magnitude >> 1) + 1;
   450      r->normalized = 0;
   451  
   452      SECP256K1_FE_VERIFY(r);
   453  }
   454  
   455  #endif /* defined(VERIFY) */
   456  
   457  #endif /* SECP256K1_FIELD_IMPL_H */