src/SS.cxx

   1 #include "DIPE.h"
   2 #include "DIPE_Internal.h"
   3
   4 #include <assert.h>
   5
   6 namespace {
   7         void dipe_ss_esf(dipe_param_t param, size_t size, size_t m, size_t excl, element_t* elements, element_t* result) {
   8                 assert(size >= m);
   9
  10                 if (m == 0) {
  11                         element_set1(*result);
  12                         return;
  13                 }
  14
  15                 /* m = n */
  16                 if (size == m || (m + 1 == size && excl <= size)) {
  17                         assert((size == m) ? excl > size : true);
  18                         element_set1(*result);
  19                         for (size_t i = 0; i < size; ++i) {
  20                                 if (i != excl) {
  21                                         element_mul(*result, *result, elements[i]);
  22                                 }
  23                         }
  24                         return;
  25                 }
  26                 /* m = 1 */
  27                 if (m == 1) {
  28                         element_set0(*result);
  29                         for (size_t i = 0; i < size; ++i) {
  30                                 if (i != excl) {
  31                                         element_add(*result, *result, elements[i]);
  32                                 }
  33                         }
  34                         return;
  35                 }
  36
  37                 /* otherwise */
  38                 element_t lhs;
  39                 element_init_Zr(lhs, param->pairing);
  40                 dipe_ss_esf(param, size-1, m, excl, elements, result);
  41                 dipe_ss_esf(param, size-1, m-1, excl, elements, &lhs);
  42                 element_mul(lhs, lhs, elements[size-1]);
  43                 element_add(*result, *result, lhs);
  44                 element_clear(lhs);
  45         }
  46
  47
  48         /* https://proofwiki.org/wiki/Inverse_of_Vandermonde_Matrix
  49          * Contract: result is allocated but not initialized size x size array
  50          */
  51         void dipe_ss_inverse_vandermonde(dipe_param_t param, bool flat, size_t size, element_t* elements, element_t** result) {
  52                 /* b_ij = (-1)^{n-i} e_{n-i}() / \Prod ()
  53                  */
  54                 element_t numerator, denominator;
  55                 element_t tmp;
  56                 element_init_Zr(numerator, param->pairing);
  57                 element_init_Zr(denominator, param->pairing);
  58                 element_init_Zr(tmp, param->pairing);
  59
  60                 for (size_t i = 0; i < size; ++i) {
  61                         if (flat && i > 0) continue;
  62
  63                         for (size_t j = 0; j < size; ++j) {
  64                                 element_init_Zr(result[i][j], param->pairing);
  65
  66                                 /* numerator */
  67                                 dipe_ss_esf(param, size, size-i-1, j, elements, &numerator);
  68                                 if (((size - i-1) & 1) == 1) {
  69                                         element_neg(numerator, numerator);
  70                                 }
  71
  72                                 /* denominator */
  73                                 element_set1(denominator);
  74                                 for (size_t k = 0; k < size; ++k) {
  75                                         if (k != j) {
  76                                                 element_sub(tmp, elements[j], elements[k]);
  77                                                 element_mul(denominator, denominator, tmp);
  78                                         }
  79                                 }
  80
  81                                 element_div(result[i][j], numerator, denominator);
  82                         }
  83                 }
  84                 element_clear(tmp);
  85                 element_clear(numerator);
  86                 element_clear(denominator);
  87         }
  88 }
  89
  90 void dipe_ss_share(dipe_param_t param, size_t id_size, element_t* ids, size_t fid_size, element_t* fake_ids, size_t share_size, element_t** shares,
  91                    element_t* secret, element_t** dummy_shares) {
  92         element_t tmp;
  93         element_t tmpz;
  94         element_t a_pow;
  95         element_init_same_as(tmp, shares[0][0]);
  96         element_init_Zr(tmpz, param->pairing);
  97         element_init_Zr(a_pow, param->pairing);
  98
  99         /* Precompute V_I^{-1} needed in several steps */
 100         element_t** b = (element_t**)calloc(id_size, sizeof(element_t*));
 101         for (size_t i = 0; i < id_size; ++i) {
 102                 b[i] = (element_t*)calloc(id_size, sizeof(element_t));
 103         }
 104         dipe_ss_inverse_vandermonde(param, false, id_size, ids, b);
 105
 106         /* Compute Secret */
 107         for (size_t k = 0; k < share_size; ++k) {
 108                 element_set1(secret[k]);
 109                 for (size_t j = 0; j < id_size; ++j) {
 110                         element_pow_zn(tmp, shares[j][k], b[0][j]);
 111                         element_mul(secret[k], secret[k], tmp);
 112                 }
 113         }
 114
 115         /* Compute Dummy Shares */
 116         /* Matrix Product */
 117         element_t** ab = (element_t**)calloc(id_size, sizeof(element_t*));
 118         for (size_t i = 0; i < fid_size; ++i) {
 119                 ab[i] = (element_t*)calloc(id_size, sizeof(element_t));
 120
 121                 for (size_t j = 0; j < id_size; ++j) {
 122                         element_init_Zr(ab[i][j], param->pairing);
 123                         element_set0(ab[i][j]);
 124                         element_set1(a_pow);
 125
 126                         for (size_t k = 0; k < id_size; ++ k) {
 127                                 element_mul(tmpz, a_pow, b[k][j]);
 128                                 element_add(ab[i][j], ab[i][j], tmpz);
 129                                 element_mul(a_pow, a_pow, fake_ids[i]);
 130                         }
 131                 }
 132         }
 133
 134         /* Matrix Product. Note this is an abuse of notation and we're doing scalar * group in additive writing */
 135         for (size_t i = 0; i < fid_size; ++ i) {
 136                 for (size_t j = 0; j < share_size; ++j) {
 137                         element_init_same_as(dummy_shares[i][j], shares[0][0]);
 138                         element_set1(dummy_shares[i][j]);
 139                         for (size_t k = 0; k < id_size; ++k) {
 140                                 element_pow_zn(tmp, shares[k][j], ab[i][k]);
 141                                 element_mul(dummy_shares[i][j], dummy_shares[i][j], tmp);
 142                         }
 143                 }
 144         }
 145
 146         for (size_t i = 0; i < id_size; ++i) {
 147                 for (size_t j = 0; j < id_size; ++j) {
 148                         element_clear(b[i][j]);
 149                 }
 150                 free(b[i]);
 151         }
 152         free(b);
 153
 154         for (size_t i = 0; i < fid_size; ++i) {
 155                 for (size_t j = 0; j < id_size; ++j) {
 156                         element_clear(ab[i][j]);
 157                 }
 158                 free(ab[i]);
 159         }
 160         free(ab);
 161         element_clear(tmp);
 162         element_clear(tmpz);
 163         element_clear(a_pow);
 164 }
 165
 166 void dipe_ss_recover(dipe_param_t param, size_t id_size, element_t* ids, size_t share_size, element_t** shares, element_t* secret) {
 167         element_t tmp;
 168         /* TODO: fix type, shares are in G_t here~ */
 169         element_init_same_as(tmp, shares[0][0]);
 170
 171         /* Precompute V_I^{-1} needed in several steps */
 172         /* Actually for recover we only need the values b[0][j] */
 173         element_t** b = (element_t**)calloc(1, sizeof(element_t*));
 174         b[0] = (element_t*)calloc(id_size, sizeof(element_t));
 175         dipe_ss_inverse_vandermonde(param, true, id_size, ids, b);
 176
 177         /* Compute Secret */
 178         for (size_t k = 0; k < share_size; ++k) {
 179                 element_set1(secret[k]);
 180                 for (size_t j = 0; j < id_size; ++j) {
 181                         element_pow_zn(tmp, shares[j][k], b[0][j]);
 182                         element_mul(secret[k], secret[k], tmp);
 183                 }
 184         }
 185
 186         for (size_t j = 0; j < id_size; ++j) {
 187                 element_clear(b[0][j]);
 188         }
 189         free(b[0]);
 190         free(b);
 191         element_clear(tmp);
 192 }