Botan  2.4.0
Crypto and TLS for C++11
gf2m_rootfind_dcmp.cpp
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1 /*
2  * (C) 2014 cryptosource GmbH
3  * (C) 2014 Falko Strenzke fstrenzke@cryptosource.de
4  *
5  * Botan is released under the Simplified BSD License (see license.txt)
6  *
7  */
8 
9 #include <botan/polyn_gf2m.h>
10 #include <botan/internal/bit_ops.h>
11 #include <botan/internal/code_based_util.h>
12 #include <botan/exceptn.h>
13 
14 namespace Botan {
15 
16 namespace {
17 
18 uint32_t patch_root_array(gf2m* res_root_arr,
19  uint32_t res_root_arr_len,
20  uint32_t root_pos)
21  {
22  volatile uint32_t i;
23  volatile gf2m patch_elem = 0x01;
24  volatile gf2m cond_mask = (root_pos == res_root_arr_len);
25  cond_mask = expand_mask_16bit(cond_mask);
26  cond_mask = ~cond_mask; /* now cond = 1 if not enough roots */
27  patch_elem &= cond_mask;
28  for(i = 0; i < res_root_arr_len; i++)
29  {
30 
31  gf2m masked_patch_elem = (patch_elem++) & cond_mask;
32  res_root_arr[i] ^= masked_patch_elem++;
33  }
34  return res_root_arr_len;
35  }
36 
37 class gf2m_decomp_rootfind_state
38  {
39  public:
40  gf2m_decomp_rootfind_state(const polyn_gf2m & p_polyn, uint32_t code_length);
41 
42  void calc_LiK(const polyn_gf2m & sigma);
43  gf2m calc_Fxj_j_neq_0( const polyn_gf2m & sigma, gf2m j_gray);
44  void calc_next_Aij();
45  void calc_Ai_zero(const polyn_gf2m & sigma);
46  secure_vector<gf2m> find_roots(const polyn_gf2m & sigma);
47  uint32_t get_code_length() const { return code_length; }
48  uint32_t code_length;
49  secure_vector<gf2m> m_Lik; // size is outer_summands * m
50  secure_vector<gf2m> m_Aij; // ...
51  uint32_t m_outer_summands;
56  };
57 
58 /*
59 * !! Attention: assumes gf2m is 16bit !!
60 */
61 #if 0
62 gf2m brootf_decomp_gray_to_lex(gf2m gray)
63  {
64  static_assert(sizeof(gf2m) == 2, "Expected size");
65  gf2m result = gray ^ (gray>>8);
66  result ^= (result >> 4);
67  result ^= (result >> 2);
68  result ^= (result >> 1);
69  return result;
70  }
71 #endif
72 
73 /**
74 * calculates ceil((t-4)/5) = outer_summands - 1
75 */
76 uint32_t brootf_decomp_calc_sum_limit(uint32_t t)
77  {
78  uint32_t result;
79  if(t < 4)
80  {
81  return 0;
82  }
83  result = t - 4;
84  result += 4;
85  result /= 5;
86  return result;
87  }
88 
89 gf2m_decomp_rootfind_state::gf2m_decomp_rootfind_state(const polyn_gf2m & polyn, uint32_t the_code_length) :
90  code_length(the_code_length), m_j(0), m_j_gray(0)
91  {
92  gf2m coeff_3;
93  gf2m coeff_head;
94  std::shared_ptr<GF2m_Field> sp_field = polyn.get_sp_field();
95  int deg_sigma = polyn.get_degree();
96  if(deg_sigma <= 3)
97  {
98  throw Internal_Error("Unexpected degree in gf2m_decomp_rootfind_state");
99  }
100 
101  coeff_3 = polyn.get_coef( 3);
102  coeff_head = polyn.get_coef( deg_sigma); /* dummy value for SCA CM */
103  if(coeff_3 != 0)
104  {
105  this->m_sigma_3_l = sp_field->gf_l_from_n(coeff_3);
106  this->m_sigma_3_neq_0_mask = 0xFFFF;
107  }
108  else
109  {
110  // dummy value needed for timing countermeasure
111  this->m_sigma_3_l = sp_field->gf_l_from_n(coeff_head);
112  this->m_sigma_3_neq_0_mask = 0 ;
113  }
114 
115  this->m_outer_summands = 1 + brootf_decomp_calc_sum_limit(deg_sigma);
116  this->m_Lik.resize(this->m_outer_summands * sp_field->get_extension_degree());
117  this->m_Aij.resize(this->m_outer_summands);
118  }
119 
120 void gf2m_decomp_rootfind_state::calc_Ai_zero(const polyn_gf2m & sigma)
121  {
122  uint32_t i;
123  /*
124  * this function assumes this the first gray code element is zero
125  */
126  for(i = 0; i < this->m_outer_summands; i++)
127  {
128  this->m_Aij[i] = sigma.get_coef(5*i);
129  }
130  this->m_j = 0;
131  this->m_j_gray = 0;
132  }
133 
134 void gf2m_decomp_rootfind_state::calc_next_Aij()
135  {
136  /*
137  * upon function entry, we have in the state j, Aij.
138  * first thing, we declare Aij Aij_minusone and increase j.
139  * Case j=0 upon function entry also included, then Aij contains A_{i,j=0}.
140  */
141  uint32_t i;
142  gf2m diff, new_j_gray;
143  uint32_t Lik_pos_base;
144 
145  this->m_j++;
146 
147  new_j_gray = lex_to_gray(this->m_j);
148 
149  if(this->m_j & 1) /* half of the times */
150  {
151  Lik_pos_base = 0;
152  }
153  else if(this->m_j & 2) /* one quarter of the times */
154  {
155  Lik_pos_base = this->m_outer_summands;
156  }
157  else if( this->m_j & 4) /* one eighth of the times */
158  {
159  Lik_pos_base = this->m_outer_summands * 2;
160  }
161  else if( this->m_j & 8) /* one sixteenth of the times */
162  {
163  Lik_pos_base = this->m_outer_summands * 3;
164  }
165  else if( this->m_j & 16) /* ... */
166  {
167  Lik_pos_base = this->m_outer_summands * 4;
168  }
169  else
170  {
171  gf2m delta_offs = 5;
172  diff = this->m_j_gray ^ new_j_gray;
173  while(((static_cast<gf2m>(1) << delta_offs) & diff) == 0)
174  {
175  delta_offs++;
176 
177  }
178  Lik_pos_base = delta_offs * this->m_outer_summands;
179  }
180  this->m_j_gray = new_j_gray;
181 
182  i = 0;
183  for(; i < this->m_outer_summands; i++)
184  {
185  this->m_Aij[i] ^= this->m_Lik[Lik_pos_base + i];
186  }
187 
188  }
189 
190 void gf2m_decomp_rootfind_state::calc_LiK(const polyn_gf2m & sigma)
191  {
192  std::shared_ptr<GF2m_Field> sp_field = sigma.get_sp_field();
193  uint32_t i, k, d;
194  d = sigma.get_degree();
195  for(k = 0; k < sp_field->get_extension_degree(); k++)
196  {
197  uint32_t Lik_pos_base = k * this->m_outer_summands;
198  gf2m alpha_l_k_tt2_ttj[4];
199  alpha_l_k_tt2_ttj[0] = sp_field->gf_l_from_n(static_cast<gf2m>(1) << k);
200  alpha_l_k_tt2_ttj[1] = sp_field->gf_mul_rrr(alpha_l_k_tt2_ttj[0], alpha_l_k_tt2_ttj[0]);
201  alpha_l_k_tt2_ttj[2] = sp_field->gf_mul_rrr(alpha_l_k_tt2_ttj[1],alpha_l_k_tt2_ttj[1] );
202 
203  alpha_l_k_tt2_ttj[3] = sp_field->gf_mul_rrr(alpha_l_k_tt2_ttj[2], alpha_l_k_tt2_ttj[2]);
204  for(i = 0; i < this->m_outer_summands; i++)
205  {
206  uint32_t j;
207  uint32_t five_i = 5*i;
208  uint32_t Lik_pos = Lik_pos_base + i;
209  this->m_Lik[Lik_pos] = 0;
210  for(j = 0; j <= 3; j++)
211  {
212  gf2m f, x;
213  uint32_t f_ind = five_i + (static_cast<uint32_t>(1) << j);
214  if(f_ind > d)
215  {
216  break;
217  }
218  f = sigma.get_coef( f_ind);
219 
220  x = sp_field->gf_mul_zrz(alpha_l_k_tt2_ttj[j], f);
221  this->m_Lik[Lik_pos] ^= x;
222  }
223  }
224  }
225  }
226 
227 gf2m gf2m_decomp_rootfind_state::calc_Fxj_j_neq_0( const polyn_gf2m & sigma, gf2m j_gray)
228  {
229  //needs the A_{ij} to compute F(x)_j
230  gf2m sum = 0;
231  uint32_t i;
232  std::shared_ptr<GF2m_Field> sp_field = sigma.get_sp_field();
233  const gf2m jl_gray = sp_field->gf_l_from_n(j_gray);
234  gf2m xl_j_tt_5 = sp_field->gf_square_rr(jl_gray);
235  gf2m xl_gray_tt_3 = sp_field->gf_mul_rrr(xl_j_tt_5, jl_gray);
236  xl_j_tt_5 = sp_field->gf_mul_rrr(xl_j_tt_5, xl_gray_tt_3);
237 
238 
239  sum = sp_field->gf_mul_nrr(xl_gray_tt_3, this->m_sigma_3_l);
240  sum &= this->m_sigma_3_neq_0_mask;
241  /* here, we rely on compiler to be unable to optimize
242  * for the state->sigma_3_neq_0_mask value
243  */
244  /* treat i = 0 special: */
245  sum ^= this->m_Aij[0];
246  /* treat i = 1 special also */
247 
248  if(this->m_outer_summands > 1)
249  {
250  gf2m x;
251  x = sp_field->gf_mul_zrz(xl_j_tt_5, this->m_Aij[1]); /* x_j^{5i} A_i^j */
252  sum ^= x;
253  }
254 
255  gf2m xl_j_tt_5i = xl_j_tt_5;
256 
257  for(i = 2; i < this->m_outer_summands; i++)
258  {
259  gf2m x;
260  xl_j_tt_5i = sp_field->gf_mul_rrr(xl_j_tt_5i, xl_j_tt_5);
261  // now x_j_tt_5i lives up to its name
262  x = sp_field->gf_mul_zrz(xl_j_tt_5i, this->m_Aij[i]); /* x_j^{5i} A_i^(j) */
263  sum ^= x;
264  }
265  return sum;
266  }
267 
268 secure_vector<gf2m> gf2m_decomp_rootfind_state::find_roots(const polyn_gf2m & sigma)
269  {
270  const int sigma_degree = sigma.get_degree();
271  BOTAN_ASSERT(sigma_degree > 0, "Valid sigma");
272  secure_vector<gf2m> result(sigma_degree);
273  uint32_t root_pos = 0;
274 
275  this->calc_Ai_zero(sigma);
276  this->calc_LiK(sigma);
277  do
278  {
279  gf2m eval_result;
280  if(this->m_j_gray == 0)
281  {
282  eval_result = sigma.get_coef( 0);
283  }
284  else
285  {
286  eval_result = this->calc_Fxj_j_neq_0(sigma, this->m_j_gray);
287  }
288 
289  if(eval_result == 0)
290  {
291 
292  result[root_pos] = this->m_j_gray;
293  root_pos++;
294 
295  }
296  if(this->m_j + static_cast<uint32_t>(1) == this->get_code_length())
297  {
298  break;
299  }
300  this->calc_next_Aij();
301  }while(1);
302 
303  // side channel / fault attack countermeasure:
304  root_pos = patch_root_array(result.data(), result.size(), root_pos);
305  result.resize(root_pos);
306  return result;
307  }
308 
309 } // end anonymous namespace
310 
312  {
313  gf2m_decomp_rootfind_state state(polyn, code_length);
314  return state.find_roots(polyn);
315  }
316 
317 } // end namespace Botan
secure_vector< gf2m > m_Aij
secure_vector< gf2m > m_Lik
#define BOTAN_ASSERT(expr, assertion_made)
Definition: assert.h:29
gf2m lex_to_gray(gf2m lex)
uint16_t expand_mask_16bit(T tst)
uint16_t gf2m
Definition: gf2m_small_m.h:20
secure_vector< gf2m > find_roots_gf2m_decomp(const polyn_gf2m &polyn, uint32_t code_length)
Definition: alg_id.cpp:13
gf2m m_j
gf2m m_sigma_3_neq_0_mask
gf2m m_j_gray
uint32_t code_length
gf2m m_sigma_3_l
std::vector< T, secure_allocator< T > > secure_vector
Definition: secmem.h:88
uint32_t m_outer_summands