Botan  2.8.0
Crypto and TLS for C++11
polyn_gf2m.cpp
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1 /*
2  * (C) Copyright Projet SECRET, INRIA, Rocquencourt
3  * (C) Bhaskar Biswas and Nicolas Sendrier
4  *
5  * (C) 2014 cryptosource GmbH
6  * (C) 2014 Falko Strenzke fstrenzke@cryptosource.de
7  * (C) 2015 Jack Lloyd
8  *
9  * Botan is released under the Simplified BSD License (see license.txt)
10  *
11  */
12 
13 #include <botan/polyn_gf2m.h>
14 #include <botan/internal/code_based_util.h>
15 #include <botan/internal/bit_ops.h>
16 #include <botan/rng.h>
17 #include <botan/exceptn.h>
18 #include <botan/loadstor.h>
19 
20 namespace Botan {
21 
22 namespace {
23 
24 gf2m generate_gf2m_mask(gf2m a)
25  {
26  gf2m result = (a != 0);
27  return ~(result - 1);
28  }
29 
30 /**
31 * number of leading zeros
32 */
33 unsigned nlz_16bit(uint16_t x)
34  {
35  unsigned n;
36  if(x == 0) return 16;
37  n = 0;
38  if(x <= 0x00FF) {n = n + 8; x = x << 8;}
39  if(x <= 0x0FFF) {n = n + 4; x = x << 4;}
40  if(x <= 0x3FFF) {n = n + 2; x = x << 2;}
41  if(x <= 0x7FFF) {n = n + 1;}
42  return n;
43  }
44 }
45 
47  {
48  int i = this->coeff.size() - 1;
49  int result = 0;
50  uint32_t found_mask = 0;
51  uint32_t tracker_mask = 0xffff;
52  for( ; i >= 0; i--)
53  {
54  found_mask = expand_mask_16bit(this->coeff[i]);
55  result |= i & found_mask & tracker_mask;
56  // tracker mask shall become zero once found mask is set
57  // it shall remain zero from then on
58  tracker_mask = tracker_mask & ~found_mask;
59  }
60  const_cast<polyn_gf2m*>(this)->m_deg = result;
61  return result;
62  }
63 
65  {
66  uint8_t b[2];
67  rng.randomize(b, sizeof(b));
68  return make_uint16(b[1], b[0]);
69  }
70 
72  {
73  if(code_length == 0)
74  {
75  throw Invalid_Argument("random_code_element() was supplied a code length of zero");
76  }
77  const unsigned nlz = nlz_16bit(code_length-1);
78  const gf2m mask = (1 << (16-nlz)) -1;
79 
80  gf2m result;
81 
82  do
83  {
84  result = random_gf2m(rng);
85  result &= mask;
86  } while(result >= code_length); // rejection sampling
87 
88  return result;
89  }
90 
92  :m_deg(other.m_deg),
93  coeff(other.coeff),
94  msp_field(other.msp_field)
95  { }
96 
97 polyn_gf2m::polyn_gf2m( int d, std::shared_ptr<GF2m_Field> sp_field)
98  :m_deg(-1),
99  coeff(d+1),
100  msp_field(sp_field)
101  {
102  }
103 
104 std::string polyn_gf2m::to_string() const
105  {
106  int d = get_degree();
107  std::string result;
108  for(int i = 0; i <= d; i ++)
109  {
110  result += std::to_string(this->coeff[i]);
111  if(i != d)
112  {
113  result += ", ";
114  }
115  }
116  return result;
117  }
118 /**
119 * doesn't save coefficients:
120 */
121 void polyn_gf2m::realloc(uint32_t new_size)
122  {
123  this->coeff = secure_vector<gf2m>(new_size);
124  }
125 
126 polyn_gf2m::polyn_gf2m(const uint8_t* mem, uint32_t mem_len, std::shared_ptr<GF2m_Field> sp_field)
127  :msp_field(sp_field)
128  {
129  if(mem_len % sizeof(gf2m))
130  {
131  throw Botan::Decoding_Error("illegal length of memory to decode ");
132  }
133 
134  uint32_t size = (mem_len / sizeof(this->coeff[0])) ;
135  this->coeff = secure_vector<gf2m>(size);
136  this->m_deg = -1;
137  for(uint32_t i = 0; i < size; i++)
138  {
139  this->coeff[i] = decode_gf2m(mem);
140  mem += sizeof(this->coeff[0]);
141  }
142  for(uint32_t i = 0; i < size; i++)
143  {
144  if(this->coeff[i] >= (1 << sp_field->get_extension_degree()))
145  {
146  throw Botan::Decoding_Error("error decoding polynomial");
147  }
148  }
149  this->get_degree();
150  }
151 
152 
153 polyn_gf2m::polyn_gf2m( std::shared_ptr<GF2m_Field> sp_field )
154  : m_deg(-1),
155  coeff(1),
156  msp_field(sp_field)
157  {}
158 
159 polyn_gf2m::polyn_gf2m(int degree, const unsigned char* mem, uint32_t mem_byte_len, std::shared_ptr<GF2m_Field> sp_field)
160  :msp_field(sp_field)
161  {
162  uint32_t j, k, l;
163  gf2m a;
164  uint32_t polyn_size;
165  polyn_size = degree + 1;
166  if(polyn_size * sp_field->get_extension_degree() > 8 * mem_byte_len)
167  {
168  throw Botan::Decoding_Error("memory vector for polynomial has wrong size");
169  }
170  this->coeff = secure_vector<gf2m>(degree+1);
171  gf2m ext_deg = this->msp_field->get_extension_degree();
172  for (l = 0; l < polyn_size; l++)
173  {
174  k = (l * ext_deg) / 8;
175 
176  j = (l * ext_deg) % 8;
177  a = mem[k] >> j;
178  if (j + ext_deg > 8)
179  {
180  a ^= mem[k + 1] << (8- j);
181  }
182  if(j + ext_deg > 16)
183  {
184  a ^= mem[k + 2] << (16- j);
185  }
186  a &= ((1 << ext_deg) - 1);
187  (*this).set_coef( l, a);
188  }
189 
190  this->get_degree();
191  }
192 
193 #if 0
194 void polyn_gf2m::encode(uint32_t min_numo_coeffs, uint8_t* mem, uint32_t mem_len) const
195  {
196  uint32_t i;
197  uint32_t numo_coeffs, needed_size;
198  this->get_degree();
199  numo_coeffs = (min_numo_coeffs > static_cast<uint32_t>(this->m_deg+1)) ? min_numo_coeffs : this->m_deg+1;
200  needed_size = sizeof(this->coeff[0]) * numo_coeffs;
201  if(mem_len < needed_size)
202  {
203  Invalid_Argument("provided memory too small to encode polynomial");
204  }
205 
206  for(i = 0; i < numo_coeffs; i++)
207  {
208  gf2m to_enc;
209  if(i >= static_cast<uint32_t>(this->m_deg+1))
210  {
211  /* encode a zero */
212  to_enc = 0;
213  }
214  else
215  {
216  to_enc = this->coeff[i];
217  }
218  mem += encode_gf2m(to_enc, mem);
219  }
220  }
221 #endif
222 
223 
225  {
226  clear_mem(&this->coeff[0], this->coeff.size());
227  this->m_deg = -1;
228  }
229 
231  {
232  int d = this->coeff.size() - 1;
233  while ((d >= 0) && (this->coeff[d] == 0))
234  --d;
235  const_cast<polyn_gf2m*>(this)->m_deg = d;
236  return d;
237  }
238 
239 
240 static gf2m eval_aux(const gf2m * /*restrict*/ coeff, gf2m a, int d, std::shared_ptr<GF2m_Field> sp_field)
241  {
242  gf2m b;
243  b = coeff[d--];
244  for (; d >= 0; --d)
245  if (b != 0)
246  {
247  b = sp_field->gf_mul(b, a) ^ coeff[d];
248  }
249  else
250  {
251  b = coeff[d];
252  }
253  return b;
254  }
255 
257  {
258  return eval_aux(&this->coeff[0], a, this->m_deg, this->msp_field);
259  }
260 
261 
262 // p will contain it's remainder modulo g
263 void polyn_gf2m::remainder(polyn_gf2m &p, const polyn_gf2m & g)
264  {
265  int i, j, d;
266  std::shared_ptr<GF2m_Field> msp_field = g.msp_field;
267  d = p.get_degree() - g.get_degree();
268  if (d >= 0) {
269  gf2m la = msp_field->gf_inv_rn(g.get_lead_coef());
270 
271  const int p_degree = p.get_degree();
272 
273  BOTAN_ASSERT(p_degree > 0, "Valid polynomial");
274 
275  for (i = p_degree; d >= 0; --i, --d) {
276  if (p[i] != 0) {
277  gf2m lb = msp_field->gf_mul_rrn(la, p[i]);
278  for (j = 0; j < g.get_degree(); ++j)
279  {
280  p[j+d] ^= msp_field->gf_mul_zrz(lb, g[j]);
281  }
282  (*&p).set_coef( i, 0);
283  }
284  }
285  p.set_degree( g.get_degree() - 1);
286  while ((p.get_degree() >= 0) && (p[p.get_degree()] == 0))
287  p.set_degree( p.get_degree() - 1);
288  }
289  }
290 
291 std::vector<polyn_gf2m> polyn_gf2m::sqmod_init(const polyn_gf2m & g)
292  {
293  std::vector<polyn_gf2m> sq;
294  const int signed_deg = g.get_degree();
295  if(signed_deg <= 0)
296  throw Invalid_Argument("cannot compute sqmod for such low degree");
297 
298  const uint32_t d = static_cast<uint32_t>(signed_deg);
299  uint32_t t = g.m_deg;
300  // create t zero polynomials
301  uint32_t i;
302  for (i = 0; i < t; ++i)
303  {
304  sq.push_back(polyn_gf2m(t+1, g.get_sp_field()));
305  }
306  for (i = 0; i < d / 2; ++i)
307  {
308  sq[i].set_degree( 2 * i);
309  (*&sq[i]).set_coef( 2 * i, 1);
310  }
311 
312  for (; i < d; ++i)
313  {
314  clear_mem(&sq[i].coeff[0], 2);
315  copy_mem(&sq[i].coeff[0] + 2, &sq[i - 1].coeff[0], d);
316  sq[i].set_degree( sq[i - 1].get_degree() + 2);
317  polyn_gf2m::remainder(sq[i], g);
318  }
319  return sq;
320  }
321 
322 /*Modulo p square of a certain polynomial g, sq[] contains the square
323 Modulo g of the base canonical polynomials of degree < d, where d is
324 the degree of G. The table sq[] will be calculated by polyn_gf2m_sqmod_init*/
325 polyn_gf2m polyn_gf2m::sqmod( const std::vector<polyn_gf2m> & sq, int d)
326  {
327  int i, j;
328  gf2m la;
329  std::shared_ptr<GF2m_Field> sp_field = this->msp_field;
330 
331  polyn_gf2m result(d - 1, sp_field);
332  // terms of low degree
333  for (i = 0; i < d / 2; ++i)
334  {
335  (*&result).set_coef( i * 2, sp_field->gf_square((*this)[i]));
336  }
337 
338  // terms of high degree
339  for (; i < d; ++i)
340  {
341  gf2m lpi = (*this)[i];
342  if (lpi != 0)
343  {
344  lpi = sp_field->gf_log(lpi);
345  la = sp_field->gf_mul_rrr(lpi, lpi);
346  for (j = 0; j < d; ++j)
347  {
348  result[j] ^= sp_field->gf_mul_zrz(la, sq[i][j]);
349  }
350  }
351  }
352 
353  // Update degre
354  result.set_degree( d - 1);
355  while ((result.get_degree() >= 0) && (result[result.get_degree()] == 0))
356  result.set_degree( result.get_degree() - 1);
357  return result;
358  }
359 
360 
361 // destructive
362 polyn_gf2m polyn_gf2m::gcd_aux(polyn_gf2m& p1, polyn_gf2m& p2)
363  {
364  if (p2.get_degree() == -1)
365  return p1;
366  else {
367  polyn_gf2m::remainder(p1, p2);
368  return polyn_gf2m::gcd_aux(p2, p1);
369  }
370  }
371 
372 
373 polyn_gf2m polyn_gf2m::gcd(polyn_gf2m const& p1, polyn_gf2m const& p2)
374  {
375  polyn_gf2m a(p1);
376  polyn_gf2m b(p2);
377  if (a.get_degree() < b.get_degree())
378  {
379  return polyn_gf2m(polyn_gf2m::gcd_aux(b, a));
380  }
381  else
382  {
383  return polyn_gf2m(polyn_gf2m::gcd_aux(a, b));
384  }
385  }
386 
387 
388 
389 
390 
391 // Returns the degree of the smallest factor
392 void polyn_gf2m::degppf(const polyn_gf2m & g, int* p_result)
393  {
394  int i, d;
395  polyn_gf2m s(g.get_sp_field());
396 
397  d = g.get_degree();
398  std::vector<polyn_gf2m> u = polyn_gf2m::sqmod_init(g);
399 
400  polyn_gf2m p( d - 1, g.msp_field);
401 
402  p.set_degree( 1);
403  (*&p).set_coef( 1, 1);
404  (*p_result) = d;
405  for (i = 1; i <= (d / 2) * g.msp_field->get_extension_degree(); ++i)
406  {
407  polyn_gf2m r = p.sqmod(u, d);
408  if ((i % g.msp_field->get_extension_degree()) == 0)
409  {
410  r[1] ^= 1;
411  r.get_degree(); // The degree may change
412  s = polyn_gf2m::gcd( g, r);
413 
414  if (s.get_degree() > 0)
415  {
416  (*p_result) = i / g.msp_field->get_extension_degree();
417  break;
418  }
419  r[1] ^= 1;
420  r.get_degree(); // The degree may change
421  }
422  // No need for the exchange s
423  s = p;
424  p = r;
425  r = s;
426  }
427 
428 
429  }
430 
431 void polyn_gf2m::patchup_deg_secure( uint32_t trgt_deg, volatile gf2m patch_elem)
432  {
433  uint32_t i;
434  if(this->coeff.size() < trgt_deg)
435  {
436  return;
437  }
438  for(i = 0; i < this->coeff.size(); i++)
439  {
440  uint32_t equal, equal_mask;
441  this->coeff[i] |= patch_elem;
442  equal = (i == trgt_deg);
443  equal_mask = expand_mask_16bit(equal);
444  patch_elem &= ~equal_mask;
445  }
446  this->calc_degree_secure();
447  }
448 // We suppose m_deg(g) >= m_deg(p)
449 // v is the problem
450 std::pair<polyn_gf2m, polyn_gf2m> polyn_gf2m::eea_with_coefficients( const polyn_gf2m & p, const polyn_gf2m & g, int break_deg)
451  {
452 
453  std::shared_ptr<GF2m_Field> msp_field = g.msp_field;
454  int i, j, dr, du, delta;
455  gf2m a;
456  polyn_gf2m aux;
457 
458  // initialisation of the local variables
459  // r0 <- g, r1 <- p, u0 <- 0, u1 <- 1
460  dr = g.get_degree();
461 
462  BOTAN_ASSERT(dr > 3, "Valid polynomial");
463 
464  polyn_gf2m r0(dr, g.msp_field);
465  polyn_gf2m r1(dr - 1, g.msp_field);
466  polyn_gf2m u0(dr - 1, g.msp_field);
467  polyn_gf2m u1(dr - 1, g.msp_field);
468 
469  r0 = g;
470  r1 = p;
471  u0.set_to_zero();
472  u1.set_to_zero();
473  (*&u1).set_coef( 0, 1);
474  u1.set_degree( 0);
475 
476 
477  // invariants:
478  // r1 = u1 * p + v1 * g
479  // r0 = u0 * p + v0 * g
480  // and m_deg(u1) = m_deg(g) - m_deg(r0)
481  // It stops when m_deg (r1) <t (m_deg (r0)> = t)
482  // And therefore m_deg (u1) = m_deg (g) - m_deg (r0) <m_deg (g) - break_deg
483  du = 0;
484  dr = r1.get_degree();
485  delta = r0.get_degree() - dr;
486 
487 
488  while (dr >= break_deg)
489  {
490 
491  for (j = delta; j >= 0; --j)
492  {
493  a = msp_field->gf_div(r0[dr + j], r1[dr]);
494  if (a != 0)
495  {
496  gf2m la = msp_field->gf_log(a);
497  // u0(z) <- u0(z) + a * u1(z) * z^j
498  for (i = 0; i <= du; ++i)
499  {
500  u0[i + j] ^= msp_field->gf_mul_zrz(la, u1[i]);
501  }
502  // r0(z) <- r0(z) + a * r1(z) * z^j
503  for (i = 0; i <= dr; ++i)
504  {
505  r0[i + j] ^= msp_field->gf_mul_zrz(la, r1[i]);
506  }
507  }
508  } // end loop over j
509 
510  if(break_deg != 1) /* key eq. solving */
511  {
512  /* [ssms_icisc09] Countermeasure
513  * d_break from paper equals break_deg - 1
514  * */
515 
516  volatile gf2m fake_elem = 0x01;
517  volatile gf2m cond1, cond2;
518  int trgt_deg = r1.get_degree() - 1;
519  r0.calc_degree_secure();
520  u0.calc_degree_secure();
521  if(!(g.get_degree() % 2))
522  {
523  /* t even */
524  cond1 = r0.get_degree() < break_deg - 1;
525  }
526  else
527  {
528  /* t odd */
529  cond1 = r0.get_degree() < break_deg;
530  cond2 = u0.get_degree() < break_deg - 1;
531  cond1 &= cond2;
532  }
533  /* expand cond1 to a full mask */
534  gf2m mask = generate_gf2m_mask(cond1);
535  fake_elem &= mask;
536  r0.patchup_deg_secure(trgt_deg, fake_elem);
537  }
538  if(break_deg == 1) /* syndrome inversion */
539  {
540  volatile gf2m fake_elem = 0x00;
541  volatile uint32_t trgt_deg = 0;
542  r0.calc_degree_secure();
543  u0.calc_degree_secure();
544  /**
545  * countermeasure against the low weight attacks for w=4, w=6 and w=8.
546  * Higher values are not covered since for w=8 we already have a
547  * probability for a positive of 1/n^3 from random ciphertexts with the
548  * given weight. For w = 10 it would be 1/n^4 and so on. Thus attacks
549  * based on such high values of w are considered impractical.
550  *
551  * The outer test for the degree of u ( Omega in the paper ) needs not to
552  * be disguised. Each of the three is performed at most once per EEA
553  * (syndrome inversion) execution, the attacker knows this already when
554  * preparing the ciphertext with the given weight. Inside these three
555  * cases however, we must use timing neutral (branch free) operations to
556  * implement the condition detection and the counteractions.
557  *
558  */
559  if(u0.get_degree() == 4)
560  {
561  uint32_t mask = 0;
562  /**
563  * Condition that the EEA would break now
564  */
565  int cond_r = r0.get_degree() == 0;
566  /**
567  * Now come the conditions for all odd coefficients of this sigma
568  * candiate. If they are all fulfilled, then we know that we have a low
569  * weight error vector, since the key-equation solving EEA is skipped if
570  * the degree of tau^2 is low (=m_deg(u0)) and all its odd cofficients are
571  * zero (they would cause "full-length" contributions from the square
572  * root computation).
573  */
574  // Condition for the coefficient to Y to be cancelled out by the
575  // addition of Y before the square root computation:
576  int cond_u1 = msp_field->gf_mul(u0.coeff[1], msp_field->gf_inv(r0.coeff[0])) == 1;
577 
578  // Condition sigma_3 = 0:
579  int cond_u3 = u0.coeff[3] == 0;
580  // combine the conditions:
581  cond_r &= (cond_u1 & cond_u3);
582  // mask generation:
583  mask = expand_mask_16bit(cond_r);
584  trgt_deg = 2 & mask;
585  fake_elem = 1 & mask;
586  }
587  else if(u0.get_degree() == 6)
588  {
589  uint32_t mask = 0;
590  int cond_r= r0.get_degree() == 0;
591  int cond_u1 = msp_field->gf_mul(u0.coeff[1], msp_field->gf_inv(r0.coeff[0])) == 1;
592  int cond_u3 = u0.coeff[3] == 0;
593 
594  int cond_u5 = u0.coeff[5] == 0;
595 
596  cond_r &= (cond_u1 & cond_u3 & cond_u5);
597  mask = expand_mask_16bit(cond_r);
598  trgt_deg = 4 & mask;
599  fake_elem = 1 & mask;
600  }
601  else if(u0.get_degree() == 8)
602  {
603  uint32_t mask = 0;
604  int cond_r= r0.get_degree() == 0;
605  int cond_u1 = msp_field->gf_mul(u0[1], msp_field->gf_inv(r0[0])) == 1;
606  int cond_u3 = u0.coeff[3] == 0;
607 
608  int cond_u5 = u0.coeff[5] == 0;
609 
610  int cond_u7 = u0.coeff[7] == 0;
611 
612  cond_r &= (cond_u1 & cond_u3 & cond_u5 & cond_u7);
613  mask = expand_mask_16bit(cond_r);
614  trgt_deg = 6 & mask;
615  fake_elem = 1 & mask;
616  }
617  r0.patchup_deg_secure(trgt_deg, fake_elem);
618  }
619  // exchange
620  aux = r0; r0 = r1; r1 = aux;
621  aux = u0; u0 = u1; u1 = aux;
622 
623  du = du + delta;
624  delta = 1;
625  while (r1[dr - delta] == 0)
626  {
627  delta++;
628  }
629 
630 
631  dr -= delta;
632  } /* end while loop (dr >= break_deg) */
633 
634 
635  u1.set_degree( du);
636  r1.set_degree( dr);
637  //return u1 and r1;
638  return std::make_pair(u1,r1); // coefficients u,v
639  }
640 
641 polyn_gf2m::polyn_gf2m(int t, Botan::RandomNumberGenerator& rng, std::shared_ptr<GF2m_Field> sp_field)
642  :m_deg(t),
643  coeff(t+1),
644  msp_field(sp_field)
645  {
646  (*this).set_coef( t, 1);
647  int degree = 0;
648  do
649  {
650  for (int i = 0; i < t; ++i)
651  {
652  (*this).set_coef( i, random_code_element(sp_field->get_cardinality(), rng));
653  }
654  polyn_gf2m::degppf(*this, &degree);
655  }
656  while (degree < t);
657  }
658 
659 
660 void polyn_gf2m::poly_shiftmod( const polyn_gf2m & g)
661  {
662  if(g.get_degree() <= 1)
663  {
664  throw Invalid_Argument("shiftmod cannot be called on polynomials of degree 1 or less");
665  }
666  std::shared_ptr<GF2m_Field> field = g.msp_field;
667 
668  int t = g.get_degree();
669  gf2m a = field->gf_div(this->coeff[t-1], g.coeff[t]);
670  for (int i = t - 1; i > 0; --i)
671  {
672  this->coeff[i] = this->coeff[i - 1] ^ this->msp_field->gf_mul(a, g.coeff[i]);
673  }
674  this->coeff[0] = field->gf_mul(a, g.coeff[0]);
675  }
676 
677 std::vector<polyn_gf2m> polyn_gf2m::sqrt_mod_init(const polyn_gf2m & g)
678  {
679  uint32_t i, t;
680  uint32_t nb_polyn_sqrt_mat;
681  std::shared_ptr<GF2m_Field> msp_field = g.msp_field;
682  std::vector<polyn_gf2m> result;
683  t = g.get_degree();
684  nb_polyn_sqrt_mat = t/2;
685 
686  std::vector<polyn_gf2m> sq_aux = polyn_gf2m::sqmod_init(g);
687 
688 
689  polyn_gf2m p( t - 1, g.get_sp_field());
690  p.set_degree( 1);
691 
692  (*&p).set_coef( 1, 1);
693  // q(z) = 0, p(z) = z
694  for (i = 0; i < t * msp_field->get_extension_degree() - 1; ++i)
695  {
696  // q(z) <- p(z)^2 mod g(z)
697  polyn_gf2m q = p.sqmod(sq_aux, t);
698  // q(z) <-> p(z)
699  polyn_gf2m aux = q;
700  q = p;
701  p = aux;
702  }
703  // p(z) = z^(2^(tm-1)) mod g(z) = sqrt(z) mod g(z)
704 
705  for (i = 0; i < nb_polyn_sqrt_mat; ++i)
706  {
707  result.push_back(polyn_gf2m(t - 1, g.get_sp_field()));
708  }
709 
710  result[0] = p;
711  result[0].get_degree();
712  for(i = 1; i < nb_polyn_sqrt_mat; i++)
713  {
714  result[i] = result[i - 1];
715  result[i].poly_shiftmod(g),
716  result[i].get_degree();
717  }
718 
719  return result;
720  }
721 
722 std::vector<polyn_gf2m> syndrome_init(polyn_gf2m const& generator, std::vector<gf2m> const& support, int n)
723  {
724  int i,j,t;
725  gf2m a;
726 
727 
728  std::shared_ptr<GF2m_Field> msp_field = generator.msp_field;
729 
730  std::vector<polyn_gf2m> result;
731  t = generator.get_degree();
732 
733  //g(z)=g_t+g_(t-1).z^(t-1)+......+g_1.z+g_0
734  //f(z)=f_(t-1).z^(t-1)+......+f_1.z+f_0
735 
736  for(j=0;j<n;j++)
737  {
738  result.push_back(polyn_gf2m( t-1, msp_field));
739 
740  (*&result[j]).set_coef(t-1,1);
741  for(i=t-2;i>=0;i--)
742  {
743  (*&result[j]).set_coef(i, (generator)[i+1] ^
744  msp_field->gf_mul(lex_to_gray(support[j]),result[j][i+1]));
745  }
746  a = ((generator)[0] ^ msp_field->gf_mul(lex_to_gray(support[j]),result[j][0]));
747  for(i=0;i<t;i++)
748  {
749  (*&result[j]).set_coef(i, msp_field->gf_div(result[j][i],a));
750  }
751  }
752  return result;
753  }
754 
755 polyn_gf2m::polyn_gf2m(const secure_vector<uint8_t>& encoded, std::shared_ptr<GF2m_Field> sp_field )
756  :msp_field(sp_field)
757  {
758  if(encoded.size() % 2)
759  {
760  throw Decoding_Error("encoded polynomial has odd length");
761  }
762  for(uint32_t i = 0; i < encoded.size(); i += 2)
763  {
764  gf2m el = (encoded[i] << 8) | encoded[i + 1];
765  coeff.push_back(el);
766  }
767  get_degree();
768 
769  }
771  {
772  secure_vector<uint8_t> result;
773 
774  if(m_deg < 1)
775  {
776  result.push_back(0);
777  result.push_back(0);
778  return result;
779  }
780 
781  uint32_t len = m_deg+1;
782  for(unsigned i = 0; i < len; i++)
783  {
784  // "big endian" encoding of the GF(2^m) elements
785  result.push_back(coeff[i] >> 8);
786  result.push_back(coeff[i]);
787  }
788  return result;
789  }
790 
792  {
793  std::swap(this->m_deg, other.m_deg);
794  std::swap(this->msp_field, other.msp_field);
795  std::swap(this->coeff, other.coeff);
796  }
797 
798 bool polyn_gf2m::operator==(const polyn_gf2m & other) const
799  {
800  if(m_deg != other.m_deg || coeff != other.coeff)
801  {
802  return false;
803  }
804  return true;
805  }
806 
807 }
std::shared_ptr< GF2m_Field > msp_field
Definition: polyn_gf2m.h:155
int get_degree() const
Definition: polyn_gf2m.cpp:230
virtual void randomize(uint8_t output[], size_t length)=0
void clear_mem(T *ptr, size_t n)
Definition: mem_ops.h:97
gf2m decode_gf2m(const uint8_t *mem)
int calc_degree_secure() const
Definition: polyn_gf2m.cpp:46
gf2m get_lead_coef() const
Definition: polyn_gf2m.h:81
bool operator==(const polyn_gf2m &other) const
Definition: polyn_gf2m.cpp:798
void set_coef(uint32_t i, gf2m v)
Definition: polyn_gf2m.h:85
std::string to_string(const BER_Object &obj)
Definition: asn1_obj.cpp:210
polyn_gf2m sqmod(const std::vector< polyn_gf2m > &sq, int d)
Definition: polyn_gf2m.cpp:325
void degppf(const polyn_gf2m &g, int *p_result)
Definition: polyn_gf2m.cpp:392
static std::vector< polyn_gf2m > sqrt_mod_init(const polyn_gf2m &g)
Definition: polyn_gf2m.cpp:677
#define BOTAN_ASSERT(expr, assertion_made)
Definition: assert.h:55
void patchup_deg_secure(uint32_t trgt_deg, volatile gf2m patch_elem)
Definition: polyn_gf2m.cpp:431
gf2m lex_to_gray(gf2m lex)
uint16_t expand_mask_16bit(T tst)
uint16_t gf2m
Definition: gf2m_small_m.h:20
void copy_mem(T *out, const T *in, size_t n)
Definition: mem_ops.h:108
Definition: alg_id.cpp:13
static std::vector< polyn_gf2m > sqmod_init(const polyn_gf2m &g)
Definition: polyn_gf2m.cpp:291
secure_vector< gf2m > coeff
Definition: polyn_gf2m.h:152
gf2m random_code_element(unsigned code_length, RandomNumberGenerator &rng)
Definition: polyn_gf2m.cpp:71
uint32_t encode_gf2m(gf2m to_enc, uint8_t *mem)
uint32_t code_length
std::vector< polyn_gf2m > syndrome_init(polyn_gf2m const &generator, std::vector< gf2m > const &support, int n)
Definition: polyn_gf2m.cpp:722
static std::pair< polyn_gf2m, polyn_gf2m > eea_with_coefficients(const polyn_gf2m &p, const polyn_gf2m &g, int break_deg)
Definition: polyn_gf2m.cpp:450
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Definition: loadstor.h:52
std::vector< T, secure_allocator< T > > secure_vector
Definition: secmem.h:88
std::shared_ptr< GF2m_Field > get_sp_field() const
Definition: polyn_gf2m.h:74
secure_vector< uint8_t > encode() const
Definition: polyn_gf2m.cpp:770
gf2m random_gf2m(RandomNumberGenerator &rng)
Definition: polyn_gf2m.cpp:64
std::string to_string() const
Definition: polyn_gf2m.cpp:104
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Definition: polyn_gf2m.cpp:791
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Definition: polyn_gf2m.cpp:256