bn_kron.c 5.5 KB

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  1. /* crypto/bn/bn_kron.c */
  2. /* ====================================================================
  3. * Copyright (c) 1998-2000 The OpenSSL Project. All rights reserved.
  4. *
  5. * Redistribution and use in source and binary forms, with or without
  6. * modification, are permitted provided that the following conditions
  7. * are met:
  8. *
  9. * 1. Redistributions of source code must retain the above copyright
  10. * notice, this list of conditions and the following disclaimer.
  11. *
  12. * 2. Redistributions in binary form must reproduce the above copyright
  13. * notice, this list of conditions and the following disclaimer in
  14. * the documentation and/or other materials provided with the
  15. * distribution.
  16. *
  17. * 3. All advertising materials mentioning features or use of this
  18. * software must display the following acknowledgment:
  19. * "This product includes software developed by the OpenSSL Project
  20. * for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
  21. *
  22. * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
  23. * endorse or promote products derived from this software without
  24. * prior written permission. For written permission, please contact
  25. * openssl-core@openssl.org.
  26. *
  27. * 5. Products derived from this software may not be called "OpenSSL"
  28. * nor may "OpenSSL" appear in their names without prior written
  29. * permission of the OpenSSL Project.
  30. *
  31. * 6. Redistributions of any form whatsoever must retain the following
  32. * acknowledgment:
  33. * "This product includes software developed by the OpenSSL Project
  34. * for use in the OpenSSL Toolkit (http://www.openssl.org/)"
  35. *
  36. * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
  37. * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
  38. * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
  39. * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
  40. * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
  41. * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
  42. * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
  43. * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
  44. * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
  45. * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
  46. * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
  47. * OF THE POSSIBILITY OF SUCH DAMAGE.
  48. * ====================================================================
  49. *
  50. * This product includes cryptographic software written by Eric Young
  51. * (eay@cryptsoft.com). This product includes software written by Tim
  52. * Hudson (tjh@cryptsoft.com).
  53. *
  54. */
  55. #include "cryptlib.h"
  56. #include "bn_lcl.h"
  57. /* least significant word */
  58. #define BN_lsw(n) (((n)->top == 0) ? (BN_ULONG) 0 : (n)->d[0])
  59. /* Returns -2 for errors because both -1 and 0 are valid results. */
  60. int BN_kronecker(const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
  61. {
  62. int i;
  63. int ret = -2; /* avoid 'uninitialized' warning */
  64. int err = 0;
  65. BIGNUM *A, *B, *tmp;
  66. /*-
  67. * In 'tab', only odd-indexed entries are relevant:
  68. * For any odd BIGNUM n,
  69. * tab[BN_lsw(n) & 7]
  70. * is $(-1)^{(n^2-1)/8}$ (using TeX notation).
  71. * Note that the sign of n does not matter.
  72. */
  73. static const int tab[8] = { 0, 1, 0, -1, 0, -1, 0, 1 };
  74. bn_check_top(a);
  75. bn_check_top(b);
  76. BN_CTX_start(ctx);
  77. A = BN_CTX_get(ctx);
  78. B = BN_CTX_get(ctx);
  79. if (B == NULL)
  80. goto end;
  81. err = !BN_copy(A, a);
  82. if (err)
  83. goto end;
  84. err = !BN_copy(B, b);
  85. if (err)
  86. goto end;
  87. /*
  88. * Kronecker symbol, imlemented according to Henri Cohen,
  89. * "A Course in Computational Algebraic Number Theory"
  90. * (algorithm 1.4.10).
  91. */
  92. /* Cohen's step 1: */
  93. if (BN_is_zero(B)) {
  94. ret = BN_abs_is_word(A, 1);
  95. goto end;
  96. }
  97. /* Cohen's step 2: */
  98. if (!BN_is_odd(A) && !BN_is_odd(B)) {
  99. ret = 0;
  100. goto end;
  101. }
  102. /* now B is non-zero */
  103. i = 0;
  104. while (!BN_is_bit_set(B, i))
  105. i++;
  106. err = !BN_rshift(B, B, i);
  107. if (err)
  108. goto end;
  109. if (i & 1) {
  110. /* i is odd */
  111. /* (thus B was even, thus A must be odd!) */
  112. /* set 'ret' to $(-1)^{(A^2-1)/8}$ */
  113. ret = tab[BN_lsw(A) & 7];
  114. } else {
  115. /* i is even */
  116. ret = 1;
  117. }
  118. if (B->neg) {
  119. B->neg = 0;
  120. if (A->neg)
  121. ret = -ret;
  122. }
  123. /*
  124. * now B is positive and odd, so what remains to be done is to compute
  125. * the Jacobi symbol (A/B) and multiply it by 'ret'
  126. */
  127. while (1) {
  128. /* Cohen's step 3: */
  129. /* B is positive and odd */
  130. if (BN_is_zero(A)) {
  131. ret = BN_is_one(B) ? ret : 0;
  132. goto end;
  133. }
  134. /* now A is non-zero */
  135. i = 0;
  136. while (!BN_is_bit_set(A, i))
  137. i++;
  138. err = !BN_rshift(A, A, i);
  139. if (err)
  140. goto end;
  141. if (i & 1) {
  142. /* i is odd */
  143. /* multiply 'ret' by $(-1)^{(B^2-1)/8}$ */
  144. ret = ret * tab[BN_lsw(B) & 7];
  145. }
  146. /* Cohen's step 4: */
  147. /* multiply 'ret' by $(-1)^{(A-1)(B-1)/4}$ */
  148. if ((A->neg ? ~BN_lsw(A) : BN_lsw(A)) & BN_lsw(B) & 2)
  149. ret = -ret;
  150. /* (A, B) := (B mod |A|, |A|) */
  151. err = !BN_nnmod(B, B, A, ctx);
  152. if (err)
  153. goto end;
  154. tmp = A;
  155. A = B;
  156. B = tmp;
  157. tmp->neg = 0;
  158. }
  159. end:
  160. BN_CTX_end(ctx);
  161. if (err)
  162. return -2;
  163. else
  164. return ret;
  165. }