API tools faq
paste
Advertisement
Guest User

Untitled

a guest
Dec 9th, 2016
73
0
Never
Add comment
Not a member of Pastebin yet? Sign Up, it unlocks many cool features!
text 9.01 KB | None | 0 0
raw download clone embed print report
  1. {
  2. "cells": [
  3. {
  4. "cell_type": "code",
  5. "execution_count": 1,
  6. "metadata": {
  7. "collapsed": true
  8. },
  9. "outputs": [],
  10. "source": [
  11. "mat1 = 0x8f7011ee\n",
  12. "mat2 = 0xfc78ff1f\n",
  13. "tmat = 0x3793fdff"
  14. ]
  15. },
  16. {
  17. "cell_type": "code",
  18. "execution_count": 2,
  19. "metadata": {
  20. "collapsed": false
  21. },
  22. "outputs": [],
  23. "source": [
  24. "F2 = GF(2)\n",
  25. "\n",
  26. "def int_to_f2(x):\n",
  27. " return vector([F2((x >> i) & 1) for i in range(32)])\n",
  28. "\n",
  29. "def ints_to_f2(xs):\n",
  30. " return vector([F2((xs[floor(i / 32)] >> (i % 32)) & 1) for i in range(32*len(xs))])\n",
  31. "\n",
  32. "def f2_to_int(vec):\n",
  33. " x = 0\n",
  34. " for i in range(32):\n",
  35. " x |= Integer(vec[i]) << i\n",
  36. " return x\n",
  37. "\n",
  38. "def f2_to_ints(vec):\n",
  39. " return [f2_to_int(vec[i*32:i*32+32]) for i in range(floor(len(vec) / 32))]"
  40. ]
  41. },
  42. {
  43. "cell_type": "code",
  44. "execution_count": 3,
  45. "metadata": {
  46. "collapsed": false
  47. },
  48. "outputs": [],
  49. "source": [
  50. "def join_matrix_yoko(mats):\n",
  51. " m = mats[0].nrows()\n",
  52. " n = mats[0].ncols()\n",
  53. " return matrix([[mats[floor(j / n)][i, j % n] for j in range(n*len(mats))] for i in range(m)])\n",
  54. "\n",
  55. "def join_matrix_tate(mats):\n",
  56. " m = mats[0].nrows()\n",
  57. " n = mats[0].ncols()\n",
  58. " return matrix([[mats[floor(i / m)][i % m, j] for j in range(n)] for i in range(m*len(mats))])"
  59. ]
  60. },
  61. {
  62. "cell_type": "code",
  63. "execution_count": 4,
  64. "metadata": {
  65. "collapsed": false
  66. },
  67. "outputs": [],
  68. "source": [
  69. "def elem_matrix(i):\n",
  70. " mats = [Mat(GF(2), 32, 32).zero() for j in range(4)]\n",
  71. " mats[i] = Mat(GF(2), 32, 32).identity_matrix()\n",
  72. " return join_matrix_yoko(mats)\n",
  73. "\n",
  74. "def xi(x):\n",
  75. " if x:\n",
  76. " return 1\n",
  77. " else:\n",
  78. " return 0\n",
  79. "\n",
  80. "def rshift_matrix(k):\n",
  81. " return matrix([[F2(xi(j - i == k)) for j in range(32)] for i in range(32)])\n",
  82. "\n",
  83. "def lshift_matrix(k):\n",
  84. " return rshift_matrix(-k)\n",
  85. "\n",
  86. "def constant_matrix(a):\n",
  87. " m = [[F2(0) for j in range(32)] for i in range(32)]\n",
  88. " for i in range(32):\n",
  89. " m[i][0] = a[i]\n",
  90. " return matrix(m)\n",
  91. "\n",
  92. "def mask_matrix(a):\n",
  93. " return matrix([[F2(a[i] * xi(i == j)) for j in range(32)] for i in range(32)])"
  94. ]
  95. },
  96. {
  97. "cell_type": "code",
  98. "execution_count": 5,
  99. "metadata": {
  100. "collapsed": false
  101. },
  102. "outputs": [],
  103. "source": [
  104. "def temper_matrix():\n",
  105. " t0 = elem_matrix(3)\n",
  106. " t1 = elem_matrix(0) + rshift_matrix(8) * elem_matrix(2)\n",
  107. " return t0 + t1 + constant_matrix(int_to_f2(tmat)) * t1\n",
  108. "\n",
  109. "temper = temper_matrix()"
  110. ]
  111. },
  112. {
  113. "cell_type": "code",
  114. "execution_count": 6,
  115. "metadata": {
  116. "collapsed": false
  117. },
  118. "outputs": [],
  119. "source": [
  120. "def next_state_matrix():\n",
  121. " y = elem_matrix(3)\n",
  122. " x = mask_matrix(int_to_f2(0x7fffffff)) * elem_matrix(0) + elem_matrix(1) + elem_matrix(2)\n",
  123. " x += lshift_matrix(1) * x\n",
  124. " y += rshift_matrix(1) * y + x\n",
  125. " st0 = elem_matrix(1) + constant_matrix(int_to_f2(mat1)) * y\n",
  126. " st1 = elem_matrix(2) + constant_matrix(int_to_f2(mat2)) * y\n",
  127. " st2 = x + lshift_matrix(10) * y\n",
  128. " st3 = y\n",
  129. " return join_matrix_tate([st0, st1, st2, st3])\n",
  130. "\n",
  131. "next_state = next_state_matrix()"
  132. ]
  133. },
  134. {
  135. "cell_type": "code",
  136. "execution_count": 7,
  137. "metadata": {
  138. "collapsed": true
  139. },
  140. "outputs": [],
  141. "source": [
  142. "def genrand_matrix():\n",
  143. " r0 = temper_matrix()\n",
  144. " r1 = temper_matrix() * next_state_matrix()\n",
  145. " r2 = temper_matrix() * next_state_matrix() * next_state_matrix()\n",
  146. " r3 = temper_matrix() * next_state_matrix() * next_state_matrix() * next_state_matrix()\n",
  147. " return join_matrix_tate([r0, r1, r2, r3])\n",
  148. "\n",
  149. "genrand = genrand_matrix()"
  150. ]
  151. },
  152. {
  153. "cell_type": "code",
  154. "execution_count": 8,
  155. "metadata": {
  156. "collapsed": false
  157. },
  158. "outputs": [
  159. {
  160. "data": {
  161. "text/plain": [
  162. "['5740a11a', '3cfe1de3', 'a5083b98', '14ef46dc']"
  163. ]
  164. },
  165. "execution_count": 8,
  166. "metadata": {},
  167. "output_type": "execute_result"
  168. }
  169. ],
  170. "source": [
  171. "[x.str(16) for x in f2_to_ints(next_state * ints_to_f2([0x63B07A71, 0x5740A11A, 0x3CFE1DE3, 0x08A80987]))]"
  172. ]
  173. },
  174. {
  175. "cell_type": "code",
  176. "execution_count": 9,
  177. "metadata": {
  178. "collapsed": false
  179. },
  180. "outputs": [
  181. {
  182. "ename": "ValueError",
  183. "evalue": "matrix equation has no solutions",
  184. "output_type": "error",
  185. "traceback": [
  186. "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
  187. "\u001b[0;31mValueError\u001b[0m Traceback (most recent call last)",
  188. "\u001b[0;32m<ipython-input-9-1043d1e321cd>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mgenrand\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msolve_right\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mints_to_f2\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0xd86e392e\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0xddb8564b\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0x44559e7f\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0x74a35ddf\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
  189. "\u001b[0;32m/projects/sage/sage-7.4/src/sage/matrix/matrix2.pyx\u001b[0m in \u001b[0;36msage.matrix.matrix2.Matrix.solve_right (/projects/sage/sage-7.4/src/build/cythonized/sage/matrix/matrix2.c:7000)\u001b[0;34m()\u001b[0m\n\u001b[1;32m 402\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 403\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrank\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m!=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnrows\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 404\u001b[0;31m \u001b[0mX\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_solve_right_general\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mC\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcheck\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mcheck\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 405\u001b[0m \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 406\u001b[0m \u001b[0mX\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_solve_right_nonsingular_square\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mC\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcheck_rank\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mFalse\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
  190. "\u001b[0;32m/projects/sage/sage-7.4/src/sage/matrix/matrix2.pyx\u001b[0m in \u001b[0;36msage.matrix.matrix2.Matrix._solve_right_general (/projects/sage/sage-7.4/src/build/cythonized/sage/matrix/matrix2.c:8147)\u001b[0;34m()\u001b[0m\n\u001b[1;32m 520\u001b[0m \u001b[0;31m# Have to check that we actually solved the equation.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 521\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mX\u001b[0m \u001b[0;34m!=\u001b[0m \u001b[0mB\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 522\u001b[0;31m \u001b[0;32mraise\u001b[0m \u001b[0mValueError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"matrix equation has no solutions\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 523\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mX\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 524\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
  191. "\u001b[0;31mValueError\u001b[0m: matrix equation has no solutions"
  192. ]
  193. }
  194. ],
  195. "source": [
  196. "genrand.solve_right(ints_to_f2([0xd86e392e, 0xddb8564b, 0x44559e7f, 0x74a35ddf]))"
  197. ]
  198. },
  199. {
  200. "cell_type": "markdown",
  201. "metadata": {},
  202. "source": [
  203. "hoge $x$."
  204. ]
  205. }
  206. ],
  207. "metadata": {
  208. "kernelspec": {
  209. "display_name": "SageMath 7.4",
  210. "language": "",
  211. "name": "sage-7.4"
  212. },
  213. "language_info": {
  214. "codemirror_mode": {
  215. "name": "ipython",
  216. "version": 2
  217. },
  218. "file_extension": ".py",
  219. "mimetype": "text/x-python",
  220. "name": "python",
  221. "nbconvert_exporter": "python",
  222. "pygments_lexer": "ipython2",
  223. "version": "2.7.10"
  224. }
  225. },
  226. "nbformat": 4,
  227. "nbformat_minor": 0
  228. }
Advertisement
Add Comment
Please, Sign In to add comment
Advertisement
Public Pastes
Advertisement
We use cookies for various purposes including analytics. By continuing to use Pastebin, you agree to our use of cookies as described in the Cookies Policy.  OK, I Understand
Not a member of Pastebin yet?
Sign Up, it unlocks many cool features!