COMP 547: Assignment 1 Solutions

+ x^383 + x^382 + x^381 + x^379 + x^378 + x^377 + x^376
+ x^375 + x^373 + x^372 + x^369 + x^368 + x^365 + x^363
+ x^359 + x^356 + x^354 + x^351 + x^350 + x^347 + x^346
+ x^345 + x^343 + x^338 + x^335 + x^332 + x^330 + x^328
+ x^327 + x^326 + x^324 + x^322 + x^320 + x^319 + x^316
+ x^315 + x^313 + x^312 + x^311 + x^310 + x^308 + x^306
+ x^305 + x^302 + x^300 + x^299 + x^298 + x^297 + x^296
+ x^291 + x^287 + x^286 + x^284 + x^283 + x^279 + x^275
+ x^274 + x^273 + x^272 + x^271 + x^270 + x^266 + x^265
+ x^264 + x^263 + x^260 + x^258 + x^254 + x^253 + x^252
+ x^251 + x^250 + x^246 + x^243 + x^239 + x^235 + x^234
+ x^231 + x^229 + x^227 + x^225 + x^223 + x^222 + x^217
+ x^213 + x^212 + x^208 + x^207 + x^205 + x^200 + x^199
+ x^198 + x^197 + x^194 + x^193 + x^192 + x^190 + x^189
+ x^186 + x^185 + x^184 + x^178 + x^177 + x^176 + x^174
+ x^173 + x^172 + x^170 + x^166 + x^165 + x^163 + x^162
+ x^160 + x^159 + x^158 + x^156 + x^154 + x^153 + x^150
+ x^147 + x^143 + x^142 + x^140 + x^138 + x^137 + x^136
+ x^135 + x^134 + x^132 + x^131 + x^129 + x^127 + x^125
+ x^118 + x^110 + x^109 + x^106 + x^104 + x^103 + x^102
+ x^100 + x^97 + x^96 + x^93 + x^91 + x^89 + x^82 + x^79
+ x^78 + x^77 + x^76 + x^75 + x^72 + x^70 + x^68 + x^66
+ x^65 + x^63 + x^62 + x^61 + x^60 + x^56 + x^54 + x^53
+ x^52 + x^51 + x^50 + x^43 + x^42 + x^34 + x^33 + x^28
+ x^27 + x^24 + x^21 + x^20 + x^19 + x^14 + x^13 + x^12
+ x^10 + x^9 + x^7 + x^4 + x^3 + x;
4. To generate two random elements i, j from F 2 1000, use the primitive element
g from above:
randomize();
x := rand(0..2^1000)();
y := x;
while y = x do
y := rand(0..2^1000)();
end do;
if x=2^1000 then
i=0;
else
i := F21000[‘^‘](g, x);
endif
if y=2^1000 then
j=0;
else
j := F21000[‘^‘](g, y);
endif
6