CMT19.txt : Multiplication circuit for binary polynomials of degree 18.

Date: July 2011.

input polynomials are A = f0 + f1*X + f2*X^2 + ... + f18*X^18 and B = g0 + g1*X + g2*X^2 + ... + g18*X^18.

output polynomial is the product A*B = h0 + h1*X + h2*X^2 + ... + h36*X^36.
Coefficients are over GF2.

Size : 498
Depth : 8

SLP:

h36 = f18 x g18
t2 = f18 x g15
t3 = f18 x g16
t4 = f18 x g17
t5 = f15 x g18
t6 = f16 x g18
t7 = f17 x g18
t8 = f17 x g17
t9 = f17 x g15
t10 = f17 x g16
t11 = f15 x g17
t12 = f16 x g17
t13 = f16 x g16
t14 = f16 x g15
t15 = f15 x g16
t16 = f15 x g15
t26 = f14 x g14
t27 = f14 x g10
t28 = f14 x g11
t29 = f14 x g12
t30 = f14 x g13
t31 = f10 x g14
t32 = f11 x g14
t33 = f12 x g14
t34 = f13 x g14
t35 = f13 x g13
t36 = f13 x g10
t37 = f13 x g11
t38 = f13 x g12
t39 = f10 x g13
t40 = f11 x g13
t41 = f12 x g13
t42 = f12 x g12
t43 = f12 x g10
t44 = f12 x g11
t45 = f10 x g12
t46 = f11 x g12
t47 = f11 x g11
t48 = f11 x g10
t49 = f10 x g11
t50 = f10 x g10
t67 = f9 x g9
t68 = f9 x g5
t69 = f9 x g6
t70 = f9 x g7
t71 = f9 x g8
t72 = f5 x g9
t73 = f6 x g9
t74 = f7 x g9
t75 = f8 x g9
t76 = f8 x g8
t77 = f8 x g5
t78 = f8 x g6
t79 = f8 x g7
t80 = f5 x g8
t81 = f6 x g8
t82 = f7 x g8
t83 = f7 x g7
t84 = f7 x g5
t85 = f7 x g6
t86 = f5 x g7
t87 = f6 x g7
t88 = f6 x g6
t89 = f6 x g5
t90 = f5 x g6
t91 = f5 x g5
t108 = f4 x g4
t109 = f4 x g0
t110 = f4 x g1
t111 = f4 x g2
t112 = f4 x g3
t113 = f0 x g4
t114 = f1 x g4
t115 = f2 x g4
t116 = f3 x g4
t117 = f3 x g3
t118 = f3 x g0
t119 = f3 x g1
t120 = f3 x g2
t121 = f0 x g3
t122 = f1 x g3
t123 = f2 x g3
t124 = f2 x g2
t125 = f2 x g0
t126 = f2 x g1
t127 = f0 x g2
t128 = f1 x g2
t129 = f1 x g1
t130 = f1 x g0
t131 = f0 x g1
h0 = f0 x g0
t161 = g10 + g15
t162 = g11 + g16
t163 = g12 + g17
t164 = g13 + g18
t165 = f10 + f15
t166 = f11 + f16
t167 = f12 + f17
t168 = f13 + f18
t170 = f14 x t161
t171 = f14 x t162
t172 = f14 x t163
t173 = f14 x t164
t174 = t165 x g14
t175 = t166 x g14
t176 = t167 x g14
t177 = t168 x g14
t178 = t168 x t164
t179 = t168 x t161
t180 = t168 x t162
t181 = t168 x t163
t182 = t165 x t164
t183 = t166 x t164
t184 = t167 x t164
t185 = t167 x t163
t186 = t167 x t161
t187 = t167 x t162
t188 = t165 x t163
t189 = t166 x t163
t190 = t166 x t162
t191 = t166 x t161
t192 = t165 x t162
t193 = t165 x t161
t210 = g0 + g5
t211 = g1 + g6
t212 = g2 + g7
t213 = g3 + g8
t214 = g4 + g9
t215 = f0 + f5
t216 = f1 + f6
t217 = f2 + f7
t218 = f3 + f8
t219 = f4 + f9
t220 = t219 x t214
t221 = t219 x t210
t222 = t219 x t211
t223 = t219 x t212
t224 = t219 x t213
t225 = t215 x t214
t226 = t216 x t214
t227 = t217 x t214
t228 = t218 x t214
t229 = t218 x t213
t230 = t218 x t210
t231 = t218 x t211
t232 = t218 x t212
t233 = t215 x t213
t234 = t216 x t213
t235 = t217 x t213
t236 = t217 x t212
t237 = t217 x t210
t238 = t217 x t211
t239 = t215 x t212
t240 = t216 x t212
t241 = t216 x t211
t242 = t216 x t210
t243 = t215 x t211
t244 = t215 x t210
t296 = g5 + g15
t297 = g6 + g16
t298 = g7 + g17
t299 = g8 + g18
t300 = g0 + g10
t301 = g1 + g11
t302 = g2 + g12
t303 = g3 + g13
t304 = g4 + g14
t305 = f5 + f15
t306 = f6 + f16
t307 = f7 + f17
t308 = f8 + f18
t309 = f0 + f10
t310 = f1 + f11
t311 = f2 + f12
t312 = f3 + f13
t313 = f4 + f14
t314 = t313 x t304
t315 = t313 x t300
t316 = t313 x t301
t317 = t313 x t302
t318 = t313 x t303
t319 = t309 x t304
t320 = t310 x t304
t321 = t311 x t304
t322 = t312 x t304
t323 = t312 x t303
t324 = t312 x t300
t325 = t312 x t301
t326 = t312 x t302
t327 = t309 x t303
t328 = t310 x t303
t329 = t311 x t303
t330 = t311 x t302
t331 = t311 x t300
t332 = t311 x t301
t333 = t309 x t302
t334 = t310 x t302
t335 = t310 x t301
t336 = t310 x t300
t337 = t309 x t301
t338 = t309 x t300
t356 = f9 x t296
t357 = f9 x t297
t358 = f9 x t298
t359 = f9 x t299
t360 = t305 x g9
t361 = t306 x g9
t362 = t307 x g9
t363 = t308 x g9
t364 = t308 x t299
t365 = t308 x t296
t366 = t308 x t297
t367 = t308 x t298
t368 = t305 x t299
t369 = t306 x t299
t370 = t307 x t299
t371 = t307 x t298
t372 = t307 x t296
t373 = t307 x t297
t374 = t305 x t298
t375 = t306 x t298
t376 = t306 x t297
t377 = t306 x t296
t378 = t305 x t297
t379 = t305 x t296
t396 = t300 + t296
t397 = t301 + t297
t398 = t302 + t298
t399 = t303 + t299
t400 = t304 + g9
t401 = t309 + t305
t402 = t310 + t306
t403 = t311 + t307
t404 = t312 + t308
t405 = t313 + f9
t406 = t405 x t400
t407 = t405 x t396
t408 = t405 x t397
t409 = t405 x t398
t410 = t405 x t399
t411 = t401 x t400
t412 = t402 x t400
t413 = t403 x t400
t414 = t404 x t400
t415 = t404 x t399
t416 = t404 x t396
t417 = t404 x t397
t418 = t404 x t398
t419 = t401 x t399
t420 = t402 x t399
t421 = t403 x t399
t422 = t403 x t398
t423 = t403 x t396
t424 = t403 x t397
t425 = t401 x t398
t426 = t402 x t398
t427 = t402 x t397
t428 = t402 x t396
t429 = t401 x t397
t430 = t401 x t396
TR1 = t111 + t115
TR2 = t117 + t89
h1 = t130 + t131
TR4 = t14 + t15
TR5 = t172 + t176
TR6 = t191 + t192
TR7 = t223 + t227
TR8 = t242 + t243
TR9 = t29 + t33
TR10 = t317 + t321
TR11 = t323 + t377
TR12 = t336 + t337
TR13 = t358 + t362
TR14 = t409 + t413
TR15 = t428 + t429
TR16 = t48 + t49
TR17 = t70 + t74
TR18 = TR1 + TR2
TR19 = TR10 + TR11
TR20 = TR13 + t364
TR21 = TR14 + t415
TR22 = TR16 + TR17
TR23 = TR18 + t90
TR24 = TR19 + t378
TR25 = TR22 + t76
TR26 = TR4 + TR9
TR27 = TR5 + t178
TR28 = TR7 + t229
TR29 = TR26 + t35
TR32 = t110 + t114
TR33 = t120 + t123
TR34 = t16 + t28
TR35 = t171 + t175
TR36 = t181 + t184
TR37 = t222 + t226
TR38 = t232 + t235
TR39 = t316 + t320
TR40 = t32 + t38
TR41 = t326 + t329
TR42 = t357 + t361
TR43 = t367 + t370
h35 = t4 + t7
TR45 = t408 + t412
TR46 = t418 + t421
TR47 = t50 + t69
TR48 = t73 + t79
TR49 = TR32 + TR33
TR50 = TR34 + TR40
TR51 = TR35 + TR36
TR52 = TR37 + TR38
TR53 = TR39 + TR41
TR54 = TR42 + TR43
TR55 = TR45 + TR46
TR56 = TR47 + TR48
TR57 = TR49 + t91
TR58 = TR50 + t41
TR59 = TR53 + t379
TR60 = TR56 + t82
TR63 = t109 + t113
TR64 = t119 + t122
TR65 = t170 + t174
TR66 = t180 + t183
TR67 = t221 + t225
TR68 = t231 + t234
TR69 = t27 + t31
TR70 = t3 + t6
TR71 = t315 + t319
TR72 = t325 + t328
TR73 = t356 + t360
TR74 = t366 + t369
TR75 = t37 + t40
TR76 = t407 + t411
TR77 = t417 + t420
TR78 = t68 + t72
TR79 = t78 + t81
TR80 = TR63 + TR64
TR81 = TR65 + TR66
TR82 = TR67 + TR68
TR83 = TR69 + TR75
h34 = TR70 + t8
TR85 = TR71 + TR72
TR86 = TR73 + TR74
TR87 = TR76 + TR77
TR88 = TR78 + TR79
h4 = TR80 + t124
TR90 = TR81 + t185
TR91 = TR82 + t236
TR92 = TR83 + t42
TR93 = TR85 + t330
TR94 = TR86 + t371
TR95 = TR87 + t422
TR96 = TR88 + t83
TR98 = t11 + t13
TR99 = t112 + t116
TR100 = t125 + t127
TR101 = t173 + t177
TR102 = t186 + t188
TR103 = t224 + t228
TR104 = t237 + t239
TR105 = t30 + t34
TR106 = t318 + t322
TR107 = t331 + t333
TR108 = t359 + t363
TR109 = t372 + t374
TR110 = t410 + t414
TR111 = t423 + t425
TR112 = t43 + t45
TR113 = t47 + t71
TR114 = t84 + t86
h2 = TR100 + t129
TR116 = TR102 + t190
TR117 = TR104 + t241
TR118 = TR105 + TR98
TR119 = TR106 + TR109
TR120 = TR107 + t335
TR121 = TR111 + t427
TR122 = TR112 + TR113
TR123 = TR114 + TR99
TR124 = TR118 + t9
TR125 = TR103 + t376
TR126 = TR122 + t75
TR127 = TR123 + t88
h32 = TR101 + TR124
TR131 = TR116 + TR124
TR133 = t10 + t12
TR134 = t108 + t77
TR135 = t118 + t121
TR136 = t126 + t128
TR137 = t179 + t182
TR138 = t187 + t189
TR139 = t2 + t5
TR140 = t230 + t233
TR141 = t238 + t240
TR142 = t314 + t365
TR143 = t324 + t327
TR144 = t332 + t334
TR145 = t36 + t39
TR146 = t368 + t373
TR147 = t416 + t419
TR148 = t424 + t426
TR149 = t44 + t46
TR150 = t80 + t85
h33 = TR133 + TR139
TR152 = TR134 + TR150
h3 = TR135 + TR136
TR154 = TR137 + TR138
TR155 = TR140 + TR141
TR156 = TR142 + TR146
TR157 = TR143 + TR144
TR158 = TR145 + TR149
TR159 = TR147 + TR148
TR160 = TR152 + t87
TR161 = TR154 + t26
TR162 = TR156 + t375
TR163 = TR157 + t67
X0 = TR23 + h1
h6 = TR8 + X0
X2 = TR29 + h36
h31 = TR27 + X2
X4 = TR12 + TR25
X5 = TR20 + TR25
X6 = TR28 + X0
h11 = X4 + X6
X8 = TR6 + X2
h26 = X5 + X8
X10 = TR23 + TR24
X11 = TR28 + h31
X12 = X5 + TR21
X13 = X10 + X12
h21 = X13 + X11
X14 = TR24 + TR29
X15 = TR6 + h6
X16 = X4 + TR15
X17 = X14 + X16
h16 = X17 + X15
X18 = h35 + TR58
h30 = TR51 + X18
X20 = TR57 + h0
h5 = t244 + X20
X22 = TR52 + TR60
X23 = TR60 + t193
X24 = TR54 + X18
h25 = X23 + X24
X26 = t338 + X20
h10 = X22 + X26
X28 = TR51 + TR57
X29 = TR59 + X22
X30 = X24 + X28
X31 = X29 + TR55
h20 = X31 + X30
X32 = TR58 + TR59
X33 = t244 + t430
X34 = X26 + X32
X35 = X33 + X23
h15 = X35 + X34
X36 = h34 + TR92
h29 = TR90 + X36
X38 = h4 + TR96
h9 = TR91 + X38
X40 = TR92 + TR93
h14 = X38 + X40
X42 = TR94 + TR96
h24 = X36 + X42
X44 = TR93 + TR94
X45 = h29 + h9
X46 = X44 + TR95
h19 = X46 + X45
X47 = h2 + TR127
h7 = TR117 + X47
X49 = TR108 + TR126
h27 = TR131 + X49
X51 = TR120 + TR126
X52 = TR103 + X47
h12 = X51 + X52
X54 = TR119 + TR125
X55 = TR127 + TR110
X56 = X54 + h32
TR128 = X49 + X55
X57 = TR117 + TR131
X58 = TR121 + X54
X59 = X57 + X58
h17 = X59 + h12
X60 = h33 + TR158
h28 = TR161 + X60
X62 = h3 + TR160
h8 = TR155 + X62
X64 = TR158 + TR163
X65 = t220 + X62
h13 = X64 + X65
X67 = h3 + t406
X68 = X60 + X65
X69 = X67 + TR162
h23 = X69 + X68
X70 = TR162 + TR163
X71 = h28 + h8
X72 = X70 + TR159
h18 = X72 + X71
h22 = TR128 + X56