Ressu random numbers

The next chapter consists of characters that try to resemble throws of a 64 sided dice as closely as possible. Characters have numbers from '0' to '9' (10 entries), lowercase letters from 'a' to 'z' (26 entries), uppercase letters 'A' to 'Z' (26 entries), '-' and '_' (2 entries). Total is 10+26+26+2 = 64 values. Characters are grouped into sets of 16 each. Throws are random, so you cannot deduce next value from previous value(s).

Ressu random numbers

LloMLiTcJFBnPehx AlHIEVu7PNJ28s6J 06Nxn2qHK4KdWpkv 7IPTlfDy3RilJE74 QgelJUO7P5aEny78 v3rn1RwWP5diL192 bdWy_FmMN6DLEz3r fEXqMMBwxajrW5ud AVqHSIEsSG8mOs0U qgdp94kEdbc11mII HlGCERe88tBjVUyu oos5VdVYx4pBsMGs 8XlOqZGNOlLcUj7V 7feXg−7_qAddMguK aoNvkZ20zBWVpY9c LvpfU4sz1y87rF1C RbTZ7OUT0aFswbWv ieP_MBS6cAADi1y− weTJaPEGXSqHck3z LCt0p9op7pdfuGeo AvOc7PAdA_L9bCXk KOmGsntM−7m9Pb7n 8d32TI9GSqx3ELym fQaPtY−kjDF77rgS Tdz7NEdQ2LFKplzm qkWAxRVBmJkRwgvL U0Dhg5mHqBgyMxJw S3pF_d81dKPiUsgO 7JS__xMF5ZtrHT1j FmU5IoiLia2xzcsS 9YprTIg0GGpwSvOy IJDVuwyaefMwdW54 lN−kmHwVb07D1Hg6 FLiCMdNSNL4rcEct s93KW−eiHseXhDBM bGpTaFgjHCur91a_ eoOtqWTAJTjDSGOY QMXMOvDsLU1DEcZP ySdD−XlLEyDh7ZfM WVZWiBudEl4bhFO− 17MB−RTe3B_bP2YS 3Ko29DrWEDwnlEam fm0ERYO4saRnZl5t GD_KSl_qx4CxBkjt 8Ux3MuWXQfmovhN_ zRBHiQg99Zk4_hkD NpYemAryxVjC−hwd lgGtFEfPPvk5TYwA I8IjdkJNM23wDISl K6iQbscpKLIE0uh2 OSvbfp3AJD0rYA5l MzyZ1PJdMBY_1IZq SMhMNCS1OxKoB−−b RYWSx754ZTOdkS_Y −UvwnMBpJ5oQ866d ZiLxtkMcp85p2o1L O6KnszuH7JQiQrW1 _a78_URgVaUfkunp tPXX1Zm2vLdaBJ3u 1LwE_kOwdGBoTvd_ thFRU9JB9z4o85Xw oBZdg5JbecvLSg7Q s_C2AK__XCLqu8Qn vukeLzHmipBdJE5J dY−EVUyDTdZ0x9KN rGjHOu8mJQdIPNm4 XlkAro4FwNbe5cGv fWu5FEUEmmuGa3FF seHnF4wbR5d6OSuc gz166vlAlzbm2B6U OHbn3aYQp−Ij0jtN eSu7b9bX44qnRiYU ma_A8QfTrkxjy2Gi Z1rClwfYR5gPgz9Q GxjMQmiej4fD−sgM Jvtpeu2GqMTmmEKq u0SE7jfjobNxeqWB WihVQ57iLqpIGIpF cXfjsdq_E6Wgv42N iopA5oFlUQdpPbiH Y3Z2ZgKQWmQMgy9h 9Emjj1ihFcznTXG2 DKjJnAFge3yId−94 Rr93ocaXhkPwIEeo XRn4CLqAhYq8RJM2 2n1jH9gyKM6yUJKg Fe3TLX5UN_zU3S5n UzzQlZktEnWyJnC_ M7zPykkfYknALMk0 9sidq7R31UuQuYOE QWNoJO7m−JyFG4bo Qh1Yf72R_6PaNrX0 BtYux3KitqYVTL4X PbzNVRoe45icNKNq NxutUaxG−SxrZOSN GfrwbjzkOuHmtF4I Umpwq7U2GXVeYBC3 YMzj9AifDiJgI2Xi 7ZJdUzZhuLmuZ8pN 5p4mq0KJqXZjC2wL O3GC_Z28AlEbu0V8 oJWLckrne2S_2Cyu V0f2zeyYtVQnl4fT VKZsCWxU7fGv_sMd zsmz−xwM3ngvjtTj lAqx3xcs_Xd947B4 HHEpp1lUh13cXDYo 0a39tR_J7cxXPEWC Ej7UXKn9R78UQN50 uSGFyhu33Eaml0er 19stoRRPBHK1CeK− wy9_BTrsOtZi3FAP 2sxtr7BQxpb6EXl2 wsW2zuFoTx5b7Usw vIKkF0uzy5vBbFGS nFXdTIAoUNsdTyqY IUyIJBa2zWHbMP1j bjo3H2RGfobn2gQJ AEelnnP2whGRfOAB 8G−hamA9FBD−pJto aDhZhDqSpkzglLBm rt−KYHNyC98p1yyq HJARgeOrDEBYuMPh j8SshYeYW4ke3GgV kPaQZVhviyiHz_EG s3qO_39Oe0ATGG1N WRyse8sAAPLk1P−C UF3TIHu4BlkY5jmQ rxHAdbJVZ9NVok3c 5Fg90Bm01XGrPxws WJroULNlFoW8GyA9 pf−uWU2qwqewFGlU B7sldReLFNJ9sJRd vt8h1−L3x2edttsP htRly9BNS_jHvgvL NoTMcQwkbAw9my9k 9amGJ−q4OVK−I69z FCnUGpoFX1tc9XeW RRjQJYnkRftGvsvh EenfXzmafjMd9F5c DFvPsQW−wIOPAIv6 5Ot−5bn5CmDuGPPv cRgJ3eKKwugeXKL5 X−d4sknSKHdTbKWM 7Z4qT−PTYXvZ_fzZ QKYNKKVXK40_NwEx ShifM−9DjvLqcsAR ULzyrrid0−yfLFSW UyFE339ThFsEolKA gwFDkvKjiytOuAPU p7SxU7oEMYFecsJ9 TP1DzDYQ4Smvsc5j BRI591nhBPLTCzT2 6l61CRsL15BnHHli EAA8parBR6D_95g3 tirdCozHGL1pf4−k 24n2EZaL95CvP3Q7 2ljmtSfpZMTe8xMY ScpR1kgkhZSGE0m1 w0XKMCx6CEigu4e3 OJ7ZwKdiXZEe6JVQ 2−j_3FuGtw05s1cO 1yhiEoxI1_Huuq3T Fs9Hf_UTe7O97Pxv vlQTxRDGOs83Hxfz UBUJam11UJJNMVdn IAC08H5S8LQ6equA 67NqFCHoyXunYK8L LkBzj7GujkpMPakn 1HFfqzEMlZAigjWo W7rUcduEeUTeQhyN D2YHToLhShK−kwa7 LCocwSWgOH1pl1eO d_ZLT1XnMwNAC4Ku 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Statistics

The next chapter has statistics calculated from earlier data:

monobit: ones: 262329(50.038340%), zeroes: 261927(49.961660%), total: 524256
bitwise monobit data: 1(0: 32803, 1: 32729) 2(0: 32670, 1: 32862) 4(0: 32579, 1: 32953) 8(0: 32826, 1: 32706) 16(0: 32816, 1: 32716) 32(0: 32897, 1: 32635) 64(0: 32922, 1: 32610) 128(0: 32816, 1: 32716)
bitwise monobit total: 524256, lowest: 32579(6.214330%), highest: 32953(6.285670%)
poker2: data: 0:65664 1:65545 2:65456 3:65463
poker2: total: 262128, lowest: 65456(24.971007%), highest: 65664(25.050357%)
poker4: data: 0:8294 1:8025 2:8112 3:8245 4:8319 5:8180 6:8170 7:8297 8:8191 9:8208 10:8172 11:8254 12:8184 13:8166 14:8177 15:8070
poker4: total: 131064, lowest: 8025(6.122963%), highest: 8319(6.347281%)
poker8: data: 0:245 1:229 2:258 3:259 4:264 5:244 6:245 7:282 8:259 9:267 10:266 11:275 12:255 13:250 14:288 15:260 16:266 17:278 18:256 19:255 20:254 21:236 22:264 23:242 24:240 25:251 26:260 27:266 28:253 29:237 30:265 31:246 32:271 33:251 34:252 35:253 36:222 37:244 38:259 39:275 40:257 41:270 42:256 43:254 44:248 45:235 46:265 47:231 48:300 49:268 50:230 51:238 52:261 53:289 54:265 55:249 56:249 57:232 58:248 59:272 60:249 61:251 62:268 63:262 64:260 65:245 66:276 67:260 68:253 69:227 70:247 71:263 72:270 73:251 74:258 75:278 76:251 77:257 78:264 79:280 80:249 81:248 82:260 83:284 84:257 85:239 86:286 87:243 88:257 89:268 90:242 91:255 92:259 93:283 94:243 95:244 96:248 97:218 98:239 99:270 100:260 101:250 102:272 103:244 104:272 105:264 106:275 107:234 108:268 109:285 110:232 111:240 112:284 113:233 114:258 115:243 116:281 117:262 118:252 119:258 120:255 121:247 122:269 123:224 124:269 125:266 126:250 127:248 128:269 129:246 130:251 131:254 132:274 133:283 134:229 135:253 136:252 137:267 138:253 139:254 140:227 141:273 142:258 143:289 144:260 145:252 146:234 147:248 148:278 149:240 150:267 151:270 152:260 153:262 154:247 155:250 156:290 157:255 158:287 159:251 160:241 161:229 162:272 163:242 164:268 165:253 166:244 167:286 168:246 169:270 170:231 171:264 172:257 173:283 174:262 175:271 176:263 177:233 178:270 179:279 180:260 181:255 182:258 183:271 184:244 185:262 186:227 187:283 188:266 189:243 190:239 191:278 192:245 193:263 194:255 195:287 196:279 197:255 198:241 199:277 200:233 201:244 202:257 203:283 204:250 205:253 206:237 207:231 208:258 209:243 210:250 211:251 212:251 213:263 214:258 215:231 216:247 217:221 218:276 219:244 220:251 221:260 222:271 223:277 224:256 225:268 226:242 227:241 228:259 229:256 230:258 231:284 232:271 233:250 234:243 235:245 236:260 237:266 238:230 239:246 240:233 241:252 242:266 243:250 244:258 245:267 246:254 247:270 248:247 249:231 250:245 251:242 252:241 253:217 254:243 255:250
poker8: total: 65532, lowest: 217(0.331136%), highest: 300(0.457792%)
6 bit poker: data: 45:1334 48:1375 49:1399 50:1347 51:1355 52:1354 53:1349 54:1260 55:1321 56:1368 57:1394 65:1364 66:1396 67:1360 68:1310 69:1442 70:1354 71:1335 72:1314 73:1297 74:1460 75:1362 76:1417 77:1383 78:1385 79:1360 80:1431 81:1332 82:1411 83:1405 84:1421 85:1370 86:1378 87:1339 88:1356 89:1316 90:1337 95:1364 97:1407 98:1330 99:1449 100:1344 101:1430 102:1387 103:1370 104:1348 105:1322 106:1357 107:1358 108:1348 109:1415 110:1388 111:1328 112:1370 113:1374 114:1343 115:1415 116:1403 117:1334 118:1314 119:1332 120:1350 121:1354 122:1351
6 bit poker: total: 87376, lowest: 1260(1.442044%), highest: 1460(1.670939%), count: 64
runs: stat: 1:65532 2:32766 3:16383 4:8191 5:4095 6:2047 7:1023 8:511 9:255 10:127 11:63 12:31 13:15 14:7 15:3 16:1 17:0 18:0 19:0 20:0 21:0
runs: zeroes: 1:65693 2:32596 3:16311 4:8333 5:4069 6:2011 7:1095 8:482 9:270 10:130 11:65 12:30 13:12 14:8 15:5 16:4 17:1 18:1
runs: ones: 1:65612 2:32792 3:16454 4:8090 5:4114 6:2034 7:968 8:539 9:259 10:120 11:63 12:36 13:19 14:8 15:4 16:1 17:1 18:1 19:0 20:0 21:1
runs: total: 524256
runs8: any: 1:65025 2:252 3:1
runs8: total: 65532
runs6: any: 1:84637 2:1330 3:25 4:1
runs6: total: 87376
average: total 8334377, count: 65532, average: 127.180260
average16: total 1068234227, count: 32766, average: 32601.911341
entropy: 7.997300
entropy6: 5.999422

Technical

Ressu makes random bits from fluctuations in repeated reading of the clock. Ressu returns an array (buffer) with random bytes. Ressu has a round function that has two phases. First phase rotates left and xors (exclusive or) every byte in the buffer with clock material. Second phase swaps all bytes in the buffer with a random byte in the buffer. In this version round function is repeated 6 * 8 = 48 times.

Rotation (first phase) is done to the left, bit 7 is moved to bit 0, and bits 0-6 are rotated one bit left, bit 6 becomes bit 7, bit 5 becomes bit 6, and so on. The rotation ensures that every bit of the byte is touched by the most active, zero bit of the clock. After eight rotations (eight rounds) we are back where we started, with all bits of the byte, and all bytes of the buffer touched.

Xor (first phase) brings randomness to the buffer and prevents undoing swaps, and thru that undoing generator. Xor is done with the most active clock material, being lowest byte of the microseconds. Most active bit in the clock is bit 0, which is xor:ed with bit 0 of byte in the buffer. Second most active is bit 1, and that is xor:ed with bit 1 of the byte in buffer. This continues for all 8 bits of the lowest byte of microseconds. Xor reverses all bits that meet bit valued 1 in clock material, so half of the bits are reversed per round.

Swapping (second phase) distributes bytes so that bytes clocked adjacent to each other are moved to different parts of the buffer. On the other hand swaps collect bytes for the next round, in a way that adjacent bytes are from different parts of the buffer. First side of this swap varies from starting of buffer to ending of buffer, position by position. Value in first side of the swap is added to position of second side of the swap. First side of the swap makes sure that every byte in buffer is swapped. Second side of the swap makes sure that swapping is random.

Clock material is a stream of bytes that has period 0-255 in it. After 255 stream reverts back to 0. Same number appears multiple times, so material could be for example: 1, 1, 1, 2, 2, 2, 3, 3, 3. Fluctuations, that are needed for this generator are missing entries, excess entries and missing numbers. Missing entry might be seen as only two ones in this example stream. Excess entries might be four threes in this stream. Missing number might be stream period with no twos. Swapping gets it's randomness from buffer, which gets randomness from clock sequence, which means that one bit change in clock changes rest of the swapping targets for rest of the run. To get random numbers ressu gives, adversary must guess whole clock stream including fluctuations.

Here are typical fluctuations (or variations) in one run of ressu in this machine: 1:4-26 2:3-21 3:2-20 4:3-25 5:2-114 6:4-123 7:1-131 8:5-116 9:3-118 10:5-113 11:1-112 12:3-27 13:7-20 14:7-33 15:29-75 16:28-65 17:27-66 18:37-90 19:44-87 20:48-105 21:63-181 22:85-284 23:86-199 24:449-1889 25:1032-2617 26:111247-114086 27:4706-4893 28:0-1 29:0-1 30:0-1 31:0-1 35:0-1 37:0-1 39:0-1 41:0-1 42:0-1 44:0-1 45:0-1 (varies between runs). So to guess clock material for one ressu run, we need from 4 to 26 chains of length 1, and we need from 3 to 21 chains of length 2, next we need 2 to 20 chains of length 3, and so on. Most often chain seems to be 26 long, we need 111247-114086 pieces of them. After we list all these, we need to just order and renumber them... There is some chains in the end (28, 29, 30, 31, 35, 37,...) where there is either one or none of them.

Changing activity of bits (see Xor) follows 2's powers. Following examples use clock series 0, 1, 2, 3, 4, 5... . Bit 0 changes every other byte (2^0=1). For earlier clock stream, bit changes would be 0, 1, 0, 1, 0, 1... . Period of bit 1 is 2 (2^1=2), so bit changes for each 2 byte numbers, shown as 0, 0, 1, 1, 0, 0, 1, 1... . Bit 2 switches every four numbers (2^2=4), and bit series might be 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, rest of the period lengths are 8, 16, 32, 64 and 128.

There is no whitening or combining of other generators, so earlier material is produced by ressu only. However at the moment there is no clearing of buffer between runs, so all earlier ressu runs gives randomness to this run.

Changes

Added reading instructions.


Ressu3 version 0.15 ©, sha256(ea3a55112dfe1c8743e7150c0e86bac86b1b8a504c8fe2b88273233480fb17fa)