595:
189:
The practical way to achieve the full entropy is to obtain from an entropy source bit strings longer than n bits, apply to them a high-quality randomness extractor that produces the n-bit result, and build the real set from these results. The ideal elements by nature have an entropy value of n. The
115:
The mathematical definition relies on a "distinguishing game": an adversary with an unlimited computing power is provided with two sets of random numbers, each containing W elements of length n. One set is
429:
27:. The output has full entropy if it cannot practically be distinguished from an output of a theoretical perfect random number source (has almost n bits of entropy for an n-bit output).
107:
Some sources use the term to define the ideal random bit string (one bit of entropy per bit of output). In this sense "getting to 100% full entropy is impossible" in the real world.
179:
102:
296:
259:
66:
212:
146:
398:
362:
326:
632:
573:
651:
424:, while providing an unbiased output, does not decorrelate groups of bits, so for serially correlated inputs (typical for many
656:
625:
194:
value H to satisfy the full-entropy definition. The number of additional bits of entropy H-n depends on W and
151:
24:
71:
533:"NIST Interagency Report NIST IR 8427 Discussion on the Full Entropy Assumption of the SP 800-90 Series"
421:
42:. With full entropy the per-bit entropy in the output of the random number generator is close to one:
618:
417:
265:
228:
125:
120:, it contains bit strings from the theoretically perfect random number generator, the other set is
45:
569:
563:
532:
197:
131:
543:
376:
340:
304:
433:
39:
35:
565:
Random Number
Generators—Principles and Practices: A Guide for Engineers and Programmers
602:
425:
645:
531:
Buller, Darryl; Kaufer, Aaron; Roginsky, Allen; Turan, Meltem Sönmez (April 2023).
148:
is achieved if an adversary cannot guess the real set with probability higher than
191:
547:
594:
437:
124:
and includes bit strings from the practical random number source after a
459:
457:
441:
432:. NIST therefore defines the "vetted conditioning components" in its
128:. The full entropy for particular values of W and positive parameter
539:
31:
190:
inputs of the conditioning function will need to have a higher
214:; the following table contains few representative values:
499:
487:
463:
510:
508:
606:
379:
343:
307:
268:
231:
200:
154:
134:
74:
48:
420:will produce the desired results. For example, the
392:
356:
320:
290:
253:
206:
173:
140:
96:
60:
626:
8:
633:
619:
384:
378:
348:
342:
312:
306:
279:
267:
242:
230:
199:
155:
153:
133:
85:
73:
47:
514:
475:
218:Minimum value of additional entropy H-n
216:
601:This cryptography-related article is a
453:
16:Cryptographic property of random output
174:{\displaystyle {\frac {1}{2}}+\delta }
7:
591:
589:
97:{\displaystyle \epsilon <2^{-32}}
30:The term is extensively used in the
14:
412:Randomness extractor requirements
593:
23:is a property of an output of a
291:{\displaystyle \delta =2^{-10}}
254:{\displaystyle \delta =2^{-20}}
428:) the output bits will not be
1:
68:, where per NIST a practical
605:. You can help Knowledge by
61:{\displaystyle 1-\epsilon }
34:random generator standards
673:
588:
652:Random number generation
548:10.6028/NIST.IR.8427.ipd
207:{\displaystyle \delta }
141:{\displaystyle \delta }
25:random number generator
394:
393:{\displaystyle 2^{56}}
358:
357:{\displaystyle 2^{48}}
322:
321:{\displaystyle 2^{32}}
292:
255:
208:
175:
142:
98:
62:
562:Johnston, D. (2018).
422:Von Neumann extractor
395:
359:
323:
293:
256:
209:
176:
143:
99:
63:
436:standard, including
418:randomness extractor
377:
341:
305:
266:
229:
198:
152:
132:
126:randomness extractor
72:
46:
219:
657:Cryptography stubs
500:Buller et al. 2023
488:Buller et al. 2023
464:Buller et al. 2023
390:
354:
318:
288:
251:
217:
204:
185:Additional entropy
171:
138:
94:
58:
614:
613:
575:978-1-5015-0606-2
409:
408:
163:
664:
635:
628:
621:
597:
590:
585:
583:
582:
558:
556:
554:
537:
518:
512:
503:
497:
491:
485:
479:
473:
467:
461:
399:
397:
396:
391:
389:
388:
363:
361:
360:
355:
353:
352:
327:
325:
324:
319:
317:
316:
297:
295:
294:
289:
287:
286:
260:
258:
257:
252:
250:
249:
220:
213:
211:
210:
205:
180:
178:
177:
172:
164:
156:
147:
145:
144:
139:
103:
101:
100:
95:
93:
92:
67:
65:
64:
59:
19:In cryptography
672:
671:
667:
666:
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663:
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661:
642:
641:
640:
639:
580:
578:
576:
561:
552:
550:
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530:
527:
522:
521:
513:
506:
498:
494:
486:
482:
474:
470:
462:
455:
450:
434:NIST SP 800-90B
426:entropy sources
414:
380:
375:
374:
344:
339:
338:
308:
303:
302:
275:
264:
263:
238:
227:
226:
196:
195:
187:
150:
149:
130:
129:
113:
81:
70:
69:
44:
43:
40:NIST SP 800-90B
36:NIST SP 800-90A
17:
12:
11:
5:
670:
668:
660:
659:
654:
644:
643:
638:
637:
630:
623:
615:
612:
611:
598:
587:
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574:
568:. De Gruyter.
559:
526:
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492:
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315:
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274:
271:
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186:
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170:
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137:
112:
109:
91:
88:
84:
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77:
57:
54:
51:
15:
13:
10:
9:
6:
4:
3:
2:
669:
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631:
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592:
577:
571:
567:
566:
560:
549:
545:
541:
534:
529:
528:
524:
517:, p. 16.
516:
515:Johnston 2018
511:
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505:
501:
496:
493:
489:
484:
481:
478:, p. 18.
477:
476:Johnston 2018
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55:
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49:
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37:
33:
28:
26:
22:
607:expanding it
600:
579:. Retrieved
564:
551:. Retrieved
502:, p. 2.
495:
490:, p. 1.
483:
471:
466:, p. i.
415:
188:
121:
117:
114:
106:
29:
21:full entropy
20:
18:
430:independent
192:min-entropy
646:Categories
581:2023-11-01
553:1 November
448:References
416:Not every
111:Definition
281:−
270:δ
244:−
233:δ
202:δ
169:δ
136:δ
87:−
76:ϵ
56:ϵ
53:−
525:Sources
442:CBC-MAC
572:
536:(PDF)
405:71.3
369:63.3
333:47.3
118:ideal
603:stub
570:ISBN
555:2023
540:NIST
402:91.3
366:83.3
330:67.3
122:real
79:<
38:and
32:NIST
544:doi
438:AES
648::
542:.
538:.
507:^
456:^
444:.
386:56
350:48
314:32
284:10
247:20
181:.
104:.
90:32
634:e
627:t
620:v
609:.
584:.
557:.
546::
440:-
382:2
346:2
310:2
277:2
273:=
240:2
236:=
223:W
166:+
161:2
158:1
83:2
50:1
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