Editing Talk:Bruteforcing

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  2<sup>128</sup> keys ÷ 2,000,000 keys/second = 1.7e+32 seconds
  2<sup>128</sup> keys ÷ 2,000,000 keys/second = 1.7e+32 seconds


For those not fluent in “calculator speak” 1.7e+32 means 1.7 x 10<sup>32</sup>, which means you move the decimal point to the right 32 times. So then the number is 17 followed by 31 zeros. This seems like a lot of seconds, but it is hard to gauge time in large numbers of seconds. So for the benefit of the humans here, lets use years instead of seconds for our measurements of time.
For those not fluent in “calculator speak” 1.7e+32 means 1.7 x 1032, which means you move the decimal point to the right 32 times. So then the number is 17 followed by 31 zeros. This seems like a lot of seconds, but it is hard to gauge time in large numbers of seconds. So for the benefit of the humans here, lets use years instead of seconds for our measurements of time.


First we need to work out how many seconds there are in a year. We will approximate to simplify the math:
First we need to work out how many seconds there are in a year. We will approximate to simplify the math:
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Or if it were to use random guesses, then every year that passes there would be a 1 in 770734 chance that someone somewhere guessed the right number.
Or if it were to use random guesses, then every year that passes there would be a 1 in 770734 chance that someone somewhere guessed the right number.
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=== Key sizes ===
{| class="wikitable sortable"
|-
! bits !! style="text-align:left" | No of keys
|-
| 1 || 2
|-
| 2 || 4
|-
| 4 || 16
|-
| 8 || 256
|-
| 16 || 65536
|-
| 32 || 4294967296
|-
| 48 || 281474976710656
|-
| 64 || 18446744073709551616
|-
| 80 || 1208925819614629174706176
|-
| 96 || 79228162514264337593543950336
|-
| 112 || 5192296858534827628530496329220096
|-
| 128 || 340282366920938463463374607431768211456
|-
| 144 || 22300745198530623141535718272648361505980416
|-
| 160 || 1461501637330902918203684832716283019655932542976
|-
| 176 || 95780971304118053647396689196894323976171195136475136
|-
| 192 || 6277101735386680763835789423207666416102355444464034512896
|-
| 208 || 411376139330301510538742295639337626245683966408394965837152256
|-
| 224 || 26959946667150639794667015087019630673637144422540572481103610249216
|-
| 240 || 1766847064778384329583297500742918515827483896875618958121606201292619776
|-
| 256 || 115792089237316195423570985008687907853269984665640564039457584007913129639936
|-
| 272 || 7588550360256754183279148073529370729071901715047420004889892225542594864082845696
|-
| 288 || 497323236409786642155382248146820840100456150797347717440463976893159497012533375533056
|-
| 304 || 32592575621351777380295131014550050576823494298654980010178247189670100796213387298934358016
|-
| 320 || 2135987035920910082395021706169552114602704522356652769947041607822219725780640550022962086936576
|-
| 336 || 139984046386112763159840142535527767382602843577165595931249318810236991948760059086304843329475444736
|-
| 352 || 9173994463960286046443283581208347763186259956673124494950355357547691504353939232280074212440502746218496
|-
| 368 || 601226901190101306339707032778070279008174732520529886901066488712245510429339761526706943586500787976175353856
|-
| 384 || 39402006196394479212279040100143613805079739270465446667948293404245721771497210611414266254884915640806627990306816
|-
| 400 || 2582249878086908589655919172003011874329705792829223512830659356540647622016841194629645353280137831435903171972747493376
|-
| 416 || 169230328010303641331690318856389386196071598838855992136870091590247882556495704531248437872567112920983350278405979725889536
|-
| 432 || 11090678776483259438313656736572334813745748301503266300681918322458485231222502492159897624416558312389564843845614287315896631296
|-
| 448 || 726838724295606890549323807888004534353641360687318060281490199180639288113397923326191050713763565560762521606266177933534601628614656
|-
| 464 || 47634102635436893179040485073748265163400240214004076398607741693502376385799646303105256699577209032590132615988260237052123652332890095616
|-
| 480 || 3121748550315992231381597229793166305748598142664971150859156959625371738819765620120306103063491971159826931121406622895447975679288285306290176
|-
| 496 || 204586912993508866875824356051724947013540127877691549342705710506008362275292159680204380770369009821930417757972504438076078534117837065833032974336
|-
| 512 || 13407807929942597099574024998205846127479365820592393377723561443721764030073546976801874298166903427690031858186486050853753882811946569946433649006084096
|-
| 768 || 1552518092300708935148979488462502555256886017116696611139052038026050952686376886330878408828646477950487730697131073206171580044114814391444287275041181139204454976020849905550265285631598444825262999193716468750892846853816057856
|-
| 1024 || 179769313486231590772930519078902473361797697894230657273430081157732675805500963132708477322407536021120113879871393357658789768814416622492847430639474124377767893424865485276302219601246094119453082952085005768838150682342462881473913110540827237163350510684586298239947245938479716304835356329624224137216
|-
| 1280 || 20815864389328798163850480654728171077230524494533409610638224700807216119346720596024478883464648369684843227908562015582767132496646929816279813211354641525848259018778440691546366699323167100945918841095379622423387354295096957733925002768876520583464697770622321657076833170056511209332449663781837603694136444406281042053396870977465916057756101739472373801429441421111406337458176
|-
| 1536 || 2410312426921032588580116606028314112912093247945688951359675039065257391591803200669085024107346049663448766280888004787862416978794958324969612987890774651455213339381625224770782077917681499676845543137387820057597345857904599109461387122099507964997815641342300677629473355281617428411794163967785870370368969109221591943054232011562758450080579587850900993714892283476646631181515063804873375182260506246992837898705971012525843324401232986857004760339316736
|-
| 1792 || 279095111627852376407822673918065072905887935345660252615989519488029661278604994789701101367875859521849524793382568057369148405837577299984720398976429790087982805274893437406788716103454867635208144157749912668657006085226160261808841484862703257771979713923863820038729637520989894984676774385364934677289947762340313157123529922421738738162392233756507666339799675257002539356619747080176786496732679854783185583233878234270370065954615221443190595445898747930123678952192875629172092437548194134594886873249778512829119416327938768896
|-
| 2048 || 32317006071311007300714876688669951960444102669715484032130345427524655138867890893197201411522913463688717960921898019494119559150490921095088152386448283120630877367300996091750197750389652106796057638384067568276792218642619756161838094338476170470581645852036305042887575891541065808607552399123930385521914333389668342420684974786564569494856176035326322058077805659331026192708460314150258592864177116725943603718461857357598351152301645904403697613233287231227125684710820209725157101726931323469678542580656697935045997268352998638215525166389437335543602135433229604645318478604952148193555853611059596230656
|-
|}
=== Pseudorandom Period sizes ===
{| class="wikitable sortable"
|-
! bits !! style="text-align:left" | Period
|-
| 32 || Xorshift [http://www.jstatsoft.org/v08/i14/paper PDF] (period 2<sup>32</sup>−1)
|-
| 64 || Xorshift [http://www.jstatsoft.org/v08/i14/paper PDF] (period 2<sup>64</sup>−1)
|-
| 96 || Xorshift [http://www.jstatsoft.org/v08/i14/paper PDF] (period 2<sup>96</sup>−1)
|-
| 128 || Xorshift [http://www.jstatsoft.org/v08/i14/paper PDF] (period 2<sup>128</sup>-1)
|-
| 160 || Xorshift [http://www.jstatsoft.org/v08/i14/paper PDF] (period 2<sup>160</sup>-1)
|-
| 192 || Xorshift [http://www.jstatsoft.org/v08/i14/paper PDF] (period 2<sup>192</sup>−1)
|-
| 250 || Mother-Of-All pseudorandom number generator algorithm [ftp://ftp.forth.org/pub/C/mother.c]
|-
| 19937 || Mersenne Twister pseudorandom number generator algorithm (period 2<sup>19937</sup>-1 ≈ 4.3 × 10<sup>6001</sup>)
|-
|}
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