Editing De Bruijn sequence (section)

===Brute-force attacks on locks===

[[File:De_Bruijn_sequence_10_4.svg|thumb|One possible ''B''&thinsp;(10,&nbsp;4) sequence. The 2530 substrings are read from top to bottom then left to right, and their digits are concatenated. To get the string to brute-force a combination lock, the last three digits in brackets (000) are appended. The 10003-digit string is hence "0 0001 0002 0003 0004 0005 0006 0007 0008 0009 0011 ... 79 7988 7989 7998 7999 8 8889 8899 89 8999 9 000" (spaces added for readability).]]
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|colspan="10"|B{10,3} with digits read from top to bottom<br />then left to right;<ref>{{Cite web|url=http://hakank.org/comb/debruijn.cgi?k=10&n=3|title = de Bruijn (DeBruijn) sequence (K=10, n=3)}}</ref> appending "00" yields<br />a string to brute-force a 3-digit combination lock
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|rowspan="12"|1
|rowspan="23"|2
|rowspan="34"|3
|rowspan="45"|4
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|rowspan="99"|9
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|001
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|002
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|003
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|004
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|005
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|006
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|007
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|008
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|009
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|011
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|012||112
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|013||113
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|014||114
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|015||115
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|016||116
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|017||117
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|018||118
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|019||119
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|021
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|022||122
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|023||123||223
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|024||124||224
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|025||125||225
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|026||126||226
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|027||127||227
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|028||128||228
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|029||129||229
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|031
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|032||132
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|033||133||233
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|034||134||234||334
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|035||135||235||335
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|036||136||236||336
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|037||137||237||337
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|038||138||238||338
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|039||139||239||339
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|041
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|042||142
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|043||143||243
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|044||144||244||344
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|045||145||245||345||445
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|046||146||246||346||446
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|047||147||247||347||447
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|048||148||248||348||448
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|049||149||249||349||449
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|051
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|052||152
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|053||153||253
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|054||154||254||354
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|055||155||255||355||455
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|056||156||256||356||456||556
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|057||157||257||357||457||557
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|058||158||258||358||458||558
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|059||159||259||359||459||559
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|061
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|062||162
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|063||163||263
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|064||164||264||364
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|065||165||265||365||465
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|066||166||266||366||466||566
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|067||167||267||367||467||567||667
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|068||168||268||368||468||568||668
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|069||169||269||369||469||569||669
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|071
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|072||172
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|073||173||273
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|074||174||274||374
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|075||175||275||375||475
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|076||176||276||376||476||576
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|077||177||277||377||477||577||677
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|078||178||278||378||478||578||678||778
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|079||179||279||379||479||579||679||779
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|081
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|082||182
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|083||183||283
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|084||184||284||384
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|085||185||285||385||485
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|086||186||286||386||486||586
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|087||187||287||387||487||587||687
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|088||188||288||388||488||588||688||788
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|089||189||289||389||489||589||689||789||889
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| ||rowspan="2"| ||rowspan="3"| ||rowspan="4"| ||rowspan="5"| ||rowspan="6"| ||rowspan="7"| ||rowspan="8"|
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|091
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|092||192
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|093||193||293
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|094||194||294||394
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|095||195||295||395||495
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|096||196||296||396||496||596
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|097||197||297||397||497||597||697
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|098||198||298||398||498||598||698||798
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|099||199||299||399||499||599||699||799||899||(00)
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A de Bruijn sequence can be used to shorten a brute-force attack on a [[Personal Identification Number|PIN]]-like code lock that does not have an "enter" key and accepts the last ''n'' digits entered. For example, a [[digital door lock]] with a 4-digit code (each digit having 10 possibilities, from 0 to 9) would have ''B''&thinsp;(10,&nbsp;4) solutions, with length {{val|10000}}. Therefore, only at most {{nowrap|{{val|10000}} + 3 {{=}} {{val|10003}}}} (as the solutions are cyclic) presses are needed to open the lock, whereas trying all codes separately would require {{nowrap|4 × {{val|10000}} {{=}} {{val|40000}}}} presses.

{{Anoto_paper_principle.svg}}