Difference between revisions of "Enigma"
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{{Source cli}} | {{Source cli}} | ||
=== If we used a 10 bit rotor === | === If we used a 10 bit rotor === | ||
| − | Or try and imagine a 32 bit wheel | + | Or try and imagine a 32 bit wheel (Then we would need a better implementation of ''frac'') |
<source lang=cli> | <source lang=cli> | ||
<input>frac(1024)</input> | <input>frac(1024)</input> | ||
Revision as of 08:38, 4 December 2010
Contents
Enigma Articles
8 bit Enigma machine
Number of possible keys when using three wheels
In the example below there is a caculation of possible keys that is
- Three whells of 8 bit each diffently coded (fx. wheel[0]=67,wheel[1]=234 .. wheel[67]=165 .. )
- An 8 bit Rotor-Reflector which is symmetricaly coded. (Fx. rr[0]=67 then rr[67]=0 etc. )
- When the encryption/decryption starts each wheel can be in 1 of 256 positions. Called the notch position
heth@MachoGPU:~/enigma$ <input>bc</input>
bc 1.06.95
Copyright 1991-1994, 1997, 1998, 2000, 2004, 2006 Free Software Foundation, Inc.
This is free software with ABSOLUTELY NO WARRANTY.
For details type `warranty'.
<input>/* Define the Factorial function */
define frac(x) {
if (x>1) {
return (x * f (x-1))
}
return (1)
}
/* Number of possible alterations of a 8 bit wheel */
wheel=frac(256)
print wheel</input>
85781777534284265411908227168123262515778152027948561985965565037726\
94525531475893774402913604514084503758853423365843061571968346936964\
75322289288497426025679637332563368786442675207626794560187968867971\
52114330770207752664645146470918732610083287632570281898077367178145\
41702505230186084953190681382574810702528175594594769870346657127381\
39286205234756808218860701203611083152093501947437109101726968262861\
60626366243502284094419140842461593600000000000000000000000000000000\
0000000000000000000000000000000
<input> /* Number of installed wheels in the Enigma engine*/
numberofwheels=3
/* Number of possible alterations of the 8 bit rotor-reflector.
The rotor-reflector can't point to it-self. (fx. location 8 can't be 8)
*/
rotorreflector=frac(255)
print rotorreflector</input>
33508506849329791176526651237548149420225840635917407025767798842862\
08799035732771005626138126763314259280802118502282445926550135522251\
85672769253319307041281108333032565932204170002979216625073425339051\
37544660457112403384627010340202629925813784231472766366436471553963\
05352541105541439434840109915068285430675068591638581980604162940383\
35658673919826878210492461407660579356286524198217620742862096977680\
31494674313868079724382476891586560000000000000000000000000000000000\
00000000000000000000000000000
<input>
/* Number of possible startpositions of the three wheels.
they are called a notch from the original mechanical solution
*/
notches=256*256*256
print notches</input>
16777216
<input>
/*Total number of Keys when using a 8 bit Enigma with three wheels */
wheel*numberofwheels*rotorreflector*notches</input>
14467425940815419878550914285328747194412838285887202913906796612290\
67116765686074239837002699523310587812021105128921519898929662849673\
80231859551685345801700678590340949512766773530970639425397581454798\
34629363249827620200556239557412599222204518999540726185192515996315\
06978129392323972906002241190936561257411009104030200763332968508802\
10053380885667825490547810051729838486330141341759611086561117956500\
02210195590742957751653052758866489611046357269440002628221514248948\
17132504901094529220429149272922120473850361954385338800798632554213\
60438811591136370963675381915493290515801660130577959111839885736840\
77541504957308491144024012326090397003948528853785364705857026051935\
47050340165465982389653696093503539510788359067272108792866788729818\
77493077624052679059588612553113715864219395902995530561734847463169\
09861780870355495760296743612825305064871402809304345105972352826182\
65297223680000000000000000000000000000000000000000000000000000000000\
00000000000000000000000000000000000000000000000000000000000000000000If we used a 10 bit rotor
Or try and imagine a 32 bit wheel (Then we would need a better implementation of frac)
<input>frac(1024)</input>
54185287960588572830769219446838547380015539635380134444828702706832\
10612073376603733140984136214586719079188457089807539319941657701873\
68260454133333721939108367528012764993769768292516937891165755680659\
66374794731451840488667767255612518869433525121367727452196343077013\
37132057962484331288700884361716546902375183904529447322778084029321\
58722061853806162806063925435310822186848239287130261690914211362251\
14468471388858788162925210404629531594994390035788241024393431503744\
41138908061814062108639532752353758850185984515822295996545585412427\
89130902486944298610923153307579131675745146436304024890820442907734\
56182736903050225279692655307296737099075874779312763510470246988966\
79614621330262371589732278578146318071564277676440645910850765647834\
56324457736853810336981776080498707767046394272605341416779125697733\
37456803747518667626596166561588468145026333704252266414186215704682\
56847733609443267374936766749150989537681129458316266438564790278163\
85730291542667725665642276826058264393884514911976419675509290208592\
71315636298329098944105273212518724952750131407167640551693619078182\
12367019122957673631170541265899299164820085157817519554669109028387\
29232224509906388638147771255227782631322385756948819393658889908993\
67087451686065309841102029985381628156433498184710577783953474253149\
96221034888075845137057698397639931039296650460461211666513451311495\
13657400869056334867859885025601787284982567787314407216524272262997\
31979156860362940662474010148269755953315573665880056292127468065728\
52015704019406922855578006114290557553245497940089398491468126398607\
50085263298820224719585505344773711590656682821041417265040658600683\
84494510435499881288680131655155171467338832334085176381971359131237\
25486737347835373163415173693875652128997265979649032412087273486906\
99802996369265070088758384854547542272771024255049902319275830918157\
44820519642107283720493729351617534195777542245315244228039137240771\
78916612030610402558300550338867900521160254087404546209383843676378\
86658769912790922323717371343176067483352513629123362885893627132294\
18356588401041872786935443907708527828855830842709046107501900718493\
31399155582127523923298797806496390753338457191738228405018695704636\
26600235265587502335595489311637509380219119860471335771652403999403\
29636024557725796367328665434895732574099971056713162327234576676193\
76514081039991936339082864205100985774545240681068973924931382873622\
26257920000000000000000000000000000000000000000000000000000000000000\
00000000000000000000000000000000000000000000000000000000000000000000\
00000000000000000000000000000000000000000000000000000000000000000000\
00000000000000000000000000000000000000000000000000000000