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IntroductionIn 1982, Alan G. Konheim wrote an article on the cryptanalysis of Kryha cipher machine (see References). He proposed a mathematical attack on a long cryptogram (over 2000 characters). The wheel used is assumed to be unknown. I confess I understood almost nothing of his mathematical proofs :-( The Wheel UsedIn fact, as shown in the solution, the offsets found correspond to the standard wheel but with a systematic offset of three notches instead of four. Is Konheim using an experimental model of the Kryha machine? If it is an experimental machine, choosing a systematic addition of three steps is a poor choice because it leads to generating only 13 alphabets instead of 26 (see below). Switching to a systematic addition of four steps corrects this effect. At the end of his article, Konheim thanks Dr. Kjell-Ove Widman of Crypto AG for his help regarding the historical aspects. Perhaps this person provided him with the description of the wheel?
The cryptogram
$ more MSGS/konheim.cry CECZDHYCFWGNVRTUA MZEDCQAMRUDWGAKCQ GQUSIFIZBMXMDOGOY WTSZRJBDOLZESLLSO VVFBPHTKYMFXDGNRN MIIPITFWNRRIZCRGN LMKNXXIDHAARQEGAH PLIYXSQYARQRQSSVX BVLUIULXQGISVXIKU YNUIZQUQVIJFEEQNH YGKIXTNIKOOQYIBFB UUGPLRJOSIYBACPGV QYFZOWOGKRLPHTKNE YLAPCOYZEXBJAYGWI EHNDHRHZKNVTVXJXS KCDNKNEKSLXMFEDGB XSKSZSBRCKKFOJDCF EEYXAHWSYMFIOUDBC BYXPMHQSDGFZGHVYO MSYMUBTVNKXHMCECA GNXAVGPCCVBBBIRFM UJQJGSKMHCGSHGXFR QMUUZOWWVWMABUAWT LNOUIGGLRHWTIKWBV XARTAYYWYYCPWXNNZ BXBLYJJHUDEYTPLLE IJCGFKHACOIOCNIKL MFOINMZOYTHRMKAMC RREFOSOPBPWRJOGVJ AZPZXAKUZIPUGVGZW WPFZKWWYITNAGLWSN ZBVKXRDVDQXFKJIWO DSYLEKXANBMTKWVVT FNLNKDPJADRPFHPHD VTKVKBEZLNIPTGFSW LJEWNQUQQCESWKEUF NWAGUHAVYMARMXKDI UAUCKXTSFKPTLENNU NEUUJDYFVRZMNEWJA YKLNCPDEROIWUXUWH HZAISFAMOKSYIOKLG JYXZCIIDITHEPGDNO WYUXPWMDLPBGPKIAL VXFADSSXTXNCORDJG NFQYOGOZZECVPQHJV FCEQPABYPFBJFZBAZ HYPQYPKICOPXKRKHR XAQJXTPSJUGKHDDTG BDGGNQUQRCWBMFSSC PABNHPCCSHJPNKTNV CVLSJMOZFVITJZGGR JRGPLGSGVSMDOALQR VUGPQKDCPKPOKHNPG DAHEMYFESLBPFZOMQ WEBOBDMGCEYDWCGXQ PJMZVWPPLXGWXCGHT XWFCELCAPZOAISTKZ VPPPMVXZEQOVJZOIG DSYLEKBVGHSUATFZA XAQCBFJFARNFSSDQY XOXUJMTXEUMQEYXVQ BWNOQLYCBFSXCDTWT IHLDNOYPKQOEKNVSQ HPWZTLZXZUYEFVKCS AUJSLBRIHMMWLKFAV VEAPGOVZEKWOVKCTM OHLXODFIXZXPFVTML UHFFUIVOCLYLQVOEN DFIHXAUWNNAUFTNAU CFNGCEMIJJWXLDWYD SMSTQBSHLWFSIDHJV MBGSEXSMGOMKROVKA SIKHDODLJUQRTSZOZ SGVTVSISYFESAXOKF BWWXWRWNJSYNBETPC PICCAYMUKHIRNXWHI YYWAVNVLZOZPGUJSL YDCKLBDDBRESGOJQU YKKGFOWSAIQETLNFC XRZPCUCOGXHOGAUMXNote: We leave it to the reader to find the solution using the methods described on this site. WARNING! The solution is provided later, but without detailed step-by-step instructions. The key (Solution)
Standard Wheel: 3, 2, 3, 1, 2, 3, 2, 4, 2, 6, 1, 2, 1, 3, 2, 1, 5 Konheim Wheel : 8, 6, 5, 6, 4, 5, 6, 5, 7, 5, 9, 4, 5, 4, 6, 5, 4 -3 : 5, 3, 2, 3, 1, 2, 3, 2, 4, 1, 6, 1, 2, 1, 3, 2, 1If we subtract 3 from each sector and shift the values to the left, we obtain the values of the sectors of the standard wheel! The key lengthIf we use the superposition method, we can calculate the length of the key and deduce the number of sectors of the wheel used.
$ python3 superpose.py -c MSGS/konheim.cry -m 500 -t 110 0 => 2272, 1.000 61 => 115, 0.051 82 => 113, 0.050 94 => 113, 0.050 116 => 110, 0.048 141 => 113, 0.050 157 => 116, 0.051 165 => 117, 0.051 221 => 140, 0.062 249 => 116, 0.051 320 => 110, 0.048 322 => 120, 0.053 327 => 110, 0.048 381 => 120, 0.053 442 => 142, 0.062 468 => 111, 0.049Two peaks are noticeable: 221 and 442 (17*26 et 17*13). Note about the problem: In fact, the problem proposed by Konheim is not so complex. Indeed, the cryptogram is over 2000 characters long, only 17 sectors are used, the key length is only 221 (there are only 13 alphabets), and the machine uses only a single disordered alphabet (the outer alphabet is ABC...Z). The plain text
$ python3 kryha_tui.py -o \ -i WGMKRUYTBZHCNXFDJLPEVOAQSI \ -s 8,6,5,6,4,5,6,5,7,5,9,4,5,4,6,5,4 -d -m \ < MSGS/konheim.cry | fold -w 70 THEISSUEOFPERFORMANCEEVALUATIONANDPREDICTIONHASCONCERNEDUSERSTHROUGHOU TTHEHISTORYOFCOMPUTEREVOLUTIONPERIODINFACTCOMMAASINANYOTHERTECHNOLOGIC ALDEVELOPMENTCOMMATHEISSUEISMOSTACUTEWHENTHETECHNOLOGYISYOUNGTHEPERSIS TENTPURSUITOFPRODUCTSWITHIMPROVEDCOSTHYPHENPERFORMANCECHARACTERISTICST HENCONSTANTLYLEADSTODESIGNSWITHUNTRIEDANDUNCERTAINFEATURESPERIODFROMTH EINITIALCONCEPTIONOFASYSTEMSARCHITECTURALDESIGNTOITSDAILYOPERATIONAFTE RINSTALLATIONPERIODINTHEEARLYPLANNINGPHASEOFANEWCOMPUTERSYSTEMPRODUCTC OMMATHEMANUFACTURERMUSTUSUALLYMAKETWOTYPESOFPREDICTIONPERIODTHEFIRSTTY PEISTOFORECASTTHENATUREOFAPPLICATIONSANDTHELEVELSOFSYSTEMWORKLOADSOFTH ESEAPPLICATIONSPERIODHERETHETERMWORKLOADMEANSCOMMAINFORMALLYCOMMATHEAM OUNTOFSERVICEREQUIREMENTSPLACEDONTHESYSTEMPERIODWESHALLELABORATEMOREON WORKLOADCHARACTERIZATIONINSECTIONONEPOINTFOURPERIODTHESECONDTYPEOFPRED ICTIONISCONCERNEDWITHTHECHOICEBETWEENARCHITECTURALDESIGNALTERNATIVESCO MMABASEDONHARDWAREANDSOFTWARETECHNOLOGIESTHATWILLBEAVAILABLEINTHEDEVEL OPMENTPERIODOFTHEPLANNEDSYSTEMPERIODHERETHECRITERIONOFSELECTIONISWHATW ECALLCOSTHYPHGNPERFORMANCETRADEOFFPERIODTHEACCURACYOFSUCHPREDICTIONRES TSTOACONSIDERABLEEXTENTONOURCAPABILITYOFMAPPINGTHEPERFORMANCECHARACTER ISTICSOFTHESYSTEMCOMPONENTSINTOTHEOVERALLSYSTEMHYPHENLEVELPERFORMANCEC HARACTERISTICSPERIODSUCHTRANSLATIONPROCEDURESAREBYNOMEANSSTRAIGHTFORWA RDORWELLESTABLISHEDPERIODONCETHEARCHITECTURALDECISIONSHAVEBEENMADEANDT HESYSTEMDESIGNANDIMPLEMENTATIONSTARTEDCOMMATHESCOPEOFPERFORMANCEPREDIC TIONANDEVALUATIONBECOMESMORESPECIFICPERIODWHATISTHEBESTCHOICEOFMACHINE ORGANIZATIONQUESTIONWHATISTHEOPERATINGSYSTEMTOSUPPORTANDWHATARETHEFUNC TIONSITSHOULDPROVIDEQUESTIONTHEINTERACTIONSAMONGTHEOPERATINGSYSTEMCOMP ONENTSHYPHENALGORITHMSFORJOBSCHEDULINGCOMMAPROCESSORSCHEDULINGCOMMAAND STORAGEMANAGEMENTHYPHENMUSTBEUNDERSTOODCOMMAANDTHEIREFFECTSONTHEPERFOR MANCEMUSTBEPREDICTEDPERIODTHETECHNIQUESUSEDFORPERFORMANCEEVALUATIONAND PREDICTIONDURINGTHEDESIGNANDIMPLEMENTATIONPHASESRANGEFROMSIMPLEHANDCAL CULATIONTOQUITEELABORATESIMULATIONPERIODCOMPARINGTHEPREDICTEDPERFORMAN CEWITHTHEACTUALACHIEVEDPERFORMANCEOFTENREVEALSMAJORDEFECTSINTHEDESIGNO RERRORSINTHESYSTEMPROGRAMMINGPERIODITISNOWAWIDELYACCEPTEDBETIEFTHATTHE PERFORMANCEPREDICTIONANDEVALUATIONPROCESSSHOULDBEANINTEGRALPARTOFTHEDE VELOPMENTEFFORTSTHROUGHOUTPERIOD $ python3 kryha_tui.py -o -i WGMKRUYTBZHCNXFDJLPEVOAQSI \ -w konheim -d -m < MSGS/konheim.cry | fold -w 70 | head -5 THEISSUEOFPERFORMANCEEVALUATIONANDPREDICTIONHASCONCERNEDUSERSTHROUGHOU TTHEHISTORYOFCOMPUTEREVOLUTIONPERIODINFACTCOMMAASINANYOTHERTECHNOLOGIC ALDEVELOPMENTCOMMATHEISSUEISMOSTACUTEWHENTHETECHNOLOGYISYOUNGTHEPERSIS TENTPURSUITOFPRODUCTSWITHIMPROVEDCOSTHYPHENPERFORMANCECHARACTERISTICST HENCONSTANTLYLEADSTODESIGNSWITHUNTRIEDANDUNCERTAINFEATURESPERIODFROMTH $ cat keys/konheim.whl 4, 2, 1, 2, 0, 1, 2, 1, 3, 1, 5, 0, 1, 0, 2, 1, 0 Reference
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