![[JoGu]](../../JGU.gif) |
CryptologyBreaking a Polyalphabetically Encrypted Text by Column Analysis |
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CryptologyBreaking a Polyalphabetically Encrypted Text by Column Analysis |
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The columns of ciphertext are arranged according to the supposed period 7:
AOWBKNL RMGEAMY CZSFJOI YYVSHYQ PYKSONE MDUKEMV EMPJBBO AYUHCBH ZPYWMOO KQVZEAH RMVVPJO WHRJRMW KMHCMMO HFSEGOW ZKIKCRV LAQDXMW RMHXGTH XMXNBYR TAHJUAL RAPCOBJ TCYJABB MDUHCQN YNGKLAW YNRJBRV RZIDXTV LPUELAI MIKMKAQ TMVBCBW VYUXKQX YZNFPGL CHOSONT MCMJPML RJIKPOR BSIAOZZ ZCYPOBJ ZNNJPUB KCOWAHO OJUWOBC LQAWCYT KMHFPGL KMGKHAH TYGVKBS KLRVOQV OEQWEAL TMHKOBN CMVKOBJ UPAXFAV KNKJABV KNXXIJV OPYWMWQ MZRFBUE VYUZOOR BSIAOVV LNUKEMV YYVMSNT UHIWZWS YPGKAAI YNQKLZZ ZMGKOYX AOKJBZV LAQZQAI RMVUKVJ OCUKCWY EALJZCV KJGJOVV WMVCOZZ ZPYWMWQ MZUKREI WIPXBAH ZVNHJSJ ZNSXPYH RMGKUOM YPUELAI ZAMCAEW ODQCHEW OAQZQOE THGZHAW UNRIAAQ YKWXEJV UFUZSBL RNYDXQZ MNYAONY TAUDXAW YHUHOBO YNQJFVH SVGZHRV OFQJISV ZJGJMEV EHGDXSV KFUKXMV LXQEONW YNKVOMW VYUZONJ UPAXFAN YNVJPOR BSIAOXI YYAJETJ TFQKUZZ ZMGKUOM YKIZGAW KNRJPAI OFUKFAH VMVXKDB MDUKXOM YNKVOXH YPYWMWQ MZUEOYV ZFUJABY MGDVBGV ZJWNCWY VMHZOMO YVUWKYL RMDJPVJ OCUKQEL KMAJBOS YXQMCAQ TYASABB YZICOBX MZUKPOO UMHEAUE WQUDXTV ZCGJJMV PMHJABV ZSUMCAQ TYAJPRV ZINUONY LMQKLVH SVUKCWY PAQJABV LMGKUOM YKIZGAV LZUVIJV ZOGJMOW VAKHCUE YNMXPBQ YZVJPQH YVGJBOR BSIAOZH YZUVPAS MFUKFOW QKIZGAS MMKZAUE WYNJABV WEYKGNV RMVUAAQ XQHXKGV ZHUVIJO YZPJBBO OQPEOBL KMDVONV KNUJABB MDUHCQN YPQJBAH ZMIBHWV THUGCTV ZDIKGOW AMVGKBB KKMEABH QISGODH ZYUWOBR ZJAJETJ TFUK
Column: 0 1 2 3 4 5 6 Letter A: 4 10 8 5 17 26 0 Letter B: 4 0 0 3 11 26 6 Letter C: 3 7 0 6 13 1 1 Letter D: 0 6 3 6 0 2 0 Letter E: 3 2 0 9 7 5 6 Letter F: 0 9 0 4 5 0 0 Letter G: 0 1 17 3 7 4 0 Letter H: 1 8 9 6 6 1 15 Letter I: 0 4 14 1 4 0 8 Letter J: 0 6 0 32 3 5 9 Letter K: 15 6 8 28 9 0 0 Letter L: 9 1 1 0 5 0 10 Letter M: 14 29 4 4 7 11 4 Letter N: 0 18 5 2 0 10 4 Letter O: 10 3 2 0 30 17 10 Letter P: 3 10 5 1 15 0 0 Letter Q: 2 5 14 0 3 6 10 Letter R: 11 0 6 0 2 4 6 Letter S: 2 5 4 4 2 3 5 Letter T: 12 0 0 0 0 6 3 Letter U: 6 0 35 3 5 5 0 Letter V: 6 5 13 10 0 6 34 Letter W: 6 0 3 11 0 8 15 Letter X: 2 2 2 11 8 2 3 Letter Y: 27 13 9 0 0 7 7 Letter Z: 22 12 0 13 2 6 5
Observation: The cipher uses strongly related alphabets.
Evidence: The »double peak« in each column catches the eye. This regularity becomes even more conspicuous, if we shift the frequency distributions to congruent positions with the double peak at the end (now written in rows):
4 4 3 0 3 0 0 1 0 0 15 9 14 0 10 3 2 11 2 12 6 6 6 2 27 22 3 10 5 0 5 0 0 5 0 2 13 12 10 0 7 6 2 9 1 8 4 6 6 1 29 18 3 2 9 0 8 0 0 3 0 0 17 9 14 0 8 1 4 5 2 5 14 6 4 0 35 13 0 4 2 0 1 0 0 4 0 3 10 11 11 0 13 5 3 6 6 9 4 3 6 1 32 28 3 2 2 0 5 0 0 8 0 2 17 11 13 0 7 5 7 6 4 3 9 5 7 0 30 15 1 2 5 0 4 1 0 5 0 0 11 10 17 0 6 4 3 6 5 6 8 2 7 6 26 26 3 7 5 0 6 1 0 6 0 0 15 8 9 0 10 4 4 10 0 10 6 5 3 0 34 15
A graphical representation shows this effect even more clearly—the first diagram showing the frequencies in the unshifted columns, the second diagram, the »fitted« frequency graphs.
![[Häufigkeiten roh]](Haeufigkeiten0.gif)
![[Häufigkeiten zurechtgerückt]](Haeufigkeiten.gif)
We adjust the columns 1 to 6 in congruence with column 0. That is the letters of column 1 are shifted by 12 positions in the alphabet: M becomes Y, N becomes Z, O becomes A and so on. In the same way column 2 is shifted by 4, column 3 by 15, column 4 by 10, column 5 by 24, column 6 by 3.
This procedure results in a text that is supposed to be monoalphabetically encrypted:
AAAQULO RYKTKKB CLWUTML YKZHRWT PKOHYLH MPYZOKY EYTYLZR AKYWMZK ZBCLWMR KCZOOYK RYZKZHR WTVYBKZ KYLRWKR HRWTQMZ ZWMZMPY LMUSHKZ RYLMQRK XYBCLWU TMLYEYO RMTRYZM TOCYKZE MPYWMOQ YZKZVYZ YZVYLPY RLMSHRY LBYTVYL MUOBUYT TYZQMZZ VKYMUOA YLRUZEO CTSHYLW MOQYZKO RVMZZMU BEMPYXC ZOCEYZM ZZRYZSE KOSLKFR OVYLYZF LCELMWW KYLUZEO KYKZRYK TKKKUZV KXVKYOY OQULOYO TYLZYZQ CYZZYZM UBEMPYY KZOYKZY KZBMSHY OBCLWUT MLVULSH VKYOYMU BEMPYTY LZYZOKY YKZBCLW UTMLJUV YBKZKYL YZUZVXC ZYKZYWA AAOYLXY LMUOAYL RYZJUTM OOYZMUB EMPYJAY KVKYYTY WYZRYXC ZBCLWUT MLYZBCL WUTMLYK ZHRWTQM ZZWMZWK RYKZEMP YBYTVYL ZMQRKCZ OPURRCZ OMUOAMH TTKORYZ UZVXKYT YWAMOHY URYOCZO RZCSHOC MZCPYLB TMYSHYZ YTYWYZR YZUYPTK SHKORPY ORUYSQY ZVKYWCY ETKSHQY KRYZHKY LJUTYLZ YZOKYKZ VKYOYLM UBEMPYQ YZZYZMU BEMPYVL YKEYORM TRUZEXC ZYKZEMP YWMOQYZ KZVYZYL ORYZPYK VYZMUBE MPYZHMP YZOKYVK YBCLWUT MLYTYWY ZRYYKZB MSHKLEY ZVACMUB VYLOYKR YHYLUWO RYHYZTM OOYZACO KYEYLMV YJUBMYT TKEHKZE YLMRYZA MLYZZMR UYLTKSH WCYSHRY ZOKYTKY PYLYKZY ZEYBMYT TKEYZPY ZURJYLB LYUZVTK SHYZMUB PMUYKZY LYKZEMP YWMOQYY LLYKSHY ZAKYWMZ VMOWMSH YZQMZZT YLZYZOK YHKYLMU BEMPYXK YLYKZYV MRYZPMZ QWMOQYV MYOOKSH WKRYKZY WQCZQLY RYZJKYT XCLMUEY ZTYKSHR YLTYLZR OCTTYZO KYHKYLY KZYYKZE MPYWMOQ YBUYLYK ZYMQRUY TTYVMRY ZPMZQMZ AYZVUZE KWQTKZK QUWVYBK ZKYLYZU ZVEYORM TRYZ
We try frequency analysis and make the following conjectures in the order from (1) to (6):
Most frequent letters: Conjecture: Y 213 18.8 % Y = e (1) Z 137 12.1 % Z = n (2) K 98 8.7 % K = i (3) M 88 7.8 % L 70 6.2 % O 61 5.4 % R 53 4.7 % T 53 4.7 % U 51 4.5 % W 39 3.4 % V 33 2.9 % E 32 2.8 % H 32 2.8 % B 31 2.7 % C 31 2.7 % P 28 2.5 % Q 25 2.2 % S 20 1.8 % A 17 1.5 % X 10 0.9 % The most frequent pairs, using (1) - (3) : YZ frequency: 57 en YL frequency: 41 e* L = r (4) KZ frequency: 31 in YK frequency: 31 ei KY frequency: 29 ie RY frequency: 26 *e R = t (6) PY frequency: 22 *e ZY frequency: 19 ne LY frequency: 18 *e SH frequency: 17 S = c, H = h (5) MU frequency: 17
AAAQUrO teiTiiB CrWUTMr einhtWT PiOherh MPenOie EeTernt AieWMni nBCrWMt iCnOOei teninht WTVeBin iertWit htWTQMn nWMnMPe rMUchin terMQti XeBCrWU TMreEeO tMTtenM TOCeinE MPeWMOQ eninVen enVerPe trMchte rBeTVer MUOBUeT TenQMnn VieMUOA ertUnEO CTcherW MOQeniO tVMnnMU BEMPeXC nOCEenM nntencE iOcriFt OVerenF rCErMWW ierUnEO ieintei TiiiUnV iXVieOe OQUrOeO TernenQ CennenM UBEMPee inOeine inBMche OBCrWUT MrVUrch VieOeMU BEMPeTe rnenOie einBCrW UTMrJUV eBinier enUnVXC neineWA AAOerXe rMUOAer tenJUTM OOenMUB EMPeJAe iVieeTe WenteXC nBCrWUT MrenBCr WUTMrei nhtWTQM nnWMnWi teinEMP eBeTVer nMQtiCn OPUttCn OMUOAMh TTiOten UnVXieT eWAMOhe UteOCnO tnCchOC MnCPerB TMechen eTeWent enUePTi chiOtPe OtUecQe nVieWCe ETichQe itenhie rJUTern enOiein VieOerM UBEMPeQ ennenMU BEMPeVr eiEeOtM TtUnEXC neinEMP eWMOQen inVener OtenPei VenMUBE MPenhMP enOieVi eBCrWUT MreTeWe nteeinB MchirEe nVACMUB VerOeit eherUWO tehenTM OOenACO ieEerMV eJUBMeT TiEhinE erMtenA MrennMt UerTich WCechte nOieTie Pereine nEeBMeT TiEenPe nUtJerB reUnVTi chenMUB PMUeine reinEMP eWMOQee rreiche nAieWMn VMOWMch enQMnnT ernenOi ehierMU BEMPeXi ereineV MtenPMn QWMOQeV MeOOich Witeine WQCnQre tenJieT XCrMUEe nTeicht erTernt OCTTenO iehiere ineeinE MPeWMOQ eBUerei neMQtUe TTeVMte nPMnQMn AenVUnE iWQTini QUWVeBi nierenU nVEeOtM Tten
This looks good and hints at a German plaintext. For M we could substitute s or a; the already identifyed text snippets make »a« much more plausible because it is a vocal. For s now virtually only O makes sense. If we moreover substitute P by b, then in the first row the text »bisher haben sie« appears—a clear affirmation of the correct way. The remainder is routine and a little bit of trial and error.
Exercise. Perform the complete cryptoanalysis of the ciphertext whose period you determined in a former exercise.
At this point it may be interesting to follow the cryptanalysis of the cryptogram from Jules Verne's Jangada.
Note. That this simple adjustment of the columns worked is a fortunate coincidence. In the next section we'll examine this phenomen.