![[JoGu]](../../JGU.gif) |
CryptologyFriedman Analysis of a Polyalphabetically Encrypted Text |
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CryptologyFriedman Analysis of a Polyalphabetically Encrypted Text |
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... that we already broke by a KASISKI analysis:
00 05 10 15 20 25 30 35 40 45 0000 AOWBK NLRMG EAMYC ZSFJO IYYVS HYQPY KSONE MDUKE MVEMP JBBOA 0050 YUHCB HZPYW MOOKQ VZEAH RMVVP JOWHR JRMWK MHCMM OHFSE GOWZK 0100 IKCRV LAQDX MWRMH XGTHX MXNBY RTAHJ UALRA PCOBJ TCYJA BBMDU 0150 HCQNY NGKLA WYNRJ BRVRZ IDXTV LPUEL AIMIK MKAQT MVBCB WVYUX 0200 KQXYZ NFPGL CHOSO NTMCM JPMLR JIKPO RBSIA OZZZC YPOBJ ZNNJP 0250 UBKCO WAHOO JUWOB CLQAW CYTKM HFPGL KMGKH AHTYG VKBSK LRVOQ 0300 VOEQW EALTM HKOBN CMVKO BJUPA XFAVK NKJAB VKNXX IJVOP YWMWQ 0350 MZRFB UEVYU ZOORB SIAOV VLNUK EMVYY VMSNT UHIWZ WSYPG KAAIY 0400 NQKLZ ZZMGK OYXAO KJBZV LAQZQ AIRMV UKVJO CUKCW YEALJ ZCVKJ 0450 GJOVV WMVCO ZZZPY WMWQM ZUKRE IWIPX BAHZV NHJSJ ZNSXP YHRMG 0500 KUOMY PUELA IZAMC AEWOD QCHEW OAQZQ OETHG ZHAWU NRIAA QYKWX 0550 EJVUF UZSBL RNYDX QZMNY AONYT AUDXA WYHUH OBOYN QJFVH SVGZH 0600 RVOFQ JISVZ JGJME VEHGD XSVKF UKXMV LXQEO NWYNK VOMWV YUZON 0650 JUPAX FANYN VJPOR BSIAO XIYYA JETJT FQKUZ ZZMGK UOMYK IZGAW 0700 KNRJP AIOFU KFAHV MVXKD BMDUK XOMYN KVOXH YPYWM WQMZU EOYVZ 0750 FUJAB YMGDV BGVZJ WNCWY VMHZO MOYVU WKYLR MDJPV JOCUK QELKM 0800 AJBOS YXQMC AQTYA SABBY ZICOB XMZUK POOUM HEAUE WQUDX TVZCG 0850 JJMVP MHJAB VZSUM CAQTY AJPRV ZINUO NYLMQ KLVHS VUKCW YPAQJ 0900 ABVLM GKUOM YKIZG AVLZU VIJVZ OGJMO WVAKH CUEYN MXPBQ YZVJP 0950 QHYVG JBORB SIAOZ HYZUV PASMF UKFOW QKIZG ASMMK ZAUEW YNJAB 1000 VWEYK GNVRM VUAAQ XQHXK GVZHU VIJOY ZPJBB OOQPE OBLKM DVONV 1050 KNUJA BBMDU HCQNY PQJBA HZMIB HWVTH UGCTV ZDIKG OWAMV GKBBK 1100 KMEAB HQISG ODHZY UWOBR ZJAJE TJTFU K
kappa[q] is the q-th autocoincidence index, that is the coincidence index of the text with itself shifted by q positions (cyclically). The sequence of autocoincidence indices of this ciphertext looks like this:
kappa[1] = 0.0301 kappa[2] = 0.0345 kappa[3] = 0.0469 kappa[4] = 0.0354 kappa[5] = 0.0371 kappa[6] = 0.0354 kappa[7] = 0.0822 <--- kappa[8] = 0.0416 kappa[9] = 0.0265 kappa[10] = 0.0309 kappa[11] = 0.0416 kappa[12] = 0.0389 kappa[13] = 0.0327 kappa[14] = 0.0787 <--- kappa[15] = 0.0460 kappa[16] = 0.0345 kappa[17] = 0.0460 kappa[18] = 0.0309 kappa[19] = 0.0327 kappa[20] = 0.0309 kappa[21] = 0.0769 <--- kappa[22] = 0.0318 kappa[23] = 0.0309 kappa[24] = 0.0327 kappa[25] = 0.0318 kappa[26] = 0.0309 kappa[27] = 0.0416 kappa[28] = 0.0875 <--- kappa[29] = 0.0477 kappa[30] = 0.0416 kappa[31] = 0.0442 kappa[32] = 0.0354 kappa[33] = 0.0318 kappa[34] = 0.0389 kappa[35] = 0.0610 <--- kappa[36] = 0.0371 kappa[37] = 0.0301 kappa[38] = 0.0477 kappa[39] = 0.0380 kappa[40] = 0.0363 ...
We clearly see the period 7 that we also detected by KASISKI analysis. The following picture confirms it.
![[Koinzidenzindizes]](Kappa.gif)
The values for q not a multiple of l = 7 scatter as expected around 1/26 ≈ 0.0385.
The values in the peaks fluctuate around the typical coincidence index near 0.08 of the plaintext language German.
Exercises
ECWUL MVKVR SCLKR IULXP FFXWL SMAEO HYKGA ANVGU GUDNP DBLCK
MYEKJ IMGJH CCUJL SMLGU TXWPN FQAPU EUKUP DBKQO VYTUJ IVWUJ
IYAFL OVAPG VGRYL JNWPK FHCGU TCUJK JYDGB UXWTT BHFKZ UFSWA
FLJGK MCUJR FCLCB DBKEO OUHRP DBVTP UNWPZ ECWUL OVAUZ FHNQY
XYYFL OUFFL SHCTP UCCWL TMWPB OXNKL SNWPZ IIXHP DBSWZ TYJFL
NUMHD JXWTZ QLMEO EYJOP SAWPL IGKQR PGEVL TXWPU AODGA ANZGY
BOKFH TMAEO FCFIH OTXCT PMWUO BOK