# Frequency Analysis

In cryptography, frequency analysis is the study of the frequency of letters or groups of letters in a ciphertext. The method is used as an aid to breaking substitution ciphers (e.g. mono-alphabetic substitution cipher, Caesar shift cipher, Vatsyayana cipher).

Frequency analysis consists of counting the occurrence of each letter in a text. Frequency analysis is based on the fact that, in any given piece of text, certain letters and combinations of letters occur with varying frequencies. For instance, given a section of English language, letters E, T, A and O are the most common, while letters Z, Q and X are not as frequently used.

The following chart shows the frequency of each letter of the alphabet for the English language:

We can assume that most samples of text written in English would have a similar distribution of letters. However this is only true if the sample of text is long enough. A very short text may lead to a significantly different distribution.

When trying to decrypt a cipher text based on a substitution cipher, we can use a frequency analysis to help identify the most recurring letters in a cipher text and hence make hypothesis of what these letters have been encoded as (e.g. E, T, A, O, etc). This will help us decrypt some of the letters in the text. We can then recognise patterns/words in the partly decoded text to identify more substitutions.

You can perform a frequency analysis on the following text to try to decrypt this text step by step:

Complete a frequency analysis to decrypt the following ciphers.
Cipher #1Cipher #2Cipher #3Cipher #4Cipher #5Cipher #6Cipher #7Cipher #8
“DJ DK C QLXDWI WF SDGDU PCX. XLRLU KQCSLKBDQK, KJXDHDET FXWZ C BDIILE RCKL, BCGL PWE JBLDX FDXKJ GDSJWXO CTCDEKJ JBL LGDU TCUCSJDS LZQDXL. IYXDET JBL RCJJUL, XLRLU KQDLK ZCECTLI JW KJLCU KLSXLJ QUCEK JW JBL LZQDXL’K YUJDZCJL PLCQWE, JBL ILCJB KJCX, CE CXZWXLI KQCSL KJCJDWE PDJB LEWYTB QWPLX JW ILKJXWO CE LEJDXL QUCELJ. QYXKYLI RO JBL LZQDXL’K KDEDKJLX CTLEJK, QXDESLKK ULDC XCSLK BWZL CRWCXI BLX KJCXKBDQ, SYKJWIDCE WF JBL KJWULE QUCEK JBCJ SCE KCGL BLX QLWQUL CEI XLKJWXL FXLLIWZ JW JBL TCUCVO…”

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Star wars opening crawl
“JVUI LUMNCJUIG KCL GIXVGEIS XO KPL KOYI AJCEIX OQ XCXOOPEI PE CE CXXIYAX XO GILWVI KPL QGPIES KCE LOJO QGOY XKI WJVXWKIL OQ XKI DPJI TCETLXIG BCHHC XKI KVXX.
JPXXJI SOIL JVUI UEON XKCX XKI TCJCWXPW IYAPGI KCL LIWGIXJM HITVE WOELXGVWXPOE OE C EIN CGYOGIS LACWI LXCXPOE IDIE YOGI AONIGQVJ XKCE XKI QPGLX SGICSIS SICXK LXCG.
NKIE WOYAJIXIS, XKPL VJXPYCXI NICAOE NPJJ LAIJJ WIGXCPE SOOY QOG XKI LYCJJ HCES OQ GIHIJL LXGVTTJPET XO GILXOGI QGIISOY XO XKI TCJCZM…”

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Star wars opening crawl
“OK OH R WRFD KOIS QPF KNS FSTSJJOPX. RJKNPAGN KNS WSRKN HKRF NRH TSSX WSHKFPCSW, OIBSFORJ KFPPBH NRYS WFOYSX KNS FSTSJ QPFMSH QFPI KNSOF NOWWSX TRHS RXW BAFHASW KNSI RMFPHH KNS GRJREC.
SYRWOXG KNS WFSRWSW OIBSFORJ HKRFQJSSK, R GFPAB PQ QFSSWPI QOGNKSFH JSW TC JADS HDCVRJDSF NRH SHKRTJOHNSW R XSV HSMFSK TRHS PX KNS FSIPKS OMS VPFJW PQ NPKN.
KNS SYOJ JPFW WRFKN YRWSF, PTHSHHSW VOKN QOXWOXG CPAXG HDCVRJDSF, NRH WOHBRKMNSW KNPAHRXWH PQ FSIPKS BFPTSH OXKP KNS QRF FSRMNSH PQ HBRMS…”

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Star wars opening crawl
“ZRTFT IH PQFTHZ IQ ZRT XBGBOZIO HTQBZT. HTWTFBG ZRLPHBQV HLGBF HYHZTSH RBWT VTOGBFTV ZRTIF IQZTQZILQH ZL GTBWT ZRT FTEPKGIO.
ZRIH HTEBFBZIHZ SLWTSTQZ, PQVTF ZRT GTBVTFHRIE LD ZRT SYHZTFILPH OLPQZ VLLAP, RBH SBVT IZ VIDDIOPGZ DLF ZRT GISIZTV QPSKTF LD CTVI AQIXRZH ZL SBIQZBIQ ETBOT BQV LFVTF IQ ZRT XBGBJY.
HTQBZLF BSIVBGB, ZRT DLFSTF NPTTQ LD QBKLL, IH FTZPFQIQX ZL ZRT XBGBOZIO HTQBZT ZL WLZT LQ ZRT OFIZIOBG IHHPT LD OFTBZIQX BQ BFSY LD ZRT FTEPKGIO ZL BHHIHZ ZRT LWTFMRTGSTV CTVI…”

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Star wars opening crawl
“FX IWBBJX PB NB PB PWX GBBD. VSP FWO, JBGX JRO, PWX GBBD? FWO IWBBJX PWUJ RJ BSA NBRK? RDL PWXO GRO FXKK RJM FWO IKUGV PWX WUNWXJP GBSDPRUD? FWO, 35 OXRAJ RNB, EKO PWX RPKRDPUI? FWO LBXJ AUIX CKRO PXQRJ? FX IWBBJX PB NB PB PWX GBBD UD PWUJ LXIRLX RDL LB PWX BPWXA PWUDNJ, DBP VXIRSJX PWXO RAX XRJO, VSP VXIRSJX PWXO RAX WRAL, VXIRSJX PWRP NBRK FUKK JXATX PB BANRDUZX RDL GXRJSAX PWX VXJP BE BSA XDXANUXJ RDL JMUKKJ, VXIRSJX PWRP IWRKKXDNX UJ BDX PWRP FX RAX FUKKUDN PB RIIXCP, BDX FX RAX SDFUKKUDN PB CBJPCBDX, RDL BDX FWUIW FX UDPXDL PB FUD, RDL PWX BPWXAJ, PBB.”

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Destination Moon – Most frequent letters: letter “E” and letter “O”
“ZE KYV KFNE NYVIV Z NRJ SFIE
CZMVU R DRE NYF JRZCVU KF JVR
REU YV KFCU LJ FW YZJ CZWV
ZE KYV CREU FW JLSDRIZEVJ
JF NV JRZCVU LG KF KYV JLE
‘KZC NV WFLEU R JVR FW XIVVE
REU NV CZMVU SVEVRKY KYV NRMVJ
ZE FLI PVCCFN JLSDRIZEV
NV RCC CZMV ZE R PVCCFN JLSDRIZEV
PVCCFN JLSDRIZEV, PVCCFN JLSDRIZEV
NV RCC CZMV ZE R PVCCFN JLSDRIZEV
PVCCFN JLSDRIZEV, PVCCFN JLSDRIZEV
REU FLI WIZVEUJ RIV RCC RSFRIU
DREP DFIV FW KYVD CZMV EVOK UFFI
REU KYV SREU SVXZEJ KF GCRP
NV RCC CZMV ZE R PVCCFN JLSDRIZEV
PVCCFN JLSDRIZEV, PVCCFN JLSDRIZEV
NV RCC CZMV ZE R PVCCFN JLSDRIZEV
PVCCFN JLSDRIZEV, PVCCFN JLSDRIZEV
(WLCC JGVVU RYVRU DI. GRIBVI, WLCC JGVVU RYVRU
WLCC JGVVU RYVRU ZK ZJ, JVIXVREK
RTKZFE JKRKZFE, RTKZFE JKRKZFE
RPV, RPV, JZI, WZIV
TRGKRZE, TRGKRZE)
RJ NV CZMV R CZWV FW VRJV
VMVIPFEV FW LJ YRJ RCC NV EVVU (YRJ RCC NV EVVU)
JBP FW SCLV (JBP FW SCLV) REU JVR FW XIVVE (REU JVR FW XIVVE)
ZE FLI PVCCFN JLSDRIZEV (ZE FLI PVCCFN, JLSDRIZEV, YR YR)
NV RCC CZMV ZE R PVCCFN JLSDRIZEV
PVCCFN JLSDRIZEV, PVCCFN JLSDRIZEV
NV RCC CZMV ZE R PVCCFN JLSDRIZEV
PVCCFN JLSDRIZEV, PVCCFN JLSDRIZEV
NV RCC CZMV ZE R PVCCFN JLSDRIZEV
PVCCFN JLSDRIZEV, PVCCFN JLSDRIZEV
NV RCC CZMV ZE R PVCCFN JLSDRIZEV
PVCCFN JLSDRIZEV, PVCCFN JLSDRIZEV”

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A song by The Beattles
“WAOUWBS HVSFS’G BC QCIBHFWSG
WH WGB’H VOFR HC RC
BCHVWBU HC YWZZ CF RWS TCF
OBR BC FSZWUWCB, HCC
WAOUWBS OZZ HVS DSCDZS
ZWJWBU ZWTS WB DSOQS
MCI, MCI AOM GOM W’A O RFSOASF
PIH W’A BCH HVS CBZM CBS
W VCDS GCASROM MCI KWZZ XCWB IG
OBR HVS KCFZR KWZZ PS OG CBS
WAOUWBS BC DCGGSGGWCBG
W KCBRSF WT MCI QOB
BC BSSR TCF UFSSR CF VIBUSF
O PFCHVSFVCCR CT AOB
WAOUWBS OZZ HVS DSCDZS
GVOFWBU OZZ HVS KCFZR
MCI, MCI AOM GOM W’A O RFSOASF
PIH W’A BCH HVS CBZM CBS
W VCDS GCASROM MCI KWZZ XCWB IG
OBR HVS KCFZR KWZZ ZWJS OG CBS”

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A song by John Lennon
“SBRL ZRFDHSRLY OHZ YLABYULK AV OPZ OVTL WSHULA VM AHAVVPUL PU HU HAALTWA AV YLZJBL OPZ MYPLUK OHU ZVSV MYVT AOL JSBAJOLZ VM AOL CPSL NHUNZALY QHIIH AOL OBAA.

SPAASL KVLZ SBRL RUVD AOHA AOL NHSHJAPJ LTWPYL OHZ ZLJYLASF ILNBU JVUZAYBJAPVU VU H ULD HYTVYLK ZWHJL ZAHAPVU LCLU TVYL WVDLYMBS AOHU AOL MPYZA KYLHKLK KLHAO ZAHY.

DOLU JVTWSLALK, AOPZ BSAPTHAL DLHWVU DPSS ZWLSS JLYAHPU KVVT MVY AOL ZTHSS IHUK VM YLILSZ ZAYBNNSPUN AV YLZAVYL MYLLKVT AV AOL NHSHEF…”

View Hint
Star wars opening crawl

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