Copyright © University of Cambridge. All rights reserved.

'Probably a Code?' printed from http://nrich.maths.org/

Show menu

When cracking text-based codes, a first step is often to look for repeated strings of characters resulting from structure in the underlying cypher-text. This can give a way in to cracking the code.

 

Alison and Steve are considering the following coded message:
 

vrucseviffsrzpvekpqmyfvfvarvfhfzecsxzvvorjbtlrkaqmcvbgyfsct
nuznglyrkqsqewtauvzpievmblcciabcfvofpymgrfnpkjuszcjrjuaur
idgznelhpycaoljzbjkrcqioguwavhlvflejbcuqkpkzsvmnpaxivovjjt
lrqmyovtpjhfkzccrctgksiwoauvzgnvfvuabnitkfnpkjuziohqmipjv
eoipivaolnwwtlgravlbwbjvfvqefpcqolfzvuwviqvlqsgvovjekuqfnr
ybdqulzplcfqimctfsmevzvuqyrwmtcrebcuqmqxpqzbtfvedcpak
wdlcvzubnumfaurbvorgwnlvjbjlfvivvswzqzgrvfkrjwnhgzwppgv
dgycimulakakafvthabdgktnxqphgzwphfkpgyrxqqubwjghhkgcu
qumnptybvorimohexitlgkpgzhequmbimxlemqupocmkafszqhqu
qurwlavzxzzvpaxbjlufzkgbeipkqznhbfzvihcvzrlglinzccmpkblzv
orimhvenqvolfctsrrdgtljquariqypycxwaffugaelavpagzgjruqpna
rdknnkwtzgymtlfewyhauntvfkitlorvkzuvlcuqjiksveoqcriiehyda
ghjvucfovecmgvlvvncipkflzrhfjqpnveequqvzuhauqpirrcvfrmm
tfevokvayqvoribqkvjkqcrimfvakpgonsqvhocmisbsmkafgzqkhtb
kvajipksvivbevaohlsmypgywwaroiowyviuauvxjlafugunfnvorym
ccretaibuqgzhelqbokmfslrzgpakpqzrlvfpftwxlevluvyzbwkrjejhg
diaubkjglkgmearuqphpfcpaepwhlgvzphycqiogrqohlkpgyruqujb
mmtauvequqiwwzcfegyjyqeonkbthpkavoremgkyvipkzrgtltltcar
rbjvhjipkpvtgzgzinvojmtcnkqqufkpcaevywpevwpslkpkzifgcnrk
wtlaumtauvqtzrvukutvkelakzkjvkqgzpfvupfkmpasfzgcriquonct
uhgzivlzpitkrebebezwupgpekaukpgzvxpvvsrxcygfnvornwtsqem
xlesmhvevdkzvkmfhauucfgimckncipkavdgyovnqyrzuryvebgkop
bjlsfwvvsdipauvaghevualakqelzvvvznelvorpitlflnhppzmpagfkq
udlmthycnghefnfhaxmtveumcaurvfabzvfbpvugabtwotrekgauz
anhofzkvhjdqfnxmypgybjlwfgcjuztfmrvtuduvvjlrdjcyxjqphyzb
vsrswcajzbjovjpqsvuiatnkmuvarvgecvlkavfvqmqzaevivzabcyqu
unkqxlezdgyolbubcgwupaxinsgymulpfvllpkctlfkwdlsrtullfceha
ewvjbebgzgkpgpavavpzrjnlovvgmvkejppyquonctevawmtvartn
tneskuqkwvorciuatvvgynkqquoplkzpfdgyveocwnjacnremcygy
mrvyvbqaufagjblvvyvvavvevieojyqeonkxtlfvvvzbdipfzfvvofrzg
yrhckzvkmqyopiujribcpazviauvagjevbqmgymohtemvduzkjpsr
bcsygwuzvstgjnewpslsmgmsvkvlqsgcuhelgygrskutjceonjukur

 

Alison computes the frequency of each letter, finding these results:

 

a b c d e f g h i j k l m n o p q r s t u v w x y z
85 55 72 22 73 77 85 48 61 58 90 77 61 55 55 87 80 78 41 58 94 166  44 21 53 80

 

After some fiddling around on a spreadsheet, Steve notices that there are seven repeated strings of 5 letters, highlighted as shown below:

 

 

 

Steve dismisses this as coincidence, saying "I would guess that these repeated 5-letter sequences  are consistent with randomly generated text based on these frequencies of letters". Alison is not convinced and thinks that this structure of 5 letter sequences would not likely occur randomly for these frequencies of letters.

 

Investigate.

 

Challenge: Crack the code, regardless of who is right!